Cognitive Child Abuse in Our Math Classrooms
By C. Bradley Thompson

The test results are in: America’s children are flunking math. In 1996 American high school seniors finished close to the bottom on an international mathematics test. At the end of last year, American eighth-graders ranked below those of Malaysia, Bulgaria, and Latvia.

     As educators scramble to explain America’s math meltdown—as the Bush administration urges more “accountability” and a National Research Council study recommends better “training”—few are willing to look at the fundamental cause: the new, “whole-math” method for teaching.

     Inspired by a strain of progressive-education theory called “constructivism,” whole-math proponents claim that all knowledge—including mathematical knowledge—is arbitrarily constructed. They reject the idea that there are objectively demonstrable right and wrong answers, and that, consequently, there are basic skills that students must be taught. Instead, the advocates of whole math believe that each student should invent his or her own math “strategies” by using a “guess-and-check” approach. They create an inability to think beyond immediate concretes.   

  In a typical whole-math classroom, children do multiplication not by learning the abstract multiplication table, but by using piles of marshmallows. They count a million birdseeds in order to understand the concept “million.” They measure angles by stretching rubber bands across pegged boards. One whole-math program preposterously claims to foster a “conceptual understanding” of math by asking fifth-graders the following stumper: “If math were a color, it would be ______ , because ______.” Surely such exercises foster in children only conceptual stultification—along with a bewildered sense of frustration and disgust.

    Another whole-math program asks sixth-graders to address the following problem: “I’ve just checked out a library book that is 1,344 pages long! The book is due in three weeks. How many pages will I need to read a day to finish the book in time?” The proper way to solve the problem would be to use the method for long division: 1,344 divided by 21. By contrast, the whole-math approach assigns students to a group, requires them to design their own problem-solving rules, and urges them to guess if all else fails. In other words, children are told that their random “strategies” are just as good as the logically proven principles of long division. They are taught that the vote of the group, rather than the reasoning of the individual mind, is the means of arriving at the truth.

     Now imagine flying on a plane designed by aeronautical engineers who have been trained to concoct their own math schemes and to use a “guess-and-check” method.

     Whole math must lead to a miasma of confusion, boredom, and despair. Rather than encouraging independent, conceptual-level thinking, it is thoroughly anti-conceptual. It dooms children to function on a primitive, perceptual level—i.e., to flounder in a chaotic sea of concretes with no objective principles to guide them. This is cognitive child abuse. Whole-math defenders are shrinking the cognitive capacities of their students to those of infants or even animals.

     Is it any wonder that most college freshman take remedial math courses, that American universities award more than half of their mathematics Ph.D.s to foreign nationals, that for-profit math remediation companies are booming, and that 200 of the nation’s leading mathematicians and scientists signed a public letter denouncing whole math?

     Mathematics is like any other field. To master it, one must acquire basic knowledge before proceeding to more advanced stages. Proficiency in math requires that grade-school children learn the standard algorithms (i.e., the methods for addition, subtraction, multiplication, and division) and the four forms of numbers (i.e., integers, fractions, decimals, and percents). This forms the foundation upon which higher and higher levels of knowledge can then be built.

     The controversy surrounding whole math is not simply about how children are taught to deal with numbers. If we undermine the capacity of our children to learn mathematics, we undercut their ability to think. More and more, our schools are turning out students whose capacity to reason has atrophied. Students who have not learned how to add and divide are also unable to perform the more demanding cognitive tasks of understanding concepts like “justice” or “truth” or “logic.” America’s children are being turned into mindless drones, who will soon be unable to distinguish freedom from tyranny.

     Today’s “math wars,” like the controversy over how to teach reading, are at root philosophic battles that will have enormous implications for the future of America. If the advocates of whole math are allowed to win, they will be taking us a huge step away from the values of reason and science that once made America great.

 

C. Bradley Thompson is Chairman of the Department of History and Political Science at Ashland University in Ohio and a senior writer for the Ayn Rand Institute in Marina del Rey, California. The Institute promotes the philosophy of Ayn Rand, author of Atlas Shrugged and The Fountainhead. Send comments to reaction@aynrand.org.

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LAUSD’s Refusal to Adopt the
California Mathematics Standards

by David Klein
Professor of Mathematics
California State University, Northridge

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BACKGROUND

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Shortly after the adoption of the California Math Standards by the California Board of Education, LAUSD Superintendent of Schools, Ruben Zacarias, issued an Informative stating that the LAUSD Standards include and go beyond the State Board standards.

No adjustment of LAUSD’s math standards is necessary to accomodate the California math standards, according to the Informative. It explains that:

 

… the high expectations for student achievement set forth by the [LAUSD] school board and the Superintendent will be met by implementing the standards-based curriculum recommended by the Los Angeles Systemic Initiative.

The Los Angeles Systemic Initiative (LASI) is a project to impose an integrated math curriculum in LAUSD. Among other weak curricula, LASI promotes the highly discredited elementary school curriculum, MathLand.

The LAUSD Informative further claims that textbooks aligned with the new California State Standards would have to be supplemented to rise to the level of the LAUSD math standards.

In response to this statement, on March 16, 1998 a number of mathematicians and others familiar with the California Mathematics Standards released a document entitled A Comparison of the LAUSD Math Standards and the California Math Standards.

This study was based on the idea that such an analysis requires comparison of the California Mathematics Standards with the Los Angeles Unified School District Standards not by what might be meant, but by what is actually stated.

On this basis it was concluded that the LAUSD Standards are woefully lacking in critical mathematical content areas and lacking in precision, clarity and completeness.

In the conclusion, the comparison of the math standards notes:

 

The vacuousness of the LAUSD math standards facilitates poor achievement of LAUSD students in mathematics. Since these standards can mean whatever a particular reader wants them to mean, they are not standards at all. They serve only to protect poor achievement in mathematics — the status quo for LAUSD.

The comparison document also forewarned of wildly inflated interpretations of the LAUSD standards. For example, it might be claimed that standards #3 and #15 … subsume all California math standards related to linear equations, quadratics, simultaneous equations, perhaps even linear algebra, and all possible functions and all possible relations.

 

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LAUSD STAFF RESPOND

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At the behest of LASI, Ruben Zacharias, LAUSD Superintendent, released a second Informative to the LAUSD Board of Education on June 4, 1998. It state, There has recently been a great deal of confusion about the LAUSD mathematics standards, their rigor, and how they align with the California state standards. The LAUSD/LASI Informative continues, While at first glance, the LAUSD standards and the state standards appear to be fairly different, this is largely due to formatting choices.

The LAUSD/LASI Informative undermines its own purpose by reinforcing many of the public criticisms of the LAUSD Standards. For example:

• Aside from a brief statement that students should know basic numerical skills, the Informatives acknowledges that students really are allowed to use calculators from the earliest ages — third grade and below. In fact, the LAUSD math standards themselves explicity require the use of technology such as calculators or computers in its third grade benchmark. The LAUSD math standards are in conflicht with California state policy which does not allow calculator usage on the STAR exams in the elementary grades. 
• The LAUSD/LASI Informative states that LAUSD has written broad statements at only the selected benchmark grades of third, seventh, ninth and twelfth. In other words, these grades are treated minimally, while other grades are missing altogether. 
• The second Informative admits that the LAUSD Standards lack not only Trigonometry, they lack second year Algebra.

Thus, the LAUSD Standards have serious defects – defects that do not disappear even with this second attempt to deny them.

 

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THE LAUSD COMPARISON ANALYZED

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The document, A Comparison of the LAUSD Math Standards and the California Math Standards, dispels any notion that LA standards are even remotely comparable to the California Mathematics Standards. Even though it was intended to rebutt criticisms of the LAUSD math standards, a careful reading of the June 4 LAUSD/LASI Informative itself provides evidence that:

 

• The LAUSD standards present some required topics too late 
• The LAUSD standards omit some required topics 
• The LAUSD standards are unclear and subject to a wide range of interpretation 
• The LAUSD standards omit grade-by-grade benchmarks and contradict the California standards

 

 

LAUSD standards present some required topics too late

The LAUSD/LASI Informative includes detailed tables which juxtapose LAUSD Math Standards with California Math Standards. In the first table, LAUSD mathematics graduation requirements are equated with California algebra I standards and geometry standards. These California algebra I and geometry standards are designed to target 8th and 9th grade students, but LASI identifies these as graduation (i.e., 12th grade) standards. This is a clear (though perhaps unintended) admission by LASI and LAUSD staff that the LAUSD standards expect less of students than the California Math Standards. Here is a list of California algebra and geometry standards which, according to the LASI/LASUD Informative, LAUSD requires only AFTER the 9th grade:

 

Algebra I

1. Students identify and use the arithmetic properties of subsets of integers, rational, irrational and real numbers. This includes closure properties for the four basic arithmetic operations where applicable.
1.1 Students use properties of numbers to demonstrate that assertions are true or false.
3. Students solve equations and inequalities involving absolute values.
4. Students simplify expressions prior to solving linear equations and inequalities in one variable such as 3(2x-5) + 4(x-2) = 12.
19. Students know the quadratic formula and are familiar with its proof by completing the square.
23. Students apply quadratic equations to physical problems such as the motion of an object under the force of gravity.
25. Students use properties of the number system to judge the validity of results, to justify each step of a procedure and to prove or disprove statements.
25.1 Students use properties of numbers to construct simple valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
25.2 Students judge the validity of an argument based on whether the properties of the real number system and order of operations have been applied correctly at each step.
25.3 Given a specific algebraic statement involving linear, quadratic or absolute value expressions, equations or inequalities, students determine if the statement is true sometimes, always, or never.

Geometry

7. Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
11. Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
13. Students prove relationships between angles in polygons using properties of complementary, supplementary, vertical, and exterior angles.
14. Students prove the Pythagorean Theorem.
17. Students prove theorems using coordinate geometry, including the midpoint of a line segment, distance formula, and various forms of equations of lines and circles.
21. Students graph quadratic functions and know that their roots are the x-intercepts.

 

The LAUSD standards omit some required topics

The LAUSD/LASI Informative acknowledges that topics of Algebra II and above are not covered in the LAUSD standards. But this admission does not go far enough. Nowhere in any of the tables of the LAUSD/LASI Informative are the following California algebra I and geometry standards assigned counterparts in the LAUSD math standards. These topics are entirely omitted by the LAUSD Math Standards:

 

Algebra I

9. Students solve a system of two linear equations in two variables algebraically, and are able to interpret the answer graphically. Students are able to use this to solve a system of two linear inequalities in two variables, and to sketch the solution sets.
10. Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, using these techniques.
11. Students apply basic factoring techniques to second and simple third degree polynomials. These techniques include finding a common factor to all of the terms in a polynomial and recognizing the difference of two squares, and recognizing perfect squares of binomials.
14. Students solve a quadratic equation by factoring or completing the square.

Geometry

1. Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2. Students write geometric proofs, including proofs by contradiction.
3. Students construct and judge the validity of a logical argument. This includes giving counter examples to disprove a statement.
18. Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them, (e.g., tan(x) = sin(x)/cos(x), (sin(x))² + (cos(x))² = 1).
19. Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20. Students know and are able to use angle and side relationships in problems with special right triangles such as 30-60-90 triangles and 45-45-90 triangles.

 

LAUSD standards are unclear and subject to a wide range of interpretation

The LAUSD/LASI Informative arbitrarily juxtaposes state standards with LAUSD standards in an effort to demonstrate consistency. However, it is evident that the Informative takes great liberties in interpreting the meaning of the LAUSD standards. For example, the LAUSD standard number 28 states:

Identify, describe, compare, and classify geometric figures; apply geometric properties and relationships to solve problems; and use geometric concepts as a means to describe the physical world.

This could mean:

 

2. Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems.
2.1 identify and describe and classify polygons (including pentagons, hexagons and octagons)
2.2 identify attributes of triangles, (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle)
2.3 identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square)
2.4 identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle
2.5 identify, describe and classify common three-dimensional geometric objects (cube, rectangular solid, sphere, prism, pyramid, cone, cylinder)
2.6 identify the common solid objects that are the component parts needed to make a more complex solid object

However, LASI AND LAUSD STAFF claim that it means:

 

2. Students compute the perimeter, area and volume of common geometric objects and use these to find measures of less common objects; they know how perimeter, area, and volume are affected under changes of scale.
2.1 routinely use formulas for finding the perimeter and area of basic two-dimensional figures and for the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, cones and circular cylinders
2.2 estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking them up into more basic geometric objects
2.3 compute the length of the perimeter, the surface areas of the faces, and the volume of a 3-d object built from rectangular solids. They understand that when the length of all dimensions are doubled or tripled, the unit measures are increased by the same factor
2.4 relate the changes in measurement under change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 12² square inches, 1 cubic inch = 2.6³ cubic centimeters)
3. Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.
3.1 identify and construct basic elements of geometric figures, (e.g., altitudes, midpoints, diagonals, angle bisectors and perpendicular bisectors; and central angles, radii, diameters and chords of circles) using compass and straight-edge
3.2 understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections
3.3 know and understand the Pythagorean Theorem and use it to find the length of the missing side of a right triangle and lengths of other line segments, and, in some situations, empirically verify the Pythagorean Theorem by direct measurement
3.4 demonstrate an understanding of when two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures
3.5 construct two-dimensional patterns for three-dimensional models such as cylinders, prisms and cones
3.6 identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and how two or more objects are related in space (e.g., skew lines, the possible ways three planes could intersect)

The LAUSD standard quoted above is a seventh grade standard. The first list is from the state’s third grade standards, while the second is from the state’s seventh grade standards. The LAUSD standard is not particularly better aligned with the state seventh grade standards than with the state third grade standards. LASI has demonstrated in the Informative that the LAUSD standards are not adequately specific.

 

LAUSD standards omit grade-by-grade benchmarks and contradict the California standards

The LAUSD/LASI Informative admits that, LAUSD has written broad statements at only the selected benchmark grades of third, seventh, ninth, and twelfth. This obvious difference leaves the students of Los Angeles without a road map for their progress – most of the grades are omitted. In addition, the California state mandated STAR exams will not allow calculator usage in the first six grades. This contradicts the LAUSD third grade benchmark which prematurely requires children to use calculators in the early grades, Kindergarten, first, second, and third grades.

The LAUSD/LASI Informative even contradicts itself.

On page 2, the LAUSD/LASI Informative indicates, in a chart, that the LAUSD math standards include topics which the California math standards do not. According to the chart, discrete mathematics is included in the LAUSD standards, but not in the California State standards. But the LAUSD/LAUSD Informative then lists topics in discrete mathematics from the California math standards on the very next page, contradicting its own assertion. The treatment of discrete mathematics in the California math standards is superior to the treatment in the LAUSD standards.

The only remaining standards included in the LAUSD document, but missing in the California math standards, correspond to those noted in A Comparison of the LAUSD Math Standards and the California Math Standards under the heading, “Topics Which Either do not Exist or Have Nothing to do with Mathematics.”

 

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CONCLUSION

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LASI’s attempt to present the LAUSD math standards in a positive light cannot mask the deficiencies. The district’s own comparison actually confirms criticisms found in A Comparison of the LAUSD Math Standards and the California Math Standards.

Why would LASI go to such lengths to defend its obviously inferior math standards? Perhaps it is merely pride of authorship. Perhaps LASI’s hollow claims are dictated by LAUSD’S need to meet or surpass the state standards in order to secure future grant funding. Perhaps the district is trying to justify itself knowing that there will eventually be a review by the state. In any case, however, the district would be well-advised simply to adopt the state standards and be done with it. Afterall, … you can’t fool all of the people all of the time. (Abraham Lincoln, 1864)

LAUSD’s current resistance to the state standards, on the advice of LASI, is likely to cause delays in revising LAUSD curriculum to meet the new state standards. This will undoubtedly contribute to an even worse showing in 1999 on the STAR exams relative to other school districts in California than occurred this year. Other districts have already either aligned their math standards with the state standards or adopted the state standards outright.

LAUSD cannot succeed merely by claiming to have high expectations. In the strongest possible terms, the Los Angeles Unified School District must make it official and clear to all involved – students, parents, teachers, principals, administrators and the public – that district students are expected to meet the California Mathematics Standards. The continuing resistance to adopting the California mathematics standards serves only to save face for LASI and district staff, but it does so at the cost of a proper mathematics education for the children of Los Angeles.

 

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Reform vs. Traditional Math Curricula

 

PRELIMINARY REPORT ON A SURVEY

OF THE GRADUATING CLASSES OF 1997 OF

ANDOVER HIGH SCHOOL AND LAHSER HIGH SCHOOL,

Bloomfield Hills, Michigan,

CONCERNING THEIR HIGH SCHOOL MATH PROGRAMS AND HOW

WELL THESE PROGRAMS PREPARED THEM FOR COLLEGE MATH

 

Gregory F. Bachelis, Ph.D.

Professor of Mathematics,

Wayne State University

Detroit, Michigan [1]

 

 

 

Dedication

This report, and the six months I spent working on the underlying survey, is dedicated to the students, past and present, of Andover and Lahser High Schools.

 

 

 

 

Acknowledgment

I would like to the thank several parents and others in the West Bloomfield and Bloomfield Hills School districts, and in particular Mark Schwartz, Ph.D., for their support and encouragement during the duration of this project

STATEMENT OF PURPOSE

 

This survey was conducted to compare how high school students with differing high school math programs do in college.  I conducted the survey in my capacity as a Professor of Mathematics at Wayne State University, where for 27 years I have taught and done research in mathematics, and more recently also in mathematics education and theoretical computer science.  I conducted this survey as a public service to parents, students and others in the Bloomfield Hills School District, the West Bloomfield School District (where I live) and other districts where new programs have been introduced which have caused concerns among community members.  It was also done as a service to the mathematical community, whose two main organizations[2] are closely following the evolution of these new math curricula and the effect they are having on incoming college students.

 

I sent the survey questionnaire (see below) along with a covering letter bearing the letterhead of the Department of Mathematics of Wayne State University.   I gave my office phone number for people to call if they had any questions or concerns.  There was also a stamped return envelope, addressed to my office, with which to return the survey.  None of the above made it a “Wayne State Survey,” nor did I imply in any of my communications with the people being surveyed that this was anything but my own research project.  Nor was any implication given that Wayne State would endorse any of the research’s conclusions.

 

In addition, the research was not funded by Wayne State University.  The stamps on the return envelopes were paid for by interested parents; I did all of the work connected with the survey — clerical, follow-up phone calls and e-mail messages, data transcription and the like — and I was not given release time from my usual duties in order to accomplish all this.

 

The report that follows is preliminary in nature. Further analysis needs to be done on the data, and this is currently being done by professors at another university.  However, the report does include all the comments made by all the respondents, with accompanying information supplied by them — GPA’s, SAT and/or ACT scores, college attended, college major, etc.– in order to give the comments a context.  Since I promised confidentiality to the respondents, I have blurred the contextual information, in a manner explained later, so as to preserve their anonymity.  I have also, in a few cases, paraphrased or deleted portions of the comments in order to protect the identity of the respondent.  In each case this is clearly indicated.  None of the above actions detract in any material way from the information that they provided.

 

In closing, I wish to reiterate that this research project was performed by myself as an individual faculty member of Wayne State University, conducting a survey on what I considered to be a matter of public interest within the area of my professional expertise.

 

 

 

The Advent of Core-Plus in Bloomfield Hills

The Bloomfield Hills School District (BHSD) is located in Oakland County, Michigan.  It is a 25-square-mile area, which is comprised of virtually the entire city of Bloomfield Hills, most of Bloomfield Township, a large portion of eastern West Bloomfield Township, and a small part of the city of Troy.  The district has two high schools, Andover and Lahser, and three middle schools, West Hills, Bloomfield Hills and East Hills.  The middle schools all house grades six through eight.  West Hills feeds Andover, East Hills feeds Lahser, and Bloomfield Hills Middle School feeds both high schools.

In the fall of 1993, Andover High School began what would be a four-year phase-out of its (non-accelerated) “traditional” math program, which had been as follows:

• Ninth grade  — Algebra 1
• Tenth Grade — Geometry
• Eleventh Grade –Algebra 2
• Twelfth Grade – Pre-Calculus[3]

In its place the Core-Plus Mathematics Project (CPMP or Core-Plus) was installed; it is an integrated math program using modeling, simulation and cooperative learning, which makes extensive use of graphing calculators.  Core-Plus was phased in on a year-by-year basis, so that by the 1996-97 school year it was the exclusive math program at Andover, with the exception of AP Calculus and AP Statistics.[4]  The latter courses are typically taken in the twelfth grade by “accelerated students,” by which I mean those who take Algebra 1 or Core 1 before the ninth grade.

“Integrated” or “Reform Math” refers at the high school level[5] to constructing the curriculum out of four “strands”:

• Algebra and Functions,
• Probability and Statistics,
• Geometry & Trigonometry,
• Discrete Mathematics.

These are woven together for a three or four-year curriculum, rather than being taught as separate courses.

Core-Plus was introduced at Andover in 1993 as a pilot project, which means that this was the first time it was used anywhere in an actual classroom setting.  According to Professor Harold Schoen, evaluation Director of Core-Plus,  “The pilot test was designed mainly to provide feedback to the authors from teachers and students concerning what worked well, what did not and what improvements were needed.”[6]   In 1994 the field testing of Core 1 began in 36 high schools in Michigan and around the country.  Core-Plus was originally intended as a three-year curriculum.  However, according to Marcia Weinhold, the Outreach Coordinator of Core-Plus, “During their senior year, [the non-accelerated Andover] students studied three prototype units for a possible fourth-year course that was envisioned by Core-Plus.  Thus, the curriculum these students pursued was not a complete four-year curriculum.”[7]   The field testing for Core 4 started in the fall of 1998.

The Accelerated Students

A substantial portion of the Andover Class of 1997 consisted of students who had been accelerated in math, and hence had not taken Core-Plus. These students as a rule had taken Algebra 1 during the 1992-93 school year, while still in middle school.  So when this group arrived at Andover in 1993, they rode the last wave of the traditional math sequence while the non-accelerated students rode the first wave of Core-Plus.  Lahser, the other high school, stayed “traditional.”  Core-Plus was introduced at the middle school level, so that accelerated students destined for Andover could take it in the eighth grade, in (I believe) January, 1994.

Controversy over Core-Plus

So, in June 1997, the first class having completed four years of Core-Plus graduated Andover High School.  Subsequently, reports of some of these graduates having difficulties on the math placement exams at the University of Michigan – Ann Arbor (UMAA) and Michigan State University (MSU) began to surface. On October 28, 1997, a joint meeting of the Bloomfield Hills and West Bloomfield School Boards was held to discuss reform math.  After the featured speaker had finished the main part of his presentation, several parents and others took to the floor to express their thoughts and concerns about Core-Plus and about how this first graduating class was doing in college.  I live in the West Bloomfield School District (WBSD), which had started introducing Core-Plus, and phasing out their existing math program, in 1995.[8]

I had participated in several meetings of my school board during the preceding year, at which Core-Plus was discussed, and I attended this joint meeting.  After attending a number of additional meetings organized by parents, in both BHSD and WBSD, concerning the impact of Core-Plus, and mindful of the intense scrutiny the mathematical community is giving the evolution of such reform math programs, I decided to do a survey of the 1997 graduates of Andover, in order to determine their opinions about Core-Plus and to get as complete as possible a picture of their mathematical experiences since graduation.[9]

I surveyed the entire Andover class of 1997; the reason being that I did not know a priori who had been accelerated and who had not.  Also, with the accelerated students I could study how well students with a traditional high school math background do in Reform Calculus courses such as “Harvard Calculus,”[10] The latter is the flagship calculus course of UMAA; it is also taught at MSU, but on a more limited basis.[11]  One of the main claims of Core-Plus and other programs of its type is that they are a better preparation for Reform Calculus courses than the more traditional curricula.[12]

The survey commenced in late April of 1998 and concluded in mid-September, as far as any activity on my part soliciting responses.  The covering letter and survey questionnaire are given below in compressed form. (Most blank lines and some lines for answers have been deleted.)  The original questionnaire consisted of three pages plus the optional section.

Covering Letter and Survey Questionnaire

******************************************************************************************

College of Science

Department of Mathematics Detroit, Michigan 48202 (313) 577-2479 (313) 577-7596 FAX

April 22, 1998

Dear __________________,

 

I am conducting a survey of 1997 graduates of several high schools, including yours, who entered college in the summer or fall of 1997.  We would appreciate your cooperation in this effort to evaluate how high school math programs are preparing students for college level mathematics.  The results of this survey will be used for independent research regarding high school math curricula and individual names will be kept confidential.  We are asking you for a few minutes of your time to complete the enclosed questionnaire and then to return it in the enclosed envelope.  Please feel free to call me at my office at Wayne State at 313-577-3178, or to send e-mail to greg@math.wayne.edu, if you have any questions or concerns.

 

Thank you for your cooperation,

 

Gregory Bachelis, Ph.D.

Professor

 

********************************************************************************************

 

MATH SURVEY

 

1. High School graduated from in 199___    ________________________________High School
2. High School GPA ______         Honors or Awards__________________________________
3. Academic interests in high school   1.______________________2._______________
4. 4.                                                5.­­­­________________                         
5. Scores on SAT      Math ________Verbal  ________    PSAT   Math______  Verbal ____

ACT   ________   PLAN _______         Other (specify) ______________________

5. Did you take any Advanced Placement tests?    Yes     No  .  If so, please specify.

Subject              Score       Year                    Subject                       Score          Year

________________ _______   _____             ________________     ______       _____

6. Did you take any ACT or SAT prep courses?   Yes   No   If so, please tell from whom and give dates.:

________________________________________________________________________

7. Math courses taken in High School: (Please fill in the appropriate box with the grade(s) received.)

 

Year

Alg 1

Alg 2

Geom

Trig

Adv Alg

Pre Calc

AB Calc

BC Calc

Core Plus 1

Core Plus 2

Core Plus 3

Core Plus 4

Other (specify)

School Name

Fresh

Soph

Junior

Senior

 

8. Did you receive any math tutoring while in high school?  (besides SAT or ACT prep, if any)  Yes    No.  If so, please give details on the next page. (Indicate if tutoring was private, provided in school, or by a commercial organization.)

I received tutoring in:

Subject    _____________________   Year   ____________   From   ________________

9. Did you participate in any summer math programs during the years you were in high school?

If so, please specify subject, year, and who sponsored them.

______________________________________________________________________________

10. Did you enter college after graduating from high school?     Yes    No.     If no, or if you haven’t taken any math courses or placement exams in college, please skip to question 16. Otherwise, please continue with questions 11 – 15.
11. Please specify any college math courses taken during the summer of 1997, or the 1997-98 academic year.

 

	Math Course	College/University	Grade	Text *
Summer ‘97
Fall ‘97
Winter ‘98

*Please identify the text by listing the author or first author, if there are several. (e.g.  Stewart, Thomas, Finney,                             Hughes-Hallett, Stein, Anton, Ostebee, Ellis, Edwards, Swokowski, Varberg, Larson, Dick, Wattenberg)

12.  Did you take a math placement exam in college?        Yes       No    .  If so, please tell where taken, the nature of              the exam and your score and/or in what course you were placed.

______________________________________________________________________________

13. Have you sought any math tutoring in college?  Yes    No    If so, please give  subject(s) tutored in and reason(s) for seeking tutoring.

______________________________________________________________________________

14. What is your intended major?  ­­­­­­­­­­_____________________________________________
15. Please answer the following two questions, when applicable, on a scale from 5 to 1.
16. a) Math courses I had in high school, other than calculus (if taken), helped me with my

college math courses  (circle one)

         5                     4                   3                  2               1                 

very much                             somewhat                       not at all

 

1. b) Calculus I took in high school helped me with my college math courses. (circle one)

         5                     4                   3                  2               1                    (Does not apply)

very much                             somewhat                      not at all

16. Please give any additional comments you wish to make concerning your math experiences in high school or   college.                              ______________________________________________________________________________

______________________________________________________________________________

Thank you for your cooperation.   There is an optional section on the next page.  When you have completed this questionnaire, please return it in the enclosed envelope to

Professor Gregory Bachelis

Department of Mathematics

Wayne State University

Detroit, MI 48202   

 

******************************************************************************

OPTIONAL SECTION

NAME ___________________________            AGE _________ SEX :    M     F

HOME ADDRESS________________________________________________________

COLLEGE ADDRESS (if different from above) _________________________________

May we contact you to obtain any further comments?    Yes       No

TELEPHONE  NUMBER(S) ________________________________________________

E-MAIL ADDRESS __________________________________

******************************************************************************

In the eighteen months prior to my decision to conduct the survey, I had spoken out about Core-Plus.  I was skeptical of the claim being made that it was suitable for all students, and I was critical of the fact that it was being implemented at certain schools to the exclusion of almost the entire previously existing math courses; the latter was the case at Andover and at West Bloomfield High School, the sole high school in WBSD.  I felt qualified to speak out, since I have been a mathematics professor for over 30 years, and I have taught, at one time or another, all of the subjects that are included in these new integrated curricula.  I felt that it was impossible to do these subjects justice by cramming them into a three or four year high school curriculum

However, I do not feel that my voicing criticisms and concerns disqualified me from conducting the survey.  Certainly I am capable of wearing different hats, and people doing surveys are entitled to have opinions on the subject under study.  The key point is whether the survey is conducted in a fair and impartial manner.  In this regard, note that the tone of the letter and questionnaire is quite neutral.  There are no “loaded” questions.  My follow-up phone calls and e-mail messages, encouraging people to respond, were also quite neutral in tone. I knew none of those surveyed beforehand. Also, only a few of them attend Wayne State, which has about 17,000 undergraduates.  For these reasons there was no pressure on them to respond.  In any case, the respondents to this survey were not analogous to a jury being picked prior to a trial. They had had the course, so to speak.

The Control Group

In surveys of this type, there is a lot of  “noise” that needs to be filtered out.  If the Core-Plus graduates were the treatment group, then who to use as controls?  It would not have been fair to the Core-Plus group to use the accelerated Andover students as controls.  Virtually all of the latter had taken calculus in the 12th grade, and it had been determined that they were among the better math students in their class – by exams, grades or other means – or else they wouldn’t have been accelerated in the first place[13].

I decided to survey the 1997 graduates of Lahser, the other high school in the district, which had stayed traditional.  I could then use the non-accelerated Lahser students, or perhaps the Lahser students who didn’t take Calculus in the 12th grade (which includes the non-accelerated ones), as controls.  With the remaining Lahser students I could study the same question as with the accelerated Andover students, concerning Traditional vs. Reform curricula.  I could also compare these Lahser students with the accelerated Andover students, pre-Core-Plus.

I believe my choice of control groups was a reasonable one. The populations of the two high schools are similar socioeconomically, they are in the same school district, and one of the middle schools even feeds both of them.  In 1993, when Core-Plus was introduced at Andover, students in the district could in fact choose which high school to attend.  I have only anecdotal evidence as to what effect, if any, the advent of Core-Plus had on traffic between Andover and Lahser, or out of the public system entirely to private schools such as Cranbrook Academy or Detroit Country Day School, or to parochial schools such as Marian High School or Brother Rice High School.  In 1997, choice of high schools in the District was ended for the time being because of an imbalance in favor of Lahser.[14]    

Survey Mechanics, Population Size and Rate of Response

In 1997, there were 228 graduates of Andover High School, and 258 of Lahser High School.[15]       I determined the size of the population being surveyed and response rate of each high school as follows:

Andover High School

• 1997: 228 total graduates
• one exchange student — returned home
• at least four other students had left the country
• probable valid addresses for all but one of the remaining students

Therefore student population size = 228 – 1 –  4 –  1 = 222

• 112 total replies

Response rate  = 112 total replies/222 population size = 50%

Lahser High School

• 1997: 258 total graduates
• one exchange student — returned home
• probable valid addresses for all but six of the remaining students

Therefore student population size = 258 – 1 –  6 = 251

• 75 total replies

Response rate  = 75 total replies/251 population size = 30%.

In late April and early May the questionnaire and covering letter were mailed to all 1997 graduates from both high schools.  A stamped envelope with my return address at Wayne State was included.  The initial mailing was followed up by phone calls or e-mail messages (when e-mail addresses could be determined).  These follow-up contacts were made by me, so that there would be consistency in the messages being sent by e-mail or left on phone answering machines, and in the phone conversations. Based on these contacts, a second questionnaire was often dispatched, as its predecessor had been misplaced or discarded for sundry reasons.  I have communicated in the ways indicated above with over 80% of the 473 graduates (or in some cases, family members) who were being surveyed.

One can only speculate as to the reasons why some graduates did not respond to the survey.    The non-respondents might include those who

• for one reason or another, never received the questionnaire;
• were apathetic, busy, etc.;
• objected to a survey in the first place;
• didn’t want to revisit high school issues.

     SOME WORDS OF CAUTION

I wish to make the following three points.

1) I want to stress that I was not trying to determine how well the various curricula were taught.  This is certainly an issue, especially with a radical new curriculum like Core-Plus.  I was simply trying to find out how the various curricula, as taught, prepared the students for college math, their reaction to their high school math experiences, and also how much extra help, such as tutoring, they sought.[16]

2) The information is only that provided by the respondents, and has not been independently verified.  They were promised confidentiality by me, and I believe they made a good faith effort to give accurate answers to the questions. Certainly a number of the comments   were quite candid.

3) Many schools besides Andover High School have phased in new math programs like Core-Plus, mainly in response to the promulgation of the 1989 NCTM Standards[17], although     some of these schools have also kept the traditional track, thus allowing for “choice” and for comparison of the two curricula.

SOME STATISTICAL ANALYSIS

The Andover respondents fall naturally into two groups:

• I:  non-accelerated (Core-Plus), and
• II: accelerated (virtually all of who took Calculus).

The Lahser respondents fall naturally into three groups, since a lot of the accelerated students did not take AP Calculus, although a number of them did take AP Statistics.  These groups are

• I: non-accelerated,
• II: accelerated, no Calculus, and
• III: accelerated, with Calculus [18]

The answers to 15a) of Andover I are compared to those of Lahser I and II in the following table.  Recall that question 15 was:

15. Please answer the following two questions, when applicable, on a scale from 5 to 1.
16. a)  Math courses I had in high school, other than calculus (if taken), helped me with my   college math courses      (circle one)

           5                     4                   3                  2               1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 very much                             somewhat                      not at all

1. b) Calculus I took in high school helped me with my college math courses. (circle one)

         5                     4                   3                  2               1                (Does not apply)                                                                                                                                                                  very much                             somewhat                      not at all

We have the following results.

Group         Mean response    Standard Deviation    Number of Responses

Andover I                  1.78                0.94                                  53

Lahser I                     3.39                 1.09                                  23

Lahser I&II               3.46                 1.05                                  35   ________

          Table I: Answers to 15a) for Andover I, Lahser I, and Lahser I&II

 

Assuming linearity of the response scale, this means that the Lahser students without calculus thought their high school math was approximately twice as helpful with college math than the Andover Core-Plus students did.

I should mention that a number of respondents appear to have been confused about 15b) and to have thought that the word “calculus” applied to college rather than high school.   So, for example, all of the respondents in the above three groups should have circled “Does not apply” in 15b), and this was not the case.  The answers to 15a) and 15b) for Andover II and Lahser III are now compared.

______________________________________________________________________

Group          Question   Mean response    Standard Deviation    Number of Responses

Andover II       15a)              3.81                             1.13                                   36

Andover II       15b)              4.01                             1.34                                   35

Lahser III         15a)             3.50                              1.24                                   28

Lahser III        15b)              3.80                              1.30                                   30

______________________________________________________________________

     Table II: Answers to 15a) and 15b) for Andover II and Lahser III

 

This means that all groups who had high school calculus answered between 3.5 and 4 on average, when asked about the helpfulness of high school calculus or of high school math before calculus, and that Andover was slightly more generous than Lahser. Considering both tables, we see that the average answer of each of the groups, except Andover Core-Plus, was roughly 2 times more than Andover Core-Plus.

Further statistical analysis of the data is needed, and this is currently being done by several professors at Stanford University.

The Comments

I have decided to report all the comments verbatim, subject to the following protocol.  I have corrected spelling errors and expanded abbreviations.  In a few instances I have deleted a word or phrase to protect the confidentiality of the respondent.  These deletions are denoted “[…]”.  In a few cases I have added a few words or paraphrased.  Such paraphrasing or additions are enclosed in square brackets.

I have given the answer and accompanying remarks to question 13 about math tutoring in college, when there were remarks made that were worth noting, since this question did indeed generate a lot of comments.  I have also included those parts of answers to question 12, which asks whether a math placement exam was taken in college, that relate to the score received and the resulting placement, since this is a matter of some controversy.[19]   I have also included affirmative answers to question 8 about math tutoring in high school, and excerpts from the answers given, since this too has been a matter of some interest; to wit, did Core-Plus generate more than the “usual” amount of math tutoring.  In this regard, I have included affirmative answers to question 9 about summer programs when they relate to summer school as opposed to summer “math camps.”  In addition, I have given the answers to question 15a) for Andover I and Lahser I&II and to questions 15 a) and b) for Andover II and Lahser III.

Besides the above, in order to give the comments more context, I supply some information about the respondent, blurred somewhat so as to preserve anonymity.  This “blurring” is accomplished as follows: High School GPA’s, and SAT and/or ACT scores, when given, are reported in a certain range, rather than by exact value.

Colleges, except for UMAA (The University of Michigan – Ann Arbor) and MSU (Michigan State University), are reported by category, these being:

Michigan-Public,

Non-Michigan-Public,

Private,

Private-regional, and

Other (specialty schools, no college attended, or college unknown).

College majors are also reported by category, these being

Science (which includes mathematics and psychology),

Engineering,

Business,

Education,

Nursing (which includes medical technicians and physical therapy),

Design,

Fine & Performing Arts;

Pre-professional (which includes architecture),

Communications (which includes journalism),

Social Science, and

Liberal Arts[20].

Unfortunately, I cannot supply an indication of grades in high school math classes, because a lot of respondents, in answering question 7, merely put X’s in the grid to indicate which courses they took, without listing the grade received, as was requested.  In some cases this was no doubt because they couldn’t remember the actual grades.  I don’t see the purpose of supplying information that can only be done so sporadically.

I want to make it very clear that I did not solicit comments beyond what people wrote in their returned questionnaires.  In a few cases respondents sent e-mail messages with comments prior to sending in their questionnaires, and I have included these where they were not duplicated by the written comments. In a number of cases, during the course of my phone calls subsequent to the mailing of the questionnaires to encourage people to respond, graduates or their parents gave opinions.  In these cases, I said that I could not do the survey over the phone, and I encouraged them to send in their questionnaires.  I made no written record of such conversations.

A majority of the respondents chose to answer the Optional Section and to answer “Yes” to the question asking whether they could be contacted for additional comments.  In these cases I thanked them, by phone or e-mail, for responding to the survey, and I encouraged them to get other graduates to respond.  In some cases I also sought clarification to their answers to one question or another, and in a few of these cases, comments were made by respondents which I then added to their written comments (and these additions are so noted); but as I said above, I did not solicit comments beyond what the respondents had chosen to write.[21]

Some Conclusions

I will let the reader draw his or her own conclusions as to the validity or reliability of the comments.  One conclusion I wish to make is that, if some of the Lahser comments give the reasons why curricula such as Core-Plus have been developed to try to make mathematics more meaningful and accessible, then surely a preponderance of the Andover comments – even some by people who were not in the program – indicate that the cure is much worse than the disease for students who need to take additional math courses in college, and perhaps for others.

The other matter I would like to comment on is the performance of Core-Plus graduates on the placement tests at UMAA, MSU, as well as other colleges.  A lot of them complained that they did not do well because of their lack of knowledge of basic algebra, and some said they did not do well even in the courses they were placed into.  Now it is all well and good to say that people are just having a bad day when they do poorly on a placement test, but as someone who has taught remedial algebra for more years than I care to remember, let me assure you that there is a big difference between learning basic algebra and then forgetting most or all of it, and never having learned it at all.  Core-Plus appears to have created a new category of students who land in remedial math courses – courses that were not designed with such students in mind.

Further Work

This is after all a preliminary report, so I welcome any suggestions or corrections, and I will make appropriate changes where indicated.  As I mentioned above, more analysis of the data is being carried out.  In this report I have chosen not to study in detail the issue of high school math vs. reform calculus in college; however some of the comments of the students do shed some light on this.[22]  Parenthetically, I wish to point out that the comments made by the respondents about the T. A.’s at The University of Michigan (called GSI’s for Graduate Student Instructors) are probably not much different than those that would be made by students at any other major university in the U.S.

There are also other groups that should be surveyed.  For example, the accelerated group that graduated from Andover in 1998 after 4 years (or maybe 3 and 1/2) of Core-Plus followed by one year of AP Calculus should be studied.  I tried to get information about this group, but I only have a few anecdotes about how they are doing.  Also, non-accelerated groups a year after graduating whom had field-tested Core-Plus, as opposed to pilot testing and testing prototypes, could be studied.  West Bloomfield High School now has a hybrid version of Core-Plus, in which certain Core modules have been deleted in favor of algebra drill.[23]  (The courses being taught at that high school this year are one year past field testing, except for Core 4.)  Groups having had this type of curriculum could be studied as well.

I leave such surveys to others, as I am not up to an encore.

                       The Comments in Context[24]

Andover Group I Students {non-accelerated (Core Plus)} who made Comments about Core Plus[25]

 

Andover 4.    2.75-3.25;  SAT M 400-500 V 500-600;  Michigan-Public; Education

• Core Plus was a waste of my time.  I have very few math skills, and none of them helped me with Algebra I in College.

Math placement exam? Yes. I suppose I didn’t pass because I was placed in 110, the second lowest.

Math tutoring in college?  Yes. I have never understood Algebra because of Core Plus math in

     High School.   I went to the tutor lab 3 times per week and I still did poorly.

15a) 1

Andover 8.  2.75-3.25; SAT M 500-600 V 500-600; ACT 18-20; Michigan-Public; Business

• With the new program of math at Andover I did not feel prepared to enter the level I was placed at in the University.

Math placement exam? Yes.  I was placed in Intermediate Algebra.

Math tutoring in college?  No.  I decided that I should prepare myself by taking a couple of math classes at a community college before I go and take it at [my university].

15a)  1

Andover 14.  2.75-3.25;  ACT 24-26;  Michigan-Public;   Business

• [Core Plus] was probably the most horrible experience I have ever gone through in high school.

Math tutoring in high school? Yes. 1996.

Andover 16.  3.25-3.75    ACT 24-26    UMAA      Communications

• Should not use notes for test, because you can’t at college.

Math tutoring in high school?  Yes.  Math.  On and off throughout High School

Math placement exam?  Yes.  I got a 6%

15a)  1

.Andover 17.    3.75 – 4.0   ACT 21-23   UMAA   Social Science

• Helped me learn new way of thinking, but high school math should have taught more basic math concepts

Math tutoring in high school?  Yes.  Basic Math.  1995-96.

Math placement exam?  Yes.  Got 0/10 because knew no traditional math.

 

Andover 19.   3.75-4.00   ACT 18-20;    UMAA      Communications

• I hated Core Plus; thought it was a waste and very boring.  

Math placement exam?  Yes.  29%.  pre-calc.

Andover 20.  2.75-3.25;  SAT M 500-600 V 600-700;  Michigan-Public; Fine & Performing      Arts or    Education.

• I thought math would be really easy at […]  because […].  But High School did nothing for me.  It seems all I took from High School math was how to use the TI-82.

Math placement exam?  Yes.  I placed into Normal.

15a)  2

Andover 27.   2.75-3.25;   ACT 21-23;   Michigan-Public;   Design

• Core Plus has got to be one of the worst math programs.  We were never taught any of the basics and most are suffering in college math courses

Math tutoring in college?  Yes. College Algebra, because I did not learn (was not taught) in high school.

15a)  1

Andover 31.  2.75-3.25;  SAT M 400-500 V 500-600;  ACT 21-23;  MSU  Communications

• The math I received in high school did not prepare me for the math I received in college.  I was    expected to know many things in my college course that I do not feel the Core Plus program prepared me for.  I was very behind in my knowledge of mathematics upon entering my college     math course    [Intermediate Algebra].

Summer School. Before freshman year.  First-level Algebra.

Math placement exam?  Yes.  I [had] a raw score of 5 right and was placed in the lowest level of math, 1825 [Intermediate Algebra].

15a)  2

Andover 40.  3.25-3.75;  ACT 24-26;   UMAA      Business

• Core Plus focused on theory instead of numbers whereas calculus at U of M focused on numbers      [and] then explained the theory behind it.

15a)  1

Andover 42       3.75-4.00   UMAA    Undeclared

• Even with having an excellent teacher and being self-motivated I felt unprepared.       Core Plus needs to focus more on teaching basic skills before diving into applications.  The program was similar to calculus and pre-calc at Michigan in terms of group homework and story problems – but fundamental concepts need more attention!

Math tutoring in college?  Yes. Made use of the math lab (free tutoring) while taking calculus to get         help with new concepts and prevent being behind.

15a)  3 (pre-calc)  1 (calculus)   [Count as 2 for statistical analysis.]

 

Andover 43.   2.75-3.25     Other    Unknown

• The math program was good and bad.  It tried to apply math to real life – but it didn’t make a   great attempt.  I live on my own in […], use math in all my taxes and bank account things and I   learned all that outside of the math program.

 

Andover 45.   2.75-3.25    ACT 18-20;   Michigan-Public;    Social Science

• The reason I have not taken any math courses in college is because the math I learned in high     school does not apply to college math.  I used the TI-82 for linear programming and colleges do math by hand which is very tedious.  Colleges all need to change to the new math.

 

Andover 53.      2.75-3.25;  SAT M+V 1000-1100 (better in verbal)  MSU   Science

• I feel let down by the integrated math program.  I felt as if there was a great deal of skills they    assumed us to already have.

Math placement exam.  Yes.  Lowest math class for no credit.

Math tutoring in college?  Yes.  Algebra, I was not taught a lot of the “basics.”

15a)  2

Andover 54.      3.25-3.75;   ACT 24-26;   Non-Michigan-Public;   Communications

• The math program at Andover sucks, and f____d me in my first year at [the] university and     did not prepare me for [the] ACT at all.

Math tutoring in college?  Yes. Trig, had no high school background.

15a)  1

Andover 55.      3.25-3.75;    ACT 21-23    MSU     Nursing

• The concepts I learned were interesting but did not prepare me for standardized tests or, more    importantly, for college mathematics.

Math placement exam?  Yes.  My score (8, I think) placed me into remedial math (1825)

Math tutoring in college?. Yes. Math 103 (College Algebra). Did not learn adequate algebra concepts in high school.  Therefore I was extremely behind.

15a)  2

Andover 57.      3.25-3.75;   SAT M 500-600 V 500-600;  ACT 21-23   MSU    Business

• My math experience in high school was terrible.  I used to be an excellent math student in middle school, but when I took Core Plus Math my math skills went downhill.  It is a terrible pro gram.  I wouldn’t recommend it to my worst enemy.

Math tutoring in high school?  Yes.  Core Plus Math.  1996

Math placement exam.  Yes.  [results not given]

Math tutoring in college?  Yes. Math – I was having trouble keeping up with all the work  [in Finite Math].  I didn’t understand half of it due to my terrible high school math program.

15a)  3

Andover 60.      2.75-3.25    ACT 18-20   MSU    Education

• I believe that the Core Plus program was horrible.  I was not prepared for college math courses, and I am now struggling in a course I am attending for the next 7 1/2 weeks at OCC.  My scores    on my ACT were all high except for math, which brought my overall score down.

Math tutoring in high school.  Yes.  Math (Core Plus).  All 4 years

Math placement exam?  Yes.  I was placed in 1825, which is a non-credit class, but I needed it to take 103 (which is a basic algebra class).

Math tutoring in college?  Yes.  It was for 1825 [Intermediate Algebra], and I received help from               [another] student, who [was] a math major.  I needed help because I was lost in the class.

15a)   1

Andover 63.      3.75-4.00;   ACT 24-26;    MSU      Business

• I think Core Plus is the worst math program I’ve ever been forced to take.    Traditional math      courses are what high schools need to teach to prepare kids for college.

Math placement exam?  Yes.  I placed into Math 120 but chose to begin in 103[College Algebra].

15a)  1

During subsequent phone conversation:  The algebra class I took in high school was the only thing    that helped in college math.

 

Andover 64.      3.75-4.00;   SAT M 700-800; V 700-800;   ACT 27-29   UMAA    Science

• Core-Plus math stinks.  It did not help me as much as other courses would have and should      have.  Do your best to end it.

Math tutoring in high school?  Yes.  Algebra.  1995

Math placement exam? Yes.  Scored in the 20th percentile.

15a)  3

Andover 68.     2.75-3.25    ACT  21-23     MSU     Communications.

• Because of the Core Plus Program I am completely unprepared and have no way to understand college math.  I have to take Math 115 (High School Math) at OCC during the summer [which is] equivalent to 1825 [Intermediate Algebra] at MSU for no credit toward graduation in order to go forward into math courses at MSU.  I have been extremely frustrated and disappointed with the “math” I took in High School.

Math tutoring in high school?  Yes.   1994-97.

Math placement exam? Yes.  I do not remember the score, but it was low.  I placed into 1825      [Intermediate Algebra].

Math tutoring in college?  No.  I was not going to take a math course because I was so unprepared.

15a)  1

Andover 70.     3.25-3.75    ACT 21-23    Michigan-Public;    Business

• I did very well in all my years of high school and got A’s and B’s in all my math courses, but when I tried taking 090 [Intermediate Algebra] at [my university], I was totally lost and didn’t know even the most basic concepts.  I took a W for the class and have made arrangements with the head of the Math Department to retake the course under his tutoring next fall.

Math placement exam?  Yes. Low, below avg. score.  Placed into Math 090.

Math tutoring in college?  Not yet, but I’m pretty sure I’ll have to.

15a)  1

During subsequent phone conversation.  My high school math helped me in my Statistics course.

 

Andover 73.   2.75-3.25; SAT M 500-600 V 600-700; ACT 21-23   UMAA   Fine & Performing Arts

• I’m not going to take and math courses in college because, although I did well in High School math, I feel I don’t understand basic math concepts well enough to keep up in college.

Mathematics courses during 1997-98 school year. None taken.  Don’t feel prepared enough.

15a)  1

Andover 74.  3.25-3.75; SAT M 400-500 V 600-700; ACT 21-23;  UMAA; Communications

• Andover Core-Math Program does not prepare a student entering college the sufficient basic skills that are necessary to function within college level courses.

Math placement exam?  Yes.  Placed in the lowest math possible.

15a)  1

Andover 77.    2.75-3.25;   ACT 21-23    MSU    Undeclared (maybe Communications)

• I liked how we did group work a lot of the time, and the material we were to be taught was taught in a very small amount of time.  Like, I think we learned algebra for 3 days.  It takes practice, but we did it anyway in 3 days.  That doesn’t work.

Math placement exam.  Yes.  It was kind of easy and I passed. I was placed into Mth 103, 116 or 132 .

15a)  3

Andover 83.  3.25-3.75; SAT M 500-600 V 700-800; ACT 27-29;  UMAA   Social  Science/Science

• I enjoyed my high school math class because it was neither overly difficult nor frustrating.  However, it did not prepare me sufficiently for standardized tests such as the ACT/SAT and college placement exam.  My high school math did somewhat help me in college.  My problem in college math [Pre-Calc] was not so much about poor preparation as it was about poor teaching.  My GSI was very difficult to understand.  He spoke little English and drew incomprehensible diagrams on the blackboard.  Also, the grading of exams was somewhat questionable.

Math placement exam?  Yes.  I placed in the 6th percentile.  Therefore I was placed in 105 (pre-  calculus).

15a)  3

Andover 84       2.25-2.75    Other

• I am currently working and feel that I cannot even do basic math calculations.  I     am missing too many fundamentals

 

Andover 91       2.25-2.75    MSU    Education :

• Andover’s math program was not helpful at all.

Math placement exam?   I was placed in Math 1825 [Intermediate Algebra].

15a)  1

Andover 94. 3.75-4.00; SAT M 500-600 V 700-800; ACT 24-26;  Michigan-Public;  Pre-Professional

• The Core math program has given me a weak math background.

Math tutoring in high school?  Yes.   1996-97.

15a)    1

Andover 95.  3.25-3.75   SAT M 500-600 V 500-600   UMAA    Science

• I am concerned with the direction math has taken in Core classes.  Math has become second nature [read “secondary”] to learning to write about math.  I am embarrassed and not the least bit confident with my math ability.  I am upset that I was ever placed in a Core class!

Math placement exam?  Yes.  Math 105 (pre-calculus).

15a)  3

Andover 100.    2.75-3.25   ACT  24-26   MSU    Communications

• When it comes to my mathematical ability here in college, I feel second compared to other students.  My high school is a nationally recognized institution and while I do feel as if I’ve been well prepared in other areas, I feel that the Core-Plus math courses were a waste of four years.

Math placement exam?  Yes. Placed in MTH 1825, an algebra class for no credit (towards graduation        requirement[s].)

Math tutoring in college?  Yes.  MTH 1825  Visit[ed] Math TA (teaching assistant) during office hours   for help on class material..

15a)   2

Andover 107.    3.25-3.75    SAT  M 500-600 V 500-600   UMAA   Social Science

• My math courses in high school barely prepared me for college.  I was very behind when it came to competitiveness and dealing with the difficulty of taking a college-level Math course.  [Respondent took Math 105, Pre-Calc.]  I was taught difficult math ideas in high school but was never taught the fundamentals!

Math placement exam?  Yes.  Placed in the 5th percentile.

Math tutoring in college?   Yes.  Repeatedly went to office hours for special attention from my teacher,   a GSI.

15a)  2

Andover 112     3.75-4.00;  SAT  M 500-600 V 600-700;  ACT 24-26;  Non-Michigan-Public; Fine &   Performing Arts

• My math experience in high school was not advantageous.  Although I received good marks in the courses, they did not help prepare me for the SAT or ACT .  I can also positively affirm that I remember almost nothing from those courses (Core-Plus).  I am very fortunate that I do not have to take any seriously math based courses in college.  My major does not require me to do so. The Core-Plus math program did not help me remember the elements and forms of algebra, calculus, geometry and trigonometry for the long term.  Also, there was no permanent index to the formulas and equations used.  If I needed to look back on something, I could only depend on my own notes.  I guess no one took it into consideration the fact that students might miss a few things in their note taking. 

          I learned the math and I studied it.  The key, however, is that I learned it the way the Core-system presented it to me.  Years of solving long word and statistical problems does not seem to help on the SAT’s.  In the SAT booklet you will find a few letters (A, b or c), a few numbers, and possibly a chart.  There are no words and no real-life situations presented.  I’ve never been superb at math, but Core-Plus didn’t make me learn and retain it any better. 

          Thankfully my parents read to me as a child.  I can read, write and spell very, very well.  A skill I desperately needed for those standardized tests.

 

Andover 126     2.75-3.25   ACT 24-26       MSU      Business

• At Andover High School I was required to take Core-Plus when I was a freshman.  The class has not prepared me for anything in college.  I am currently finishing a math class      at MSU that I will not receive credit for [1825].  In this class we only use our calculators to solve simple computations.  It is not acceptable to give answers produced by advanced calculator programs as we were taught in high school.  By participating in the Core-Plus program I was essentially handicapped when I went to college.  I don’t know where this survey will take you, but it seems to me that a positive effort is being made [by this survey] to evaluate the current situations.  Please keep me informed of your progress.

Math tutoring in high school?  Yes.   Only to prepare for a test that contained subjects that I did not understand.  I went, probably once a month.

Math placement exam?  Yes.  Placed into Math 103 [College Algebra]

Math tutoring in college?  Yes.  Tutoring for everything.  I have much difficulty understand[ing] math.

15a)  1

Andover 128     2.75-3.25   SAT M+V 900-1000   SAT  18-20       MSU      Business

• I received A’s B’s and a C in math [in high school], but I still didn’t know anything in the lowest Math class at State.

Math placement exam?  Yes. I placed [by?] one point into regular Algebra, but they advised me to go    into Intermediate Algebra.

15a)   2

Content of an e-mail message sent in response to an e-mail query of mine.

     I never received the questionnaire and would like to take it.  I will also tell you this, Not one person who took the Math Core program is even close to prepared for college level math, not even the Intermediate Algebra at MSU (unless they received help from a tutor, or took extra math classes at OCC)   I feel the Math Core Program at Andover is the (excuse my language) dumbest thing the Bloomfield Hills School District has ever done.  Most students who graduated from Andover do not even know simple Algebra.  I find it idiotic that a school like Andover who has a 99% graduation record and about a 95% future college bound body changes their math program to one for students planning not to go to college. 

     Last year, a math teacher at Andover told his Calc. class that this was the last year Andover had any chance of doing good in the Quiz Bowl because of the new math program.  He then turns around and tells our class that the Math Core program is great and will prepare everyone for college.  Excuse my language but that was a bunch of  bull %$&#.  As you can see, I am a little bit sour about this whole thing.  As you will see if you haven’t found out yet, is that Andover screwed everyone who was forced to take the Math Core program, and is costing parents extra money on math tutors, classes that shouldn’t be needed (like MTH 1825 at State)…etc.  It also wastes students’ time.  I must go, but if you need anything else just ask.

 

Andover 132     3.25-3.75   ACT 21-23        MSU     Business

• The Core Plus program was a poor excuse of a math program.  Because of it, I am well behind all other students in Math at MSU, and have struggled to the point where I have now failed a math class.

Math placement exam?  Yes.  I was placed in algebra.

15a)  1

Content of an e-mail message sent in response to an e-mail query of mine.

      I seem to have misplaced the questionnaire that you sent.  You can send me another if you like, but I will tell you right now that I am going to tear the math class to pieces.  I am going to give it all the lowest marks     because it was the most ridiculous class, that made the majority worse math students than at other schools, and has been the primary factor behind the failure of many students in math thus far in college.

 

Andover 133     3.25-3.75   SAT M 600-700 V 300-400  ACT 18-20  MSU    Education

• Math has been my strong subject.  I could simply understand whatever I learned in math classes.  So I never spen[t] [a] long time studying for math, even before exams.

Math placement exam?  Yes.  The score was 18.  Placed into MTH 201, math investigation[s].

15a)  4

Andover 145     2.25-2.75     ACT 21-23    Michigan-Public   Pre-Professional

• I think the Core Plus program does not help especially when you get to college.

Math tutoring in college? Yes. Failing class, was not able to keep up with other students.

15a)  1

Andover 146     2.75-3.25;   ACT 21-23   Michigan-Public    Undecided

• Andover math left me totally unprepared for college math.

Math tutoring in college?  Yes.  Trouble with Intermediate Algebra.

15a)  1

Andover 148     3.25-3.75   SAT  M 700-800 V 500-600     UMAA   Undecided

• I didn’t really like the new [math] program we had in our high school.  It didn’t prepare me well for college calculus.

15a)  1.5

Andover 150     3.25-3.75;   SAT M 400-500 V 500-600   ACT 21-23      MSU     Business:

• I was not properly prepared for College Math from the Core Plus program.  I never completely   grasped the concept of Algebra in college because of a lack of experience in high school.

Math placement exam?   Yes. Placed into Algebra I.

Math tutoring in college?  Yes.  Algebra I – did not understand material..

15a)  2

Andover 152     3.25-3.75    MSU   Liberal Arts/Business

• I feel that the preparation I received in High School with Core Plus was hardly adequate enough for College Algebra.  I struggled with many basic mathematical principles that I should have mastered in High School.

Math tutoring in college?  Yes.  Algebra, because my High School Program was so weak and I was having a hard time with Algebra.

15a)  1

Andover 154     2.75-3.25     SAT M 400-500  V 500-600   ACT 21-23     MSU   Business

• The Core Plus system was horrible to my learning.  I don’t know one person who was happy    with it besides the teachers.

Math placement exam?  Yes.  I placed in College Algebra.

15a)   2

Andover 159     2.75-3.25     SAT M+V 900-1000   ACT  24-26        MSU    Pre-Professional:

• I sometimes regret that I hadn’t taken math very seriously over the past years.  I hear from my graduat[ing] class that Core Plus did not help in their college math courses.  I am planning to go      into the […] field so I am going to take math more seriously.

Summer School.  Algebra.  1996.

 

Andover 162     2.25-2.75       ACT 21-23     Michigan-Public     Social Science

Math tutoring in college?  Yes.  Math, because I was not adequately prepared.

15a)   1

Andover 163.   3.25-3.75;  SAT M 600-700 V 600-700;  ACT 27-29;  Michigan-Public;  Business

• Core Plus taught me math well; however, it did not teach me how to show my work.  Because of   that I failed college math.

Math placement exam? No.  ACT placement.

15a)  3

Andover 164     3.25-3.75   ACT 30-34       MSU       Science/Pre-Professional:

• Core Plus was useless.  It helped me very little for college level calculus.

Math tutoring in high school?  Yes.  Just 2 sessions prior to ACT.

Math placement exam?  Yes. Received a 36 out of 40.

15a)   2

Andover 168     2.25-2.75             Other

• I don’t think the Math was any good.  It’s like going to a restaurant and sampling every item from the buffet table and not having any main course.

Math tutoring in high school?  Yes.  Junior year.

 

Andover 178     3.75-4.00     ACT   24-26             UMAA         Social Science:

• My high school math program stunk.  Andover should be ashamed for hindering the futures of their students.!!

Math tutoring in college?  Yes.  This semester because I am not comfortable with my math ability.

15a) We’ll see!!

Andover 187     2.75-3.25     ACT 18-20      MSU     Pre-Professional

• The Core Plus math program is the worst thing I could have taken.  I learned nothing I needed to know for college !!!

Math placement exam?  I placed into the lowest, Math 1825 [Intermediate Algebra].  I scored a zero.

Math tutoring in college?  Yes.  Intermediate Algebra by my math teacher there.

15a)  1

Andover 189     3.25-375      ACT 24-26     MSU     Education

• The high school math program was good.  The problems arose because colleges haven’t restructured their math programs accordingly.

Math tutoring in high school?  Yes.  1996-97

Math placement exam?  Yes.  Scored below primary math course.  Had to take 1825 which is no credit     towards graduating.

15a) 3

Andover 190     3.25-3.75    ACT 27-29     Private      Science

• High school math was easier to apply to situations outside of the class.  College math [Respondent took College Algebra] has been completely abstract.

15a)   3

Andover 191     3.25-3.75     SAT M+V 1100-1200     UMAA        Business.

• I have never been so disappointed in a type of schooling such as this course.  I am the epitome of mathematical ignorance in a top ten [high] school with a 4.0 in math.

Math tutoring in high school?  Yes. 1996-97. Also audited Algebra classes at OCC, 1996-97.

Math placement exam?  Yes.    Pre-Calc.

Math tutoring in college?  Yes.  My Pre-Calc. Class has far surpassed my capabilities and under- standing in Math.

15a)  1

Andover 204   3.25-3.75      ACT  21-23     UMAA     Nursing

• The math program in high school did not sufficiently prepare me to continue in college level mathematics!

Math placement exam?  Pre-Calc – failed – 4%

15a)   3

Andover 205     2.75-3.25       ACT 18-20              MSU         Education

• I took Core Plus all through high school and it did not prepare me at all for college math.  I should have learned basic algebra in the 9th grade and because of this program, I    learned it this past year.  I know that many others also struggled in college math and ended up in low math classes because of Core Plus

Math tutoring in high school?   Yes.   1995-96.

Math placement exam?  Yes.  I was placed in Math 1825 or Intermediate Algebra.

Math tutoring in college?  Yes.   I received tutoring in College Algebra, because I had never learned     the material in high school.

15a)  1.5

. Andover 206  3.25-3.75         SAT M 500-600 V 500-600       UMAA    Social Science:

• I’m horrible at math and do not intend on taking any math courses in college.  However, I think it has much more to do with my interests and little to do with my high school math background.

Math placement exam?  Yes.  I fell into the 0 – 1 percentile (the last percentile).

15a)  N/A

Andover 207.   3.75-4.00;  SAT M 500-600 V 500-600;  ACT  27-29;  UMAA;   Science

Math placement exam?  Yes.  Placed into Precalculus.  Scored 1- %tile.

Math tutoring in college?   Yes.  Algebra, through the free tutoring through the University.  I didn’t   know algebra.

15a) 1.5

Andover 209     3.25-3.75     SAT  M 400-500 V 500-600     MSU    Pre-Professional

• My experience of math in high school was a waste of my time!  The only reason I did good [in College Algebra] at MSU was because I took math courses at OCC for audit.

Math tutoring in high school?  Yes.  1994-97.

Summer School   Algebra, 1996 and math at OCC, 1996, to get me ready for College Algebra at MSU.

Math placement exam?  Yes.  Do not remember the score, though I ended up guessing on a lot of the     questions.

Math tutoring in college?  Yes.  Math. (College Algebra), to improve my understanding of the course.

15a)  2  (only helped me by teaching me how to use the TI-82 Calculator)

Andover 213     2.75-3.25        ACT 18-20        MSU    Undecided

• I did not enjoy Math at Andover High School.  I feel it did not prepare me for College Math.

Math placement exam?   Yes.   3%/100%

15a)   N/A

Andover 220     225-2.75       ACT 18-20    Michigan-Public      Education

• I did not have much success in the Core Plus Math Program in High School. Since it wasn’t regular algebra or calculus, it was difficult.

Math placement exam?  Yes.  Beginner course. I will take [exam] over again (didn’t take the class).

 

Andover 224     3.25-3.75    SAT  M 600-700 V 600-700   UMAA   Liberal Arts

• Core Plus may be a good idea for non-college bound students – but almost 100% of Andover’s [graduating] classes go to college.  I feel like I was screwed over.

Summer School.  Algebra 1, summer before freshman year.

Math placement exam?  Yes.  Received < the 10th %tile; placed in 105 (pre-calc).

Math tutoring in college?  Yes.  Math – I had no idea what was going on.

15a)  1

Andover 228     3.25-3.75      ACT  21-23    Michigan-Public     Fine & Performing Arts

• My class (1997) was the first class to use Core-Plus, so the kinks were still being worked out.  However, I do not feel I can hold a conversation about math problems, using math vocabulary, due to the lack thereof using Core-Plus.

Math placement exam?  Yes.  Placed in entering freshman math (basic).

15a)  3

Andover 229  3.25-3.75; SAT M 500-600 V 700-800; ACT 27-29; Michigan-Public; Communications

• My Math teachers seemed to make math a chore, rather than a subject to be learned and studied.  I always ask “why” and “how”, and in math, those questions were never answered.  It was always “Just do it!”  That is a large part of why I do not take an interest in math.

Summer School?  Yes

15a)   1

 Remaining Andover Group I Students {non-accelerated (Core Plus)}

 

Andover 5    3.25-3.75   ACT 24-26    UMAA       Social Science

• Calculus at Michigan is not hard, but the TA’s that teach it make it hard.  Exams are extremely difficult.

Math placement exam?  Yes.  Placed in Calc. 115.

Math tutoring in college? Yes.  Instructor was a Teaching Assistant [and] was incapable of     teaching     material well.

15a)  5

Andover 102.    3.25-3.75;  ACT 21-23     MSU    Pre-Professional

Math tutoring in high school?  Yes.  1993-95

Math placement exam?  Not yet (I want to start from the lowest.)

 

Andover 109     3.25-3.75;   SAT  M 500-600 V 700-800     UMAA     Liberal Arts

 

Andover 182     2.75-3.25    MSU     Social Science

Math placement exam?  Yes.

15a)  1

Andover Group II Students {accelerated} who made comments about Core Plus[26]

 

Andover 37   2.75-3.25     ACT  27-29      UMAA    Liberal Arts

• The new math program has made math difficult for many college students.

15a)  3    b)   3

Andover 41.   3.25-3.75; SAT  M 600-700 V 500-600;   ACT 30-34;   UMAA   Pre-Professional

• I was [one of few] to ever take both Core Plus and “regular” math at Andover High School.  Thus making me a “guinea pig” in this heated debate.  I have a lot of good views on this so feel free to contact me.  PS  I saw the article in the News and I believe I can add to what was said.

Math tutoring in high school?  Yes.  Geometry 1993-94.  Pre-Calc 1995-96

Math placement exam?  Yes.  Placed into Calc. I.  I think I was the only Andover student who took a    Core-Plus class to place into Calc I (Math 115).

15a)  5    b)    N/A

Content of subsequent e-mail message.   My views about Core Plus are not necessarily negative but      I    think more constructive if anything.  There are some things about the program that are better than “traditional” and some that aren’t and vice versa.

          First, and I have thought this since the beginning, I don’t think that the high schools are in the      authoritative position to initiate a major change in the way that math is taught.  The biggest     argument when Core Plus (CP) first came aboard was that it wouldn’t complement what colleges      were teaching.  That proved right, and the educators who were firmly behind CP neglected to hear      out and respect the students’ and their parents’ worries.  An alternative route would have been to work in conjunction with universities and maybe have the universities change first and then the high    schools would follow.  I remember that I was told in the beginning that CP is the new wave of    mathematics and that it is the way everything will be in the future…including colleges.  Well, guess      what, I’m in college and there isn’t a CP program here, although some people    claim that “Harvard    Calculus” (Math 115-116 here) is a good fit with CP.  I will have to check this out further, but that   still leaves the schools that don’t feature reform calculus, and there are    many of those, including    many top schools.  

           I found that CP was interesting, much more interesting than “Hey, let’s do 1-99 odd and look in the back of the book for the answers”.  It explained the “How”s, “What”s, and “Why”s of the     math problems.  Though what it forgot to do is emphasize the mechanics of the problems.  The important steps were never really emphasized.  It seemed almost like they were steering away      from directly solving the problem.  Why beat around the bush?  I found myself a lot of times using     my past knowledge from traditional classes to solve CP problems.  Maybe that’s where I go wrong     but hey, a math program isn’t supposed to make the student make adjustments to it, it should be      flexible enough for anyone to respond to it.  Working in groups was often a bonus.  Though a lot more teamwork and feedback is produced during group work, it is also easy to have some members     trail off into no man’s land, and thus hindering the group’s performance, and their own.

          From the start of my CP class, I found the material quite insufficient. No practice problems,    examples, and insufficient explanations were all what I found as a problem with the thin color coded packets.  Sometimes you would have to rely on the explanation of your group but then would     have to question if the explanation was correct or not.  Thus, slowing down the learning process. 

          In conclusion, I want to be clear that I am not trying to insult the program.  I do think that     it could be a useful method in Mathematics if presented correctly.  I have a lot of respect for      my high school and for what they strive to do.  I believe that Andover is amongst the elite sec-ondary schools in the nation, and for that I am proud of it.  The faculty of Andover has always    striven for the best, though it seems as if they are selling themselves short with CP. 

 

Andover 50       2.75-3.25  SAT M 600-700 V 500-600   UMAA     Pre-Professional

• The traditional math courses in high school helped me tremendously in my college calculus course.  I cannot understand how someone without these basic skills can take a college level calculus course.  In high school I had many friends in the Core-Plus program and by senior year they could not even factor or do other basic mathematics which I learned in 8th grade!      And there were above 3.5 GPA students.  Personally, from experience and observation of my peers, I don’t think there is a way to get around learning basic math skills.  For example, when teaching a child to tell time one does not need to impart the interworkings of a clock.  The explanations of the “Why”s come much later. after the fundamentals are in place. 

     It seems to me that this whole Core-Plus movement is geared toward the “laziest” common denominator.  It discriminates against those who want to excel in math and take the time to learn/memorize the basics.  Where is the common sense in all of this?  It is non-existent.  Where else would you teach advanced concepts without the fundamentals?  In life you have to start out with a base and then move on to greater and more complicated things.

          Do you teach a child thermodynamics when teaching them not to touch a hot stove?  No.  You just teach them that the stove is hot, don’t touch.  2+2 is 4 and 8×7 is 56.  There’s no way to talk around   it.  One just needs to memorize it.  If one doesn’t have this base, how can one move on to greater    things like calculus.  In college-level courses one can explain why certain answers are arrived at, but at lower-level courses, explaining why 4+5 equals 9 is completely unnecessary!

          Some people don’t seem to realize how this new approach has sealed the fate on many students. They are so far behind that I doubt they will ever be able to make up for what has been lost.  I found the U of M placement test to be very basic.  Any student with the fundamentals of algebra and geometry should be able to either pass the test or at least get most of the problems correct.  However with many of my “Core-Plus friends,” this was not the case.  Some, even 3.9 students, received a near 10% score, if that, on their placement test.

          It seems quite obvious that many of the Bloomfield Hills Core-Plus students are ill-prepared for higher level learning.  Shame on the Bloomfield Hills School District.

Math placement exam?  Yes.  I was placed in Calculus 115.

15a)  5    b)  3

Andover 59    3.75-4.00    SAT M 700-800 V 700-800        UMAA    Liberal Arts

• I think the Core-Plus program stinks! It babysteps around the true concepts of math and instead kids learn a ‘watered-down” version which they can’t really use.  I feel very fortunate that I did not have to take Core-Plus classes.  If you would like to reach me for additional comments you may do so through e-mail […].  Thanks.

 

Andover 62.   3.25-3.75    SAT M 600-700 V 600-700;  Non-Michigan-Public;  Business

• 99% of my circle of friends were part of the new math program implemented by Andover.  My knowledge is that they are having an extremely difficult time with college math courses and their SAT math scores were very low.  I feel that Andover should return to the standard math curriculum and teaching of it.

Math tutoring in high school?  Yes. Calculus.  1996-97.

15a)  5    b)  1

Andover 113     3.25-3.75    SAT M 700-800 V 700-800;  ACT 30-34    UMAA    Engineering

• I found that taking High School Calculus helped a great deal when I took Calculus II.  I also found that I performed much better on standardized math exams than my peers who took Core Plus.

Math placement exam?   Yes.  Score = 80%.  Placed into Calculus II.

15a)  3    b)  5

Andover 116    2.75-3.25;  SAT M 600-700 V 700-800;  ACT 30-34   Other    Fine & Performing Arts:

• I enjoy math and enjoyed the classes I took, but because I am going to an Art School, I am not required to take Math courses.  In eighth grade, because ours was the first class to start the Math Core program in high school, we were given a choice.  If we got into the advanced class, Algebra 1, we would continue on in the original, classic Math program.  I had no interest in entering into a new experimental program, and so [I] worked extra hard to get into the Advanced Algebra 1 class.  Luckily, I made it.

15a)  1    b)  1

Andover 151     3.75-4.25;  SAT M 700-800 V 600-700   ACT 30-34  UMAA   Engineering

• I attended Andover during the transition from the traditional math program (which I took) to Core-Plus.  As a student at the UM College of Engineering, I firmly believe that Core-Plus does not adequately prepare students planning to enter any field that requires math (math, science, engineering, etc.).  Students [in Core Plus] depend too heavily on calculators, due to the fact that they have no knowledge of the fundamental aspects of algebra.  True, “Core-Plus” may tie math in with “real-world” situations, but problems in fields that require math are seldom “real-world” situations.  

Math placement exam?  Yes.  Placed into Calculus. [Took higher level course due to AP test score.]

15a)  5    b)   5

Andover 165  3.75-4.00; SAT M 600-700 V 700-800; ACT 30-34; UMAA; Science/ Pre-Med

• I feel like I was one of the lucky ones who escaped the horror of Core Plus.  I’m not a math person and luckily I was able to do well enough in high school to avoid as much [math] as possible in college; but if I was a math-oriented student and I had had a Core-Plus background, I’d be in BIG TROUBLE.

Math placement exam?   Scored in 80th percentile.  Placed into Calc 115.  (AP credit placed me out of      Calc 115/116, though)

15a)  5     b)   5  (I haven’t taken a math class yet, but I assume it would have helped.)

 

Andover 185     3.75-4.00;  SAT  M 700-800 V 700-800    ACT  30-34    UMAA    Undecided

• I really believe that having specialized math classes (i.e. geometry, calculus, algebra, etc.), rather than Core Plus classes, truly helped me in preparation for standardized tests.

15b) N/A

Andover 222       3.75-4.00        ACT 24-26      UMAA      Business

• My experiences have led me to believe that my high school math program prepared me for college and SAT/ACT much better than [the] Core Plus Program.

Math placement exam?   Placed in Math 115/116  [Calc I/II]

15a)   5   b)  5

Remaining Andover Group II Students

 

Andover 1    3.75-4.00; SAT M 600-700 V 700-800   ACT 30-34   UMAA   Science

Math placement exam?  Yes.  [Passed]

 

Andover 2   3.25-3.75     SAT  M 700-800 V 700-800   ACT 30-34   UMAA    Engineering

• Very good program [at Andover].  Calc. teacher taught at and involved with U of M, so he taught appropriate subjects and style for intended U of M students.

Math placement exam? Yes.  Calc 116.

15a) 5  b) 5

Andover 15       3.75-4.00    SAT  M 600-700 V 600-700        UMAA       Liberal Arts

• For the above two questions (#15) I was considering physics a “math course” since I have not taken any others in college.

Math placement exam?  Yes.  Placed into Math 115, which is Calc. I.

15a)  4  b) 4

Andover 26       3.75-4.00      SAT M 600-700 V 700-800      UMAA       Pre-Professional

Math placement exam?  Yes.  Placed into Calc I (115).

15a)  4  b) 2

Andover 28       3.75-4.00     SAT M 600-700 V 600-700      ACT  27-29     UMAA    Science

• I [was] definitely not impressed with the quality of grad. student instructors (GSI’s) at the U of M.  There was a communication barrier and I believe that the courses [Calc I&II] lacked a lot.

Math tutoring in high school?  Yes.  Calculus BC.   1997

Math placement exam?   Yes.  I placed into Calculus 116.  I opted to take Calc. 115 instead so I would     be more prepared.

15a)  3    b)  4

Andover 29        3.25-3.75      SAT  M 600-700 V 600-700     UMAA       Engineering

• My 2nd Semester Calculus course [Calc II] was identical; to my AP Calculus course [AB Calc.] in high school.

Math placement exam?  Yes.  [No score given.  Took Calc. II and Calc III]

15a)  3   b) 5

Andover 35       3.25-3.75      ACT 27-29    UMAA    Social Science

• Because of taking calculus (traditional) in high school and because of my teacher (Dr. Shelly), I was able to slide through Calc 115 – I barely studied while others failed – you were expected to teach yourself

Math placement exam?  Yes.  Placed into Calc. 115.  Don’t know scores.

15a)  5    b) 5

Andover 44       3.75-4.00        ACT 30-34    UMAA    Business

• Dr. Michael Shelly was an excellent Calculus teacher (Andover High School).  U of M need[s] more GSI’s that speak English.

Math placement exam?  Yes.  Score – ?;  Math 115.

15a)  3      b)  5

Andover 46    3.25-3.75;  SAT  M 600-700 V 600-700    ACT 27-29;    UMAA    Engineering

• The division of subdivisions within math helped my focus.  Furthermore, it helped me identify each subdivision in more complex math courses.

Math placement exam?   Yes.  Top 5%.

Math tutoring in college?  Yes.  Math 116, problems with integrals.

15a)  5     b)  5

Andover 48       3.25-3.75        ACT 27-29         UMAA    Science

Math tutoring in high school? Yes.   Algebra.  1995

Math placement exam?  Yes.  Placed into Calc. 115, but because of AP’s, I went into 116.

15a)   5    b)  5

Andover 58       3.25-3.75;    SAT M 600-700 V 600-700    UMAA    Business

• I was able to get by in High School courses with severely limited knowledge and still pull a “B”.

Math tutoring in high school?  Pre-Calc.  Junior year.

Math placement exam?  Yes.  Placed in low level course. [Took Stat. 100].

15a)  2    b)   1

Andover 61       3.75-4.00       ACT 30-34         UMAA          Pre-Professional

Math placement exam?  Yes.  I placed into Math 115 or Calc. I.  [Took Calc. II.}

15a)  3   b)  5

Andover 85       3.75-4.00;  SAT M 700-800 V 600-700; ACT 30-34;  Private;   Science

Math placement exam?  Yes.  Calc.I/II Placement Test: Calc. II

15a)  3   b)  5

Andover 88       2.75-3.25     SAT M 700-800 V 700-800       Other

 

Andover 96       3.25-3.75    SAT M 600-700 V 600-700   ACT  27-29   UMAA    Science

• The U of M Math department is terrible.

Math placement exam?  Yes.  Placed into Calc. 115.  The highest possible placement without AP credit.

15a) 3    b) 3

.Andover 103    3.75-4.00;  SAT M 600-700 V 700-800     ACT 30-34    UMAA   Liberal Arts

• Calculus BC was the most exciting and interesting course in high school.  Although I think I would do well, I don’t plan on taking any math courses in college.

Math placement exam?   Yes.  I placed out of Calc. I and II.

15a) N/A     b) N/A

Andover 104.    3.75-4.00    ACT 30-34       Private     Business

• My high school math teachers were wonderful.  I learned more from them than I did from my college professor.  Dr. Shelly was able to successfully explain concepts of calculus and make it interesting at the same time.

15a) 5    b) 5

Andover 117     3.75-4.00; SAT M 700-800 V 600-700;   ACT 30-34   Private   Social Science

• I placed out of the calculus courses that a majority of my college peers took freshman year.

Math placement exam?  AP tests served as placement.

15a)  N/A   b)  N/A

Andover 119     2.75-3.25     ACT 24-26       Private-regional      Engineering

Math placement exam?  Yes.  Scores were not revealed but I was suggested to take Pre-Calc.

15a)  3   b)  3

Andover 127     3.75-4.00     SAT M 700-800 V 500-600   ACT 27-29    UMAA    Science

Math placement exam?  Yes.  Calculus placement.

15a) 4    b) 5

Andover 138     3.75-4.00  SAT M 600-700 V 600-700    ACT 27-29    UMAA    Business

• My math experience in high school was satisfactory; I was very fortunate to have had good teachers.  As for college, I enjoyed Math 115 [Calc. I] because the teacher was very thorough, but I disliked Math 116 [Calc. II] because the teacher was very disorganized and didn’t seem to enjoy teaching.  Teachers (rather than the curriculum) play such a crucial role in my math education.  I would like to add, though, that I had no complaints about the traditional math program.

Math placement exam?  Yes.  Score 88%.  Placed into Calc. I.

15a)  4   b)  5

Andover 140     3.25-3.75     SAT M+V 1100-1200    ACT 27-29   Other    Fine & Performing Arts

• We had 3 levels of Math achievement.  I was placed in the accelerated class and could never keep up!

Math tutoring in high school?  Yes.

Summer School?  Algebra.

Math tutoring in college?  I will attend U of M in the Fall and will need a math tutor.

15a) 3.5    b)  3.5

Andover 156     3.75-4.00    SAT  M 600-700 V 700-800        UMAA       Social Science

• [A complimentary remark, by comparison with other teachers, about Miss Cathy King.]

Math placement exam?  Yes.  I was placed in 115.  .

Math tutoring in college?  Yes.  Calc.  To prove that I was at least making an effort at trying to perform better on the exams.

15a)  2.5   b)   1

Andover 158     3.75-4.0     SAT M 700-800 V 600-700   ACT 30-34    UMAA     Science

• I had 3 excellent years of traditional high school math and one fair year of […].  I was very well equipped to handle college math, which was perhaps easier than that taken during high school.

Math placement exam?  Yes. [Doesn’t give score. Placed in Multivariable Calculus because of AP    score.]

15a) 5    b) 5

Andover 161     3.25-3.75     SAT M 700-800 V 700-800    ACT  30-34    Private    Science

• College math classes (including calculus) and high school math, I believe, are entire[ly] different endeavors.  Although high school math should be the basis and is necessary for further education in higher math, it does not necessarily help in college math (taking into account only the curriculum).

15a) 1  b) 4

Andover 166   3.25-3.75;  SAT M 600-700 V 500-600;  ACT 24-26;  Private;  Social Science

• Math has always been one of my favorite subjects and I’ve enjoyed it throughout high school and college.

15a)  5   b)  5

Andover 176     3.25-3.75      SAT M 600-700 V 500-600    UMAA    Science

• I was lucky enough in high school to have pretty good math courses with good teachers.  These math classes prepared me for college math classes because I had a stable math background coming into college.

Math placement exam?  Yes.  Placed into Math 115.

15a)  4    b)  4

Andover 179    3.75-4.00       SAT M 70-800 V 700-800         Private        unsure

15a)  4    b) 5

Andover 181    3.25-3.75     SAT M 700-800 V 500-600     ACT 27-29    Private-regional

Social Science

• I found the math courses prior to Calculus AB fairly easy.

15a)  3    b)  4

Andover 183     3.25-3.75    SAT M 700-800 V 500-600    ACT 24-26    UMAA   Business

• I was forced to memorize math concepts in High School and it wasn’t valuable to my learning.  College math [Calc. I] has taught me to learn and apply ideas.  More beneficial.

Math tutoring in high school?  Yes.  Geometry.  1994.

Math placement exam?  Yes.  I placed into Calc. 115

15a)  4   b)  4

Andover 198   3.25-3.75; SAT M 600-700 V 500-600   ACT 27-29   Non-Michigan-Public    Science

 

Andover 219     3.75-4.00; SAT M 700-800 V 500-600; ACT 27-29;   UMAA;   Pre-Professional or      Education

Math placement exam?  Yes.  94th %tile

15b) N/A

Andover 221     3.25-3.75     SAT M 600-700 V 600-700   ACT 27-29    UMAA   Liberal Arts

 

Andover 232     3.25-3.75; SAT M 700-800 V 700-800; ACT 30-34;  UMAA    Social Science

• Calculus class [was] very good at Andover.  Michigan math program is embarrassing.  It is the worst thing I have ever been a part of.  The math base [in Calc II] was ignored and short cuts were taught.  The program is horrendous.

Math placement exam? Yes.  Basic Algebra.  90th percentile?

Math tutoring in college?  Yes.  Calc. 116.  From GSI to get better grade.

15a)  4  b) 5

Lahser Group I Students {non-accelerated}

 

Lahser 10  325-3.75;  SAT M 600-700 V 600-700;  ACT 27-29;  Private-regional; Science/Engineering.

Math Placement Exam?  Placed in Calc. I

15a)  4

Lahser 11     3.25-3.75     ACT 21-23      MSU       Liberal Arts

• I dislike math.  I feel as if I will never use any of it in life later on.  When will I ever use Descartes’ Rule?

Math tutoring in college? Yes.  Math 1825 and 103, very bad in math.

15a)  3

.Lahser 34    2.75-3.25     ACT 21-23    Other       Nursing.

Math Placement Exam?  Yes.  Normal level for my grade.

15a) 4

Lahser 38. 3.25-3.75; SAT M 500-600 V 600-700; ACT 24-26; Non-Michigan-Public; Communications

• I lacked basic knowledge of Calculus or Trig. [Respondent took neither in H.S.]

15a)  4

Lahser 46.    3.25-3.75;  SAT M 600-700  V 600-700;  ACT 24-26   UMAA   Social Science/Business

• The Math. Dept. at U of M doesn’t know how to teach.  It is all applied non-memorized tests. [Respondent took Calc 1.]  The stuff in high school is so easy and basic – you do problems that   are all the same.  In college it is taking a deeper understanding of that simple problem and using    it in combination with others for something complex.

Math Placement Exam?  Yes. I was placed in pre-calc. (105).

Math tutoring in college?  Yes.  Math Lab – for homework question help.

15a)  2

Lahser 54   3.25-3.75;   SAT M 500-600 V 500-600    ACT 24-26   UMAA    Pre-Professional

• I thought my high school prepared me well for all of my non-math classes at U. of  M.; however, the math classes at U of M are supposed to be very hard, and I have heard people did not feel prepared for the math classes at U. of M.

Math Placement Exam?  Yes.  Placed into Math 105, which is equivalent to pre-calc.

15a) 3

Lahser 64   2.25-2.75;  SAT M 500-600 V 400-500; ACT 21-23;   Michigan-Public;  Business

• I feel that I had a good math experience in high school, but I think the math placement test      given by [my University] was poor and did not place me correctly into the math class I should     have been in. [Respondent evidently felt placement was too high, judging by grade received.]

Math Placement Exam?  Yes. I was placed into finite math.                                                                15a)  4

Lahser 68.  2.75-3.25; SAT M 600-700 V 600-700;  ACT 21-23;  Michigan-Public;  Undecided

Math tutoring in high school?  Yes.  Alg. II  1995-96.

Math Placement Exam?  Yes.  College Algebra.

15a)  3

Lahser 96     3.25-3.75     SAT M 600-700  V 500-600     ACT 24-26    UMAA   Social Science

• High school math course needs to teach students how to solve and get right answer.  Not just getting the answer. [Respondent took Calc I].

Math Placement Exam?  Yes.  Placed in Math 115 [Calc. I].  Passed exam with 95%.

15a) 4

Lahser  117       3.25-3.75     ACT 21-23    Michigan-Public     Nursing

• Although I placed into only Intermediate Algebra in College,  I found the class to be very easy and not challenging at all.  I am sure I would have done fine in regular College Algebra, but instead I have to take it this year.

Math placement exam?  Yes.  Placed into Intermediate Algebra.

15a)  5

Lahser 136        2.75-3.25      Michigan-Public      Education

• I hate, hate, hate math!  I think that some Math courses are pointless and will never be used.

Math tutoring in high school?  Yes.  Algebra.  1993-94.

15a)  N/A

Lahser  141       3.4    ACT 21-23    UMAA      Design

• It was really hard for me to understand some things in Math, but when you get a great teacher that will take the time to help me, I can finally understand.

Math tutoring in high school?  Yes.  Algebra 2.  Sophomore year.

 

Lahser 148        3.25-3.75       ACT 27-29                    MSU             Business

15a) 3

Lahser 154    3.25-3.75     SAT M 500-600 V 600-700   ACT 24-26    MSU  Fine & Performing Arts

Math Placement Exam? Yes. I was placed into Math 103 [College Algebra], the lowest credit math   course.

15a)  3

Lahser 170     3.25-3.75        ACT  24-26       UMAA      Education

• I just had a hard time in Pre-Calc. but had a very easy time in Algebra II.  I think it was the teaching style.

Math Placement Exam?  Placed into 105 or 115.

Math tutoring in college?  Yes.  I went in for math help from my teacher during Math Lab and office   hours.

15a)  4

Lahser 175  3.75-4.00     SAT M 600-600  V 500-600      ACT 24-26     Private    Science

Math tutoring in college?   Yes.  Calc 140 – At [my college] there are 3 levels of calculus.  I had the requirements for the middle level; however, due to the extreme demands of the upper level (whose   requirements were one year of calculus) the majority of those students dropped down a level into    my section.  My professor then stopped teaching to the level of the students (like myself who the      class was intended for) and taught only to the students that had already learned the material.      Therefore the original students (approx. 20) worked with the math intern assigned to our class. (Of   the 20 of us, 13 changed our class grade to pass/fail because we had no idea what was going on.      [Respondent passed.])   I have now just finished a summer class at OCC and have learned what I     was supposed to      have [learned] last year.

15a)   1

Lahser 195  2.25-2.75       ACT 18-20      Michigan-Public    Engineering

Math tutoring in high school?  Yes.  Algebra 1.  Freshman year.

Math tutoring in college?  Yes.  Math 110, tutoring to get help pass class.

15a)  4

Lahser 198  2.75-3.25    SAT M 500-600 V 500-600    Private     Business/ Design

• Minimal math – didn’t prepare me well – need to catch up in college.  [Respondent took only Algebra 1 and Geometry in H.S.]

15a)  2

Lahser 206      [not given]      ACT 24-26      Other          Fine and Performing Arts.

• I am an art major – no math in college.

 

Lahser 212        3.25-3.75         Non-Michigan-Public       Fine & Performing Arts

• It was fun.

Math Placement Exam?   Yes.  Basic Math.

15a)  4

Lahser 219   3.25-3.75; SAT M 500-600 V 700-800 ; ACT 27-29; MSU  Communications/Business

• I think there is still a sex bias in which men are driven into the areas of math and science here and encouraged to more than girls.

Math tutoring in high school?    Algebra I  1992 (8th grade).  Pre-Calc. 1997.

Math Placement Exam?  Yes.  I received an 11/20 – Placed in Math 110.[College Algebra and Finite     Math.]

15a)   4

.Lahser 222        2.75-3.25      ACT  18-20      Private-regional          Education

15a)  3

Lahser 230  2.25-2.75   SAT M 500-600 V 500-600   Michigan-Public   Nursing

• It was overall pretty good; I know that I’m bad at math, so my grades reflected the fact that I didn’t try too hard.  I need to put in extra time for those classes.

Math tutoring in high school?  Yes. Spring, 1997, Pre-Calc.  Fall, 1997, College Algebra

Math placement exam?  Yes. I was placed in Intermediate Math

Math tutoring in college?  Yes.  College Algebra, because I was doing poorly in the class and I wanted   to improve my grade.

15a)   5

Lahser 233     3.25-3.75  SAT M +V 1100-1200   ACT 24-26    UMAA     Science

Math placement exam?  Yes..  Math 105 (Pre-Calc). [Took Stat 100.]

15a)   3

Lahser 241    3.75-4.00     ACT 24-26     Michigan-Public   Science and Liberal Arts

15a)  5

Lahser 250   2.25-2.75; SAT M 300-400 V 600-700; ACT  18-20;  Non-Michigan-Public;       Liberal Arts

• I am a horrible math student (I have had trouble all throughout schooling.), but  in high school I was in advanced English.

Math tutoring in high school?  Algebra I, 1994.  Geometry, 1997.

Math Placement Exam?  Yes.  It was 30 questions.  I failed.

15a)  1

Lahser Group II Students {accelerated, no calculus}

 

Lahser  14    2.25-2.75       Other

 

Lahser 17     3.25-3.75       ACT  24-26                 MSU                  Business

• I believe that by taking AP Statistics senior year I scored poorly on the math placement test in college, because I had not used general algebra for quite some time, but once I took algebra in college [Math 103: College Algebra], it was very easy.

Math placement exam?   Raw Score: 10. Eligible to enroll in Math 103, 110, 116 or 120.

15a)   5

 

Lahser 20.    2.75-3.25;  SAT M 600-700 V 700-800    Non-Michigan-Public;  Communications

• High school math departments need to encourage, not discourage, girls to succeed and continue their mathematic[al] careers.

15a)  4

Lahser 60     3.75-4.00   SAT M 600-700 V 600-700  ACT 30-34    UMAA    Business

Math placement exam?  Yes.   I scored in the 60th percentile and was placed in Calculus.

15a)  4

Lahser 62     3.75-4.00    SAT M 600-700 V 500-600      ACT 24-26       UMAA    Science

• The tests in college (at least at U of M) are MUCH harder than high school tests  [Respondent took Calc I&II],  which test only the concepts in a way already studied.  College tests test the application of the concepts through story problems, ones different from any already in the text.

Math tutoring in high school?  Yes.  Algebra II, 1994-95.  Pre-Calculus, 1995-96.

Math placement exam? Yes.  Placed into Calculus I.

15a)  4

Lahser 74     3.75.-4.00   SAT M+V 1100-1200;   ACT 27-29;   Michigan-Public     Business

• Math was definitely not my favorite class in high school.  However, I have really enjoyed the math courses I took in college.  I like math a lot more now.

Math placement exam?   Yes.  I don’t remember my score, but it was not high enough to place into   Calculus.

Math tutoring in college? Yes. Attended Supplemental Instruction right after class, for group study and    review.

15a)  4

Lahser 87   2.75-3.25    SAT M 600-700 V 400-500    ACT 21-23      MSU   Engineering

15a)  3

Lahser 92     3.75-4.00  SAT M 600-700 V 700-80     ACT 30-34    UMAA    Liberal Arts

Math Placement Exam?  Yes.  Placed into Pre-Calculus.

 

Lahser 101  2.75-3.25   SAT M 500-600 V 500-600    ACT 24-26      MSU       Science

• College TA’s have been more detrimental to my learning than helpful.  Most of my work has been on my own.  High School math was completely unhelpful.

Math Placement Exam?  Yes.  [Score not given.  Took Intro. College Algebra and College Algebra.]

15a)  2

Lahser 108   2.75-3.25;  SAT M 600-700 V 60-700;  Private-regional  Social Science/Business

• High school math teachers (at Lahser) were far better than those at [my college].

15a)   5

Lahser 127   3.25-3.75   SAT M 500-600 V 500-600     UMAA    Science/Liberal  Arts

• In high school I learned in math more from the teachers than in college.  However, I overall learned more in college because of tutoring.  I think that the math program at U of    M needs improvement.  I along with many others did not learn anything without help from others.

Math tutoring in high school?  Yes. Pre-Calc.  Junior Year.

Math placement exam? Yes.  Pre-Calc.

Math tutoring in college?  Yes.  Pre-Calc., because they don’t know how to teach math at all.

15a)  2

Lahser 142        3.25-3.75     SAT M 600-700 V 700-800  ACT  30-34   Other;  Liberal Arts

• I didn’t do well in pre-calc. Because, well, I didn’t really like it.  So I didn’t do my homework. (Isn’t that terrible?)  That’s why my grades went down.

 

Lahser 178   2.75-3.25       ACT  24-26       Non-Michigan-Public   Liberal Arts

15a)  3

Lahser 186        2.75-3.25    ACT 21-23      Michigan-Public      Science/Education

• Math classes taught do not always apply back to life; because of that it is hard to learn what can’t be applied.

15a)  3

Lahser 243     2.0-2.25            Michigan-Public          Engineering

• Teachers who are enthusiastic about their subject get a better response.

15a)  4

Lahser Group III Students {accelerated, with calculus}

 

Lahser 2       3.75-4.00; SAT M 700-800 V 700-800;   ACT 30-34;  Private;  Science

• Calc. BC gives excellent preparation for Multivariable Calc., other applications.  I think it is very reasonable to cover Algebra II/Trig/Pre-Calc. in three semesters instead of the traditional four, leaving room to introduce Multivariable Calc. in Senior Year, if desired.

Math placement exam?   Yes.  Credit received for Probability and Statistics. Score around 130/200.

15a) 5   b) 5

Lahser 18     3.75-4.00   SAT M 700-800 V 500-600   ACT 27-29     UMAA     Science

Math placement exam?  Yes.  Placed in the 97% percentile or out of Calc. 116 [Calc. II].

15a)  N/A   b) N/A

Lahser 30     3.75-4.00      ACT  30-34        MSU             Engineering

• I think there are gap[s] between High School and College Math level[s].

15a)   1   b)  3

Lahser 32   3.25-3.75   SAT M 600-700 V 600-700   ACT 27-29    UMAA   Science/Pre-Professional

Math placement exam?  Yes.  Score of 99th percentile.

15a)  5  b)  4

Lahser 71     3.25-3.75   SAT M 600-700 V 500-600   ACT 24-26    UMAA      Science

• Math in high school was very easy and did not go very in depth.  In college we covered a broad variety of topics and went into greater detail.  Teaching in college math courses are [read “is”] very poor.

Math placement exam?   I scored in the top 20% of students and was placed into Calc. II because of the    high score and AP test score.

15a)  3   b)  5

Lahser 77.   3.75-4.00      SAT M 700-800 V 600-700      Private;     Science/Liberal Arts

• Math is based on rules whereas some other subjects (e.g. English) are based on connotations; therefore, math needs to be taught (at least in the beginning) in a format stressing rules rather than interconnections, which may be interesting, but are confusing to the beginner. 

Math placement exam? Yes.  More a test of ability than for placement.

15a)  5   b)  5

Lahser 83     3.25-3.75     SAT M 600-700 V 600-700      MSU      Engineering

Math tutoring in college?  Yes.  Help from my T.A.

15a)  4  b)  5

Lahser  95      3.75-4.00    SAT M 600-700 V 700-800    Private    Science

15a)  N/A  b) 5 (I received 2 semester’s credit for Calculus.)

Lahser  106     3.75-4.00    SAT M 700-800 V 600-700   ACT 30-34   UMAA  Engineering

15a)  2   b) 4

Lahser 118     2.75-3.25; SAT M 600-700 V [not given];  ACT 21-23;   Michigan-Public;  Business

Math placement exam?  Yes.  Placed into Algebra 2.

15a)  3   b)  1

Lahser 120      2.25-2.75     SAT M 600-700 V 500-600   ACT 27-29    MSU     Business

• Math was much harder in High School than college.

Math placement exam?  Yes.  I placed into the highest math, Calc. 132

15a)  5  b)  5

Lahser 139     2.75-3.25    SAT M 700-800 V 500-600   ACT 27-29    UMAA    Business

Math placement exam?  Yes.  Placed into Calc. 116.

15a)  3   b)  5

Lahser 153      3.25-3.75   ACT 24-26       MSU     Business

15a)  2   b)  4

Lahser 161     3.25-3.75    SAT M+V 1200-1300   ACT 21-23   UMAA     Undeclared

15a)  4  b)  4

Lahser 162    3.75-4.00;  SAT M 600-700 V 700-800; ACT 30-34;  Non-Michigan-Public;  Education

Math placement exam?  Yes.  Placed into Statistics.

15a)  2   b)  1

Lahser 165     3.25-3.75;  SAT M 700-800 V 700-800   Non-Michigan-Public;  Science and Fine &   Performing Arts

• I feel that I learned almost all of my high school math during Freshman and Sophomore years.      [I did not mesh with my advanced math teacher’s ] teaching style, which was more concerned with “Did you get the right answer?” than “Do you know the method to get the right answer?”.

15a)  5   b)  2

Lahser 172.   3.75-4.00; SAT M 700-800 V 700-800; ACT 30-34; UMAA;  Science, Liberal   Arts, Engineering

• I wish we had learned Abstract Algebra in High School, because it is the basis for many substantial theoretical math courses in college (for math majors).

15a)  2   b)  3

Lahser 174     3.25-3.75   ACT 30-34   Non-Michigan-Public  Pre-Professional/Business

15a)  4   b)  4

Lahser 181    3.25-3.75;  SAT M + V 1200-1300; ACT 27-29; UMAA;  Social Science/Science

Lahser 182      325-3.75;  SAT M 600-700 V 600-700  ACT 27-29; Non-Michigan-Public      Science

15a)  4   b)  5

Lahser 185      3.75-4.00    ACT 27-29    Michigan-Public     Science

Math placement exam?   Yes.  Placed in Calc. I

15a)  5   b)  5

Lahser 191     3.75-4.00   ACT 27-29     UMAA    Science

I hate numbers and formulas.  I only like people.  T. Koehler was my teacher Senior year.  Per his absence most of the year, I was not able to expand and strengthen my already feeble math skills Math placement exam?  Yes.  If you can’t tell, I hate math and have a very bad memory.  I don’t keep track of scores either.  I almost passed into Calc, but not quite per placement exam. [Took Calc. I]

15a)  1   b)  1

Lahser 201     3.75-4.00    SAT M 700-800 V 700-800    UMAA   Social Science

• Math 115 [Calc. I] at U of M  SUCKS.  My graduate student instructor hardly spoke English and                        never properly prepared us for exams.

Math tutoring in high school?  Yes.  Geometry Honors,  1993-94.  Calculus AB, 1996-97.

Math placement exam?  Yes.  Placed into 185 Calculus but only took 115 Calculus

15a)   3   b)   3

Lahser 202     3.25-3.75     SAT M 600-700 V 600-700   ACT  27-29     MSU     Engineering

• My school district has changed [its] math program (doesn’t offer Algebra 1 in BHMS) [the middle school that feeds both high schools], and I’m very displeased since I don’t think kids will be as well prepared for math classes at college.  I know of kids that came from Andover High School who had a change in their math program, and those kids are having a hard time at college math.  I also know of kids who came from other areas that required taking 2 math classes for 1 year (usually geometry and algebra), or that took Algebra 1 sooner than the rest, and I think that’s a great idea.  Personally, I think teachers should concentrate more on math than they do, and try to help everyone to excel at it, (although this is hard to do).  Maybe having more math teachers available from grade school on?

15a)  3  b)  5

Lahser 207.   3.75-4.00; SAT M 700-800 V 700-800;  ACT 30-34;  Private;  Engineering

• High School math did not prepare me for the rigor of college math.  […]

15a)  3   b)  4

Lahser 209     3.75-4.00;  SAT M 700-800 V 700-800   ACT 30-34   UMAA    Social Science

• Pre-Calculus and Calculus were a good foundation.  The entrance exam as well as  the AP exam was approachable because of the good math foundation I had Junior and Senior year, largely due to the teacher’s capabilities.

Math placement exam?  Yes.  Placed out of Calc. 1 & 2.

15a)  4   b)  4  (I didn’t take a specific math course, but I did take courses for which I had to recall and apply high school math.)

 

Lahser 220    3.25-3.75;   SAT M 700-800 V 500-600   ACT 27-29   UMAA   Engineering

• I had some great teachers.  Mr. Dobosinski and Mr. Koehler.  They helped me a   great deal, although to be truthful, math has always [been] quite easy for me.

Math placement exam?  I got 97, give or take 3%.

15a)  3   b)  5

Lahser 236      3.75-4.00    SAT M 600-700 V 700-800   ACT 30-34    UMAA   Liberal Arts

Math placement exam?  Yes.  Calc. II.

15a)  N/A  b)  2

Lahser 242     3.25-3.75    SAT M 600-700 V 500-600   ACT 24-26    MSU      Business

15a)  3   b)  3

Lahser 245     3.75-4.00     SAT M 700-800 V 700-800   ACT 30-34;   Private    Science

• My AP Calc. BC and AP Statistics courses were very well taught and have really   prepared me!

Math placement exam?  No.  The AP’s were our placement tests.

15a)  4   b)  4

Lahser 252.  2.75-3.25; SAT M 600-700 V 500-600;  ACT 21-23;   Non-Michigan-Public; Business

• I’ve always been good at math.  I like math.  To me it just makes sense, and that is exactly why Finance will be my major.

Math placement exam?  Yes. I placed right below Calculus.

15a)  5   b)  3 (so far)

. Lahser 254     3.25-3.75     SAT M 500-600 V 700-800   ACT 30-34    UMAA   Undecided

• Calculus at UM really was not a good experience. [Took Calc. I] Syllabus and method need revamping.

Math placement exam?  Yes.  Placed into Calc. 115.

15a)  5   b)   5

Lahser 255    3.25-3.75   SAT M 700-800 V 600-700   ACT 30-34    Private    Science

 

* This is the original report, as issued in November 1998.  An update will appear shortly. (G.B.  11/15/99)

©  1998, Gregory F. Bachelis

[1] Address: Department of Mathematics, Wayne State University, Detroit, MI 48202

Telephone: 313-577-3178; e-mail: greg@math.wayne.edu

[2] The American Mathematical Society and the Mathematical Association of America

[3] Another designation would be Trigonometry and Topics in Advanced Algebra.

[4] AP = Advanced Placement.  Students taking these courses can then take AP exams, which, depending on their scores, entitles them to place out of college courses.  There are two levels of AP Calculus courses, AB and BC.

[5] There is also “Reform Calculus” at the college (or high school) level, such as “Harvard Calculus”.  However, it cannot be described as “Integrated,” since it strives to cover fewer topics than traditional calculus.

[6] This is from a letter from Harold Schoen to me concerning the difference between pilot and field-testing.   The entire letter is in Appendix A.I.

[7] This is from excerpts of an e-mail message sent by Marcia Weinhold; the excerpts can be found in Appendix A.II.

[8] WBSD is adjacent to BHSD and contains the greater part of West Bloomfield Township, plus the cities of Orchard Lake Village and Keego Harbor.

[9] BHSD did a survey of Andover parents’ opinions about Core-Plus.  See Appendix B.

[10] “Harvard Calculus” is a product of the Consortium based at Harvard.  There are several versions.  The one used at UMAA is Calculus, Single Variable 2nd ed., by Hughes-Hallett, Gleason et al.  There is a pre-calculus sibling, also used at UMAA: Functions Modeling Change: A Preparation for Calculus, by Connally, Hughes-Hallett et al. The publisher is J. Wiley & Sons.

[11]  Course descriptions for some lower division math courses at UMAA and MSU can be found in Appendix D.

[12] I don’t think that “Harvard Calculus” is  “Core-Plus goes to College,” as some would have you believe.  For one thing, the former doesn’t integrate a lot of topics, and there is some pencil and paper algebra.  The two do have some things in common, such as extensive use of graphing calculators, cooperative learning and “real world” problems.

[13] Of course other factors enter into advanced placement, but it is safe to assume that the accelerated students were, on average, better in math than those who weren’t.

[14] Detroit News, 1/27/97

[15] Birmingham Bloomfield Eccentric, 6/12/97

[16] In retrospect, I should have asked a question about how well they felt their high school math courses prepared them for college science courses, since this is a non-trivial issue as well.

[17]  The Curriculum and Evaluation Standards of the National Council of Teachers of Mathematics.  They are currently under revision.

[18] Recall that “accelerated” refers to people taking Algebra I (or Core 1 in subsequent years at Andover) before the ninth grade.

[19] See Appendix A.I

[20] Since Social Science is considered part of Liberal Arts, when someone gives two majors, one in the former and one in the latter but not the former, they are reported simply as Liberal Arts.

[21] The Comments in Context are reported in a separate section following this one.

[22] See e.g. the comments in Andover 40, 42, 83, 107, 148, 5, 35, 138, 232; Lahser 46, 96, 62, 127.

[23] I don’t think that injecting algebra drill is a viable solution to what I consider to be the problems with Core-Plus, in part because of the vast differences in approach of Core and the traditional method.

[24] Please note:  I have included all responses.  Even those which had no comments.  The first line contains GPA, SAT, ACT,

college, and college major information.  If comments were given in response to item 16, then they start on the second line, preceded by a “bullet” and written in boldface.  Successive items are labeled.   Other comments may be highlighted in italics or boldface.

[25] See also Appendix A.II.

[26] See also Lahser 202.

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Reform Mathematics Education
How to “Succeed” Without Really Trying

by Paul Clopton
Cofounder, Mathematically Correct

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Since the 1980’s, there have been substantial efforts nation wide to weaken mathematics education in America, and these efforts have largely been successful. This is not a communist conspiracy [Note 1]. It flows from an honest desire to help the less fortunate. This effort is based on the misguided notion that weaker mathematics will be helpful to the traditionally disadvantaged groups in our society. It is this effort, curiously known as reform, that is the root cause of what has come to be known as the math wars.

You won’t find many reformers who will openly admit that they favor “dumbed-down” mathematics. In fact, the reform movement is characterized by a plethora of rhetoric to the contrary. The diatribes are extensive and frequent and are laden with phrases like “higher order thinking” and “conceptual understanding” and “real-world problems” while shy on terms like “arithmetic” and “algebra.” Reformers have learned their scripts well, and the rhetoric comes gushing forth with little provocation.

The conditions that prompted this movement are obvious. Poor people, minorities, and women are under-represented among those who reach high levels of mathematical achievement. Those who cannot master arithmetic and algebra are unlikely to achieve a decent college education. There is no question that the educational system in this country is not successful for a great many students.

One way to deal with this problem is to make the mathematics easier. This means less rigor, less emphasis on arithmetic and algebra, more reading and art and creative projects, less emphasis on correct answers, more calculators, and a host of other reform-minded solutions. Stylish pedagogical methods combined with rhetoric about higher order thinking while downplaying or condemning outright both computation skills and mathematical proof complete the package. This is reform mathematics education.

Sometimes dubbed traditional or anti-reform, the second perspective has come in abreaction to the first and is mainly supported by parents and mathematicians. This perspective holds out that the mathematics must not be “dumbed-down.” The key in this perspective is to increase achievement rather than to decrease expectations. Central to this position is that the traditionally less fortunate are not well-served by weaker mathematics and, in fact, should be insulted by it. The real key to success is real mathematics achievement, and every effort should be made to foster this achievement.

Ironically, the struggle to promote real mathematics education is left up to those outside of the field – mostly parents. The perspective is traditional in the sense that it seeks to prevent learning expectations from being further eroded away by putative reform efforts. Mathematics education in America has not been very successful. However, do not look for relief in the reform notions. We would be better off if all the energy behind the reform was redirected toward clearly defined achievement goals and we measured progress toward those goals frequently and objectively.

Obliterating Distinctions between Success and Failure

The reform designs open the door to claims of successfully teaching mathematics without really doing so. The reform writings and methods are many and varied, but a common feature is that they end up obscuring the failure to teach mathematics. In reform mathematics education, the goal of success for all is not supported by achievement but rather by redefining success and, mostly, by obscuring failure. Here are but a few examples:

Group Learning and Group Tests – The story of Apollo 13 is used to promote group learning and group assessments with the argument that our students must learn to work together like people do in the real world. Never mind that people in the real world don’t sit in groups doing algebra problems. Group learning is plagued by inequities that most parents identify quickly – some do the work while others learn that they can “succeed” without learning the material and without effort. Group assessments effectively erase the ability to monitor individual achievement or to provide useful diagnostic information. Whether or not individuals are learning is obscured by these methods.

Calculators – Many argue that routine skills are out of date, and that technology has changed the mathematics that today’s students need to know. The position includes multiplication and division, obviously. However, today’s calculators can manipulate fractions and solve equations as well. Distancing students from these activities takes away the learning experiences that help form the foundation of mathematical understanding. By far, most American parents want their children to be able to solve problems without calculators. The reliance on calculators allows reformers to claim success even when children do not learn the fundamental operations of arithmetic. Soon they will claim success in algebra for students who have not learned how to solve equations.  Authentic Assessment – One of the greatest evils from the reform perspective is objective testing. It would have to be because these measures can identify failure. Many arguments are advanced for this perspective, but addressing them in detail is beyond the scope of this report [Note 2]. The proposed alternative is frequently called authentic assessment. Translating this bit of jargon into English isn’t easy. Basically, it refers to a variety of procedures that involve less mathematics, more writing or talking, and very subjective evaluation. In the worst instances, students suffer if they do not support the intended politically correct perspective in their response. But, politics aside, these methods are reliably unreliable. The subjective nature leaves little opportunity for valid information to be obtained. Sometimes, one cannot even tell who actually did the work. In the long run, many invalid assessments tend to average out (false equity) and, again, real differences in achievement go undetected.

Measuring Content With the educational bureaucracy in this country prone to jump on the bandwagon of pedagogical fads, assuring that children receive a decent education becomes the responsibility of their parents. Effective parenting now includes keeping a watchful eye on what happens in school and what the children are and are not learning. When deficiencies are found, parents can try to change the schools, to increase learning experiences at home, or to find outside resources to provide the needed learning experiences. The entire process of monitoring and remedying this situation is very demanding. The first stage of this process, examining the content of the school program, can be a little easier for parents who make use of existing resources that identify content by grade level. Coming on the heels of failed reform efforts in California, expectations for achievement that are roughly in line with those of the most successful countries of the world were developed. These documents identify achievement levels in terms that are sufficiently clear for parents to evaluate. Parents are encouraged to measure the school programs against these contents as a way of finding out whether or not important content is being covered. The California Mathematics Standards The San Diego Mathematics Standards The NCITE-LA Achievement Test Items Number Sense in California With the aid of these materials, parents can more easily find what is present and what is absent in the programs used in local schools. These documents enable parents to match local content to grade levels according to high-level standards.

Projects – The reform programs are loaded with projects and activities, often called investigations. Part of the argument for these methods relates to stimulating student interest. There are also claims of richer mathematics and the importance of context. Even a casual inspection of these activities will show that they tend to be very time consuming while involving very little mathematics. Time for mathematics, both in class and at home, is seriously limited and must be used as efficiently as possible. These activities are inefficient learning methods. But, beyond that limitation, they promote the evaluation of students on the basis of non-mathematical dimensions such as how artistic the display is or the writing style of the report or the social value of the application.

Standards – The reform movement claims to be based on standards, although most parents will be surprised by what they find – and what they don’t find – in reform standards documents. It is contrary to the goal of the reform to produce explicit statements about what students know and should be able to do – again, spotting failure would be too easy. Consequently, the reform movement produces standards that are so vague that one cannot tell whether they have been met or not. Any attempt to write tests for these standards, for example, will be unreliable because the required content is unclear. Reformers hate lists of clearly stated objectives and call them laundry lists. However, vague learning expectations are effectively the same as no learning expectations at all. Again, it becomes impossible to differentiate success from failure.

Strands – When attempts are made to subdivide mathematics into content areas, such as algebra and geometry, the subdivisions are often called strands. The reform movement uses this technique while simultaneously avoiding explicit content. Thus, all of the elementary school work with arithmetic falls into one strand which becomes just one of many topic areas students are supposed to address. The consequence is that students can still succeed while failing in arithmetic. The same thinking reduces algebra to just one component of mathematics in later grades with similar consequences.

Pedagogical Fads – The reform movement places great emphasis on classroom methods, such as those that involve groups, calculators, activities and projects, manipulatives, explorations, art work, and non-mathematical themes. Irrespective of any relationship between these methods and learning (or lack thereof), there are consequences of the fact that the emphasis on these styles is pervasive in reform documents. Even reformers bemoan the fact their followers often carry out reform by adding a few new gimmicks to their bag of classroom tricks. The heavy emphasis on style quite naturally takes attention away from mathematical content. As teachers attend to implementing these processes, their evaluations of students become biased toward process and away from content. Mathematical learning will often take a back seat to artistic ability, cooperation, or even political correctness again blurring the distinctions between success and failure when it comes to learning mathematics.

With the demise of our ability to differentiate success from failure, the reform movement will claim broad successes. School systems in America have the uncanny ability to claim improvements and reforms year after year while the content is gradually leeched out of the system. Meanwhile, fewer students will suffer wounds to their self-esteem because their failures will go undetected. Such a system will identify fewer failures among poor and minority group students, so reformers will claim a victory for equity.

Unfortunately, success in this approach will have lost its value. The claims of success operate like social promotion as applied to education bureaucrats. We may gain some “equity” at the cost of achievement, but the more advantaged parents will continue to find ways to make sure that their children learn in spite the best efforts of the reform-minded. Meanwhile, the net effect of the reform will be further deterioration in the mathematical abilities of America’s youth. The majority of these students will not find alternative forms of education to make up this deficit. It is from this majority that we will draw our next generation of teachers.

 

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Note 1: Although not a communist conspiracy, there is some justification for the belief that some sort of conspiracy is at work. The reform designs are heavily promoted by the National Council of Teachers of Mathematics (NCTM). In turn, the educational branch of the National Science Foundation (NSF) then funds the development of curriculum materials that align with the NCTM dictates. The products of these efforts are then advertised by the U. S. Department of Education, while the NSF pushes for their adoption by states and districts.

Note 2: The interested reader should see Chapter 6, “Test Evasion,” in The Schools We Need and Why We Don’t Have Them by E. D. Hirsch, Jr., Doubleday, New York, 1996.

Mathematically Correct

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Recent Directions in San Diego Mathematics Education

by Paul Clopto

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Background

State textbook adoptions are made on the basis of frameworks. The last mathematics adoption by the state was made under the guidelines of the 1992 Mathematics Framework. This was from a time before the state had mathematics standards at all. This framework had little or no emphasis on mathematical content and instead stressed an extreme version of discovery learning based on a radical constructivist view of learning. Textbooks were judged on their adherence to the pedagogical ideas of the framework. Not surprisingly, the textbooks adopted by the state under this framework were awful. The 1992 framework and the direction we were headed lead directly to the birth ofMathematically Correct.

It was clear that the state was lacking in direction relative to the content of mathematics education. A new California Mathematics Framework was drafted at the same time that the new California Mathematics Standards were developed.

Following the state adoption of the standards, it became evident that schools lacked the materials they needed to allow students to learn the required content. If nothing had been done, money to buy new textbooks aligned with the new framework wouldn’t have been available for years. To correct this problem, AB2519 authorized $1 Billion in a special, one time allocation, split over several years, so that schools could buy new materials to meet the standards. Textbooks aligned with the standards and authorized for purchase with AB2519 funds were selected by the state for use in grades K-8, as is the custom in California for textbook adoptions. Because the state standards now describe algebra as a grade 8 course, algebra I textbooks are, for the first time, subject to the state textbook approval process.

The Past

Members of Mathematically Correct served on the San Diego Math Standards Committee for many months. The committee produced high level Mathematics Standards that were unanimously approved by the Board. The “math wars” issues were actually resolved and everyone was in agreement about the direction to take.

District adoption committees for mathematics were ongoing at this time. These were run by administrators, but the members included teachers and parents. The recommendations of the committees were passed on to the board which ruled in public on the recommendation. This is the typical adoption method in use throughout the state. Those committees recently began to make reasonable decisions. Prior committees had not, and the evidence suggests that this was caused by administrators, not by teachers.

Then, the new Superintendent came in and the Standards were ignored. The district lost funding for the USI grant for lack of attention to mathematics and science, which was the truth.

Next, a draft document circulated around the district math advisory panel. It indicated that Mr. Alvarado had decided that the textbooks approved by the state under AB2519 were not going to be used in San Diego. Instead, the district would seek alternative funding to get around the state guidelines.

When questioned a little too publicly, the draft document was quickly changed to wording that was more vague on this point to obscure the truth.

While the state and district standards continued to be ignored in San Diego, the Blueprint was drafted by the district. Following this the so-called San Diego Math Framework was developed. These documents together are essentially worthless as they provide no direction. The standards and frameworks provided by the state are vastly superior. Nonetheless, these local documents are important to the administrators as they can claim that there actions are aligned with policy (it is hard to find actions not aligned with these policy statements), and continue as if their ideas are already approved.

The Present

Indeed, the district has now adopted textbooks for the lowest achieving schools that are not approved by the state, and HAS done so without a public hearing, without public involvement, and with no board action.

District administrators stressed Everyday Mathematics in their “informational” presentation to the board. They noted that this program was approved by the state. However, it was approved only under the 1992 framework, not as part of AB2519. In fact, the 1995 edition was approved under the old framework. The district wants to buy the 1999 edition. The publishers applied for approval of the 1999 edition under AB2519, but the review committee found the material to be inadequate. The curriculum commission and the state Department of Education worked together to inform the publisher of the changes that would be required to be considered adequate for AB2519. The publisher withdrew from the adoption process, never making the changes needed.

So, we know that this program is not aligned with the state standards. This fact has not been disclosed by the district to the board. The board members were mislead by the administrators.

However, it is quite likely that the Everyday Math program highlighted by the administrators is actually the best of the programs they adopted without a board vote. When districts in Texas were looking at textbooks for adoption, we did a review of several programs. Since the standards in Texas were not as high (or as clear) as ours were, we used the San Diego standards as the benchmarks for our evaluations. We gave Everyday Mathematics grades of C and C- in our review. We also happened to review one of the other programs in the new San Diego list, Connected Mathematics. The program received an F rating. It is simply awful. It is completely and totally unrealistic to think that this program comes anywhere close to meeting either the state or the district math standards.

It is obvious that the district is planning to used dumbed-down mathematics in the focus schools. They are taking the approach we have fought so hard to avoid – lowing expectations while claiming otherwise.

The Future

In March, April, May, and June, we are likely to see evaluations made by the district of the success of their methods. They will issue glowing reports of their accomplishments in the focus schools. At this point, they will try to use their own evaluations to press for more dumbed-down mathematics in non-focus schools in San Diego. When the truth comes out with the state test results next summer, it will be too late.

Mathematically Correct is not in the business of endorsing political candidates. A rare exception has been made in the support of Frances O’Neill Zimmerman for her support of mathematics education in San Diego. Regarding this problem, she has said:

 

… the Board of Education … now has a 3:2 rubber stamp majority voting yes for anything that is proposed. At present, I am one of two members looking skeptically at a weak proposal for a new math framework which has been severely criticized as empty by mathematicians from Stanford and Berkeley…

The 3:2 rubber stamp majority allowed the district administrators prescribe watered-down math for the children in San Diego’s focus schools without so much as a vote or a hearing. Until this situation changes, there is little hope for any real improvement.

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Cal State Northridge   1999 Conference on Standards-Based K-12 Education California State University Northridge Transcript of R. James Milgram (edited by the speaker) Biography
.		Return to conference page Return to transcript of Norman Herr   Mr. Milgram: I would like to start by again thanking David Klein and Cal State Northridge for arranging and organizing this wonderful opportunity to get together and compare ideas on the incredibly challenging times ahead of us.  Professor Wu brought up a number of critical points in his discussion and one of them that he mentioned — that this is a long term challenge — is particularly important. I’d like to fill in somewhat what the problem is here. First of all, “long term” has generally been understood to be in the order of perhaps three years, and there seem to be real expectations of being able to meet the standards in that time frame.  But this is very unrealistic! A realistic long term is maybe 15 years. If we are lucky, in 15 years the average student may get near the standards if everything goes just right. In a shorter time than that, it is almost inconceivable to believe that this will happen. California today ranks just about at the bottom in the United States, in terms of the level of mathematical achievements of students in K-12. The United States ranks near the bottom among all the developed countries in the world in terms of math achievements of students. We have an incredibly long way to go because you have to remember that the new California Mathematics Standards were written to match the levels of the standards of the top achieving countries in the world. Meeting these standards is a daunting challenge and we had better take it seriously. We now look at the reasons we clearly needed new standards in mathematics.  They can be subsumed in three main areas. REASONS FOR NEW STANDARDS The increasing failure of the present system to produce enough technically skilled graduates to meet national needs  Curricular problems which leave more and more students without the prerequisites needed for their majors, particularly in technical areas  Lack of a clear understanding – on the part of teachers and math educators – of the major goals of the mathematics component of K-12 education   The next three slides explain a little bit about how we see some of this so we cannot escape from these issues.  The facts quoted in these slides come from recent newspaper articles for the most part. INDICATIONS OF FAILURES From 1990 to 1996 there has been a 5% decline in high-tech degrees — engineering, math, physics, computer science — in this country and the trend is continuing.  Of the decreasing number of high-tech degrees awarded a significant and growing proportion go to foreign nationals.  At the doctorate level 45% of high-tech degrees were granted to non-U.S. Citizens   From 1990-96, there’s been a 5% decline in high-tech degrees overall in this country. And the trend is continuing — in fact, the trend is accelerating.  Even though the number of high-tech degrees is decreasing, it is vital to note that an ever increasing portion go to foreign nationals. At the doctorate level, for example, 45% of high-tech degrees are granted to non-U.S. Citizens and at Stanford, in the mathematics department, two thirds  of our graduate students are foreign-born. Even 10 years ago, less than half were. As a result of this situation it has been impossible to fill all our technical jobs with United States citizens.  This is particularly true in Silicon Valley.  To find qualified people to fill these positions Congress was intensely lobbied by Silicon Valley, and Congress was forced, much against their will, to provide 142,500 more visas for foreign nationals to fill jobs in Silicon Valley. Currently it is estimated that the number of foreign-born residents of Silicon Valley is about 25% of the population. Among all the states as I said in the beginning, California colleges showed the greatest decline in high tech degrees. INDICATIONS OF FAILURES – II Last year Congress was forced to provide 142,500 more visas for foreign nationals with high-tech skills  Currently it is estimated that the number of foreign born residents of Silicon Valley is about 25% of the population  Among all states, California’s colleges showed the greatest decline in high-tech degrees awarded.   So the first point is that the system today is simply failing to produce enough technically qualified graduates to meet national needs. The foremost problems and most dramatic declines are here in California. Curricular problems are overwhelming here and leave more and more students without prerequisites needed for developing and learning technical skills in college. When they come to us, even at Stanford, more and more of them are just not able to become engineers and scientists, even though this is their original intent. They just don’t have the background any more. It is a dramatic change. Finally, and sadly, because I have the utmost respect, and I think we all do, for the practicing teachers, the level of understanding on the part of teachers and above all of math educators — that is members of the educational schools throughout the country — that is required for teaching mathematics in K-12 is just not there any more. Look at the effect of this lack of understanding on our students. INDICATIONS OF FAILURES – III The percentage of entering students in the California State University System who are place into remedial mathematics courses after taking the ELM placement exam is about 88%  Overall, well over 50% of entering students are placed into remedial mathematics courses.  The average level of the questions on the recent version of the ELM is about grade level 6.9 according to the new California Standards.   This 88% is a statistic that astounded me. And it is correct, differing from the failure rates commonly reported (which are bad enough). The percentage of entering students in the California State system who are placed into remedial mathematics courses after taking the ELM placement exam is 88%.  Let me emphasize this: 88% of those students taking the exam fail it. Some of you may know a statistic of about 55% for the failure rate.   Unfortunately, this is calculated by counting the 40% of the entering students who are not required to take the exam as having passed it. These 40% are counted as passing it probably so the statistic will look reasonable.  I reiterate that the actual statistic is 88% taking the ELM fail it, and it is not that hard an exam overall.  In any case, well over 50% of entering students in the California State University system are placed into remedial math courses. Those are some of the reasons for our current problems. They stare at us. We can’t avoid or deny them. Now, I would like to give you an idea of the real complexity of the problem and the consequent difficulty with trying to fix it. On our first slide the second problem with mathematics that I indicated is the lack of understanding of curricular development on the part of math educators. Curricular development is a very complicated issue.  As an illustration, I’m going to look at one topic, long division, now. Long division is something that a lot of professional math educators want to take out of curriculum. So let’s just look at why it is in the curriculum.   CURRICULAR PROBLEMS The recent fashion of not teaching material like long division and factoring polynomials is based on claims that such skills are no longer useful.  This reflects a deep lack of understanding of the role of mathematics in fields like science, engineering and economics.  In mathematics many skills must be developed for many years before they can be used effectively or before applications become available.   First of all, I claim that taking — even asking to take it out of the curriculum — shows a profound ignorance of the subject of mathematics. The point is, in mathematics, many, many skills develop over an extended period of time and are not really fully exploited until perhaps 10, 12, or even 15 years after they’ve been introduced.  Some skills begin to develop in the first or second grade and they do not come to fruition or see their major applications until maybe the second year of college. This happens a lot in mathematics and long division is one of the key examples. SOME SKILLS DIRECTLY ASSOCIATED WITH LONG DIVISION Students cannot understand why rational numbers are either terminating or (ultimately) repeating decimals without understanding long division.  Long division is essential in learning to manipulate and factor polynomials.  Polynomial manipulation and factoring are skills critical in calculus and linear algebra: partial fractions and canonical forms.   So just to start, understanding that decimals represent rational numbers if and only if they are terminating or ultimately repeating — a skill that was requested be put into the standards by math educators — cannot be understood without long division.  It is only in understanding of the process of taking the remainder in long division that you see the periodicity or termination happen. I regard the repeating decimal standard as relatively minor, but some people seem to think it is important. The next topic is critical and almost everyone thinks it’s minor (Laughter). Long division is essential to learning to manipulate polynomials. Without it, you simply cannot factor polynomials. So what, you ask?  Again, this is a question that doesn’t come up until the third year in college.  At this point the skills that have come from long division through handling polynomials become essential to things like partial fraction decomposition which is important in calculus but finds its main applications in the study of systems of linear differential equations, particularly in using Laplace transforms, which is the critical construction in control theory.  It is also essential in linear algebra for understanding eigenvalues, eigenvectors, and ultimately, all of canonical form theory — the chief underpinning of optimization and design in engineering, economics, and other areas. The previous slide indicated  what I call the static applications of long division. The next slide illustrates  some of the “dynamic” applications.   DYNAMIC SKILLS ASSOCIATED TO LONG DIVISION The process of long division is one of successive approximation, with the accuracy of the answer increasing by an order of magnitude at each step.  The skills associated with this process become more and more fundamental as students advance.  They include all infinite convergence processes, hence all of calculus, as well as much of statistics and probability, to say nothing of differential equations.  Long division is the main application of the previously learned skills of approximation.   Long division is the only process in the K – 12 mathematics curriculum in which approximation is really essential. The process of long division is a process of repeatedly approximating and improving your estimates by an order of magnitude at each step. There is no other point in K – 12 mathematics where estimation comes in as clearly and precisely as this. But notice that long division is also a continuous process of approximation, the answer keeps getting more and more accurate and when the students learn how to do long division with decimals they learn to carry the process to many decimal places.  This leads naturally — in a well conceived curriculum — to students understanding continuous processes, and ultimately even continuous functions and power series. The development of these skills are all contingent on a reasonable development of long division.  I don’t know of any other or any better preparation for them. What happens when you take long division out of the curriculum? Unfortunately, from personal and recent experience at Stanford, I can tell you exactly what happens. What I’m referring to here is the experience of my students in a differential equations class in the fall of 1998.  The students in that course were the last students at Stanford taught using the Harvard calculus. And I had a very difficult time teaching them the usual content of the differential equations course because they could not handle basic polynomial manipulations.   Consequently, it was impossible for us to get to the depth needed in both the subjects of Laplace transforms and eigenvalue methods required and expected by the engineering school. But what made things worse was that the students knew full well what had happened to them and why, and in a sense they were desperate. They were off schedule in 4th and 3rd years, taking differential equations because they were having severe difficulties in their engineering courses. It was a disaster.  Moreover, it was very difficult for them to fill in the gaps in their knowledge.  It seems to take a considerable amount of time for the requisite skills to develop.   APPLICATION OF THE SKILLS ASSOCIATED TO LONG DIVISION The combination of these skills is used critically in economics, engineering and the basic sciences via Laplace transforms and Fourier Series.  Without a thorough grounding in these topics it is impossible to do more than routine work in most areas of engineering, the most active current areas of economics and generally, any area involving optimization.   So you see the problem. The problem is that the scope of things in mathematics is so long that an ordinary second, third, fourth grade teacher is not equipped to make a judgment about whether a subject is needed or not needed.     SCOPE IN THE MATHEMATICS CURRICULUM The long division story illustrates one of the chief problems with curricular development in mathematics. The period needed before a learned skill can be fully utilized can be as long as eight to ten years.  It takes real knowledge of mathematics as well as how it is applied to make judgements regarding curricular content.   I think the long division problem illustrates the problem described on the slide above very well. And I put that dragon up there advisedly.   EDUCATORS TELL US OF THE NEED FOR CONCEPTUAL UNDERSTANDING AND MATH REASONING SKILLS IN OUR STUDENTS These skills ARE critical in todays technological society.  What many math educators tell us represent examples and exercises for developing these skills are NOT relevant and/or NOT correct.   The first slide mentioned a third aspect of the problem, which was the lack of knowledge of the subject on the part of math educators. To make it clear, I’m talking about math educators and not teachers. Teachers learn what they are told in the education schools and just hope that this background prepares them sufficiently.  They do the best they can and have the most demanding job that I know of.  As a group I believe they are the most dedicated people I know of. But if you do not provide teachers with the proper tools, they can’t do a proper job.   MATH EDUCATORS OFTEN HAVE LIMITED KNOWLEDGE OF MATHEMATICS For example, three of the 14 problems originally proposed by the presidential commission on the eighth grade national mathematics text and/or the “solutions” they gave were INCORRECT. This commission included many of the best known math education experts in the country.  The next slides discuss one of these problems.   I just want to spend a few minutes, now, looking at some of the problems that we have seen in the last few years when we — as professional mathematicians — have looked at some of the things that math educators are trying to tell the world is mathematics.  I will concentrate on problems that these people suggest for testing mathematical knowledge.   A PROBLEM FROM THE NATIONAL EIGHTH GRADE EXAM   We are given the following pattern of dots: At each step more dots are added than were added at the last step. How many dots are there at the twentieth step?   This is a problem from the original proposed 8th grade national exam, produced by a presidential commission including most of the best known math educators in the country.  The problem appears to be simple and every person I’ve asked, who I haven’t warned to think hard and carefully about it, has answered immediately, “Oh, it’s of the form n times n plus 1, so you are looking at the 20th stage, therefore the answer is 20 times 21.” But that’s not right. The words need to be read carefully. The point is, the words tell you the only thing you are actually given — namely, that there are more dots added at each stage than the previous stage. That’s all you are given, and the picture is just a picture.   ANALYSIS OF THE PROBLEM The answer given by the Presidential Commission on the National Eighth Grade Exam was 20 X 21 = 420 This is incorrect! The correct answer is that any number of dots is possible as long as there are at least 267.  As was pointed out, the Presidential Commission that proposed this problem included many of the best known math educators in the country.       ANALYSIS OF THE PROBLEM – II This can be seen by considering that you must add at least seven dots to get to the fourth stage, eight to get to the fifth, nine to get to the sixth, and so on, but, of course, you can always add more.  So the formula for the number of dots at the nth stage with n>2 becomes: any number at least as big as 6+(6+7+8+…+(n+3)) which equals any number at least as big as (n+3)(n+4)/2 – 9 = 267   Hmm?  Actually that problem was about as complicated as any problem I’ve seen at this level, and it was proposed for the 8th grade national exam! When you read it carefully, it is a problem a 12th grade senior would have trouble solving. So what is the moral here? If you want to learn mathematics, you must learn it precisely. Mathematics is precision and one of the first objectives in teaching K – 12 mathematics is for students to learn precise habits of thought. The next slide presents a problem that Wu is very fond of (Laughter).  It can be found in many sources, but in particular it was included as part of the original Mathematics Standards Commission’s proposed California Mathematics Standards.   A PROBLEM FROM THE ORIGINAL STANDARDS COMMISSION STANDARDS   You have a friend in another third grade class and want to determine which of your classrooms is bigger. How do you do it? This problem is often proposed as an example which shows that “there is no single correct answer” since you could use perimeter or volume or area to measure size. Of course, this is incorrect!   The trouble is that bigger is not precisely defined. And if every term is not precisely defined, your problem is not well posed. So technically this is not a well-posed problem. Of course, we realize that is a little technical.  We have an idea that bigger has certain connotations — but unfortunately, a lot of them: perimeter, area, volume, and maybe even combinations of the three such as 3A + 2.4P + 7V.   ANALYSIS OF THE COMMISSION PROBLEM   The difficulty here is that bigger is not precisely defined, and to do mathematics you generally have to know exactly what each term means. However, mathematics does provide for the situation where terms can have different meanings. There is still a single “correct” answer. It consists of the set of all answers. But since bigger can mean anything, the set of answers is uncountably infinite, and this problem is totally inappropriate for any but the most advanced high school students.   You see, when you put in a linear combination of the three, you get an uncountable number of possible definitions of bigger. That’s all right. Mathematics allows for this, as long as you can make some sense of the problem.  Mathematics says the correct answer to the problem is all possible answers to the problem (Laughter). If you are going to take that problem at face value, you have to give me an uncountable number of answers.   MORE DETAIL ON SOLUTIONS   Here is an example which illustrates the point that the “answer” is a collection of “all solutions”. Consider the system of two equations in three unknowns: 2x + y + z = 1 x + 2y + z = 0 A solution is x = 1, y = 0, z = -1. The answer is x = 1 + y z = -1 – 3y     So, what is the point? One of the most important things, as I indicated, that students should learn in doing mathematics is precise habits of thought. Suppose we start with a “real world problem”, given, as is typical for such problems, very imprecisely.  We want students to be able to break the problem apart into smaller problems, make sense of them, and solve them or recognize that it is not possible to solve them with the information given.  One of the first things that mathematics should prepare student for is making the best possible (rational) decisions when faced with real problems.   SUMMARY – I   One of the most important things that students should learn from studying mathematics is precise thinking. They should understand how to recognize when a problem is well-posed. They should be able to decompose a possibly ill-posed problem into pieces which can be made well-posed, and solve the individual sub-problems.   Now, I don’t for a minute want to minimize the fact that students have to learn basic number skills, certainly they have to do that too. And they have to learn things like statistics, I mean, this is critical in our world today, and it is a wonderful thing that it is commonly taught today.  It helps prepare students to defend themselves from tricky claims and fake uses of statistics.  Students also have to learn how to survive in the monetary world. So a key part of our request for changes  when the State Board of Education asked some of us at Stanford to help revise the California Math Standards was that compound interest be put back into the 7th grade standards.   SUMMARY – II   They should also learn the basic mathematical skills needed to survive in today’s society. These include basic number-sense They also include skills needed to defend themselves from sharp practices, such as being able to determine the real costs of borrowing on credit cards. Additionally, they include being able to recognize illegitimate uses of statistics.   I think everybody has the idea now. I have many more problems here, all of which are incorrect and all of which are due to some of the top math educators in the country. But I think you all get the idea of what the level is here and what we are trying to deal with, so I think we can skip most of them.  But there is one more example that is  worth noting (Laughter).   A PROBLEM FROM THE NEW NCTM STANDARDS   The following is proposed as a Kindergarten problem: How big is 100? This suffers from exactly the same difficulty. I asked one of our best graduating seniors this problem (he has a fellowship to study in Germany for next year and the year afterwards will continue his graduate work at Harvard).   This is from the current new proposed version of the NCTM standards. “How big is 100?” It suffers from every one of the flaws I mentioned before. But I loved the response from the student above. A PROBLEM FROM THE NEW NCTM STANDARDS II   Without even a moment’s hesitation he answered: Oh, about as big as 100! Indeed, any other answer would involve elements of perception and psychology, not mathematics.   Okay. I think probably I’ll finish up now and say again that it’s a long process ahead. It is a serious, serious thing we are trying to do. But I think it is something that we can do. It’s just something we cannot treat lightly and cannot treat in any way as a casual enterprise.  For example if you hear someone say something to the effect that “Oh, we’re going to give the teachers the Standards. We are going to say, now teach — and it’s over — no problem,” be very suspicious. IMPLEMENTING THE MATH STANDARDS   Problems California students rank at or near the bottom among all the states in average mathematics competency Generally teachers in grades K-4 have little competence in mathematics above their grade levels Expectations We cannot solve these problems all at once Time is needed, and skills and competencies should be introduced gradually. The new California Math Framework shows the most important skills that must be learned first.     It is a huge process — of re-education on everyone’s part, it is a process we all have to contribute to and work on with full attention. But I think there are grounds to hope that we can actually do it. And the one thing that has the potential to help with this process is the Framework.  The Framework is something that Wu and I worked on with Janet and the Curriculum Commission, and with many of the best people in many aspects of education throughout the country.  The Framework has been designed to ease our way into the teaching to the Standards. It’s something that I think we have to focus on a lot more in the next few months as we try to figure out how to reach the levels needed. I would like to just say one word about one of the ways in which the new Framework can help. IMPLEMENTING THE STANDARDS   In first grade there are only five emphasis topics in the Framework out of 30 total topics: Count, read and write whole numbers to 100 Compare and order whole numbers to 100 using symbols for less than, greater than or equal to Know the addition facts and corresponding subtraction facts (sums to 20) and commit to memory Show the meaning of addition and subtraction Explain ways to get the next element in a repeating pattern     The critical thing about this is that the Standards for first grade have about 30 basic topics. Well, those topics are, for the most part, quite difficult at the first grade level and will take a great deal of time and effort to teach properly. Fortunately, it turns out that only 5 or so of them are essential. The Framework identifies the essential standards and makes your jobs as teachers and your jobs as curriculum developers much easier because the textbooks in the next textbook adoption will be focused on the emphasized topics, rather than the entire 30 topics in the Standards. So this will allow us to focus on just a few pieces and make your job of reaching the levels needed a little simpler. I think this is where I’ll stop (Applause).
.		Contact the organizers Postal and telephone information: 1999 Conference on Standards-Based K12 Education College of Science and Mathematics California State University Northridge 18111 Nordhoff St. Northridge CA 91330-8235 Telephone: (Dr. Klein: 818-677-7792) FAX: 818-677-3634 (Attn: David Klein) email: david.klein@csun.edu clipart: http://www.clipartconnection.com/, http://web2.airmail.net/patcote1/partydan.gif

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Bloomfield parents fight for old math

They say new method hurts kids

January 19, 1998

BY TRACY VAN MOORLEHEM
Free Press Education Writer

Controversy over a new math curriculum that emphasizes problem-solving over memorizing theorems and functions is growing exponentially in the Bloomfield Hills School District.

Parents say they’ve listened to teachers, speakers and administrators, and they’re more determined than ever to bring back traditional math.

“I think I’m like a lot of parents that moved to the Bloomfield Hills district and thought, ‘Now I don’t have to worry about my child’s education.’ I think I’ve been living with my head in the sand,” said Mark Schwartz, an electrical engineer whose three children attend Bloomfield Hills schools.

But school board members and administrators say parents need to open their minds to new ideas instead of jumping to conclusions.

“We’re dealing with middle and elementary parents who have anxiety about this high school program. There’s some fear of the unknown, some misinformation,” board President Mindy Nathan said last week.

Frustrated by an inability to engage the school board in discussions about the math program, called Core-Plus, Schwartz is helping to organize a group called Parents for Excellence in Math Education to figure out how to turn up the heat.

“This is an unproven system,” he said. “They are making experiments on our children — something no one, in any other profession, would be allowed to do.”

Critics of this style of math call it “math-lite,” saying it is a watered-down version of algebra, geometry and trigonometry that kids will like. They say the reliance on graphing calculators, the de-emphasis on the teacher as lecturer and the emphasis on teamwork are anti-intellectual.

Supporters say Core-Plus is actually more challenging than traditional math because students can’t just memorize theorems; they have to put math to work.

Though concerned Bloomfield Hills parents have doubts about Core-Plus, most say they aren’t asking to eliminate it; they just want the opportunity to opt out.

The desire for choice is exacerbated by the fact that one of the district’s high schools, Lahser, still offers a traditional track of algebra, geometry and calculus in addition to Core-Plus.

“We’re not anti-Core-Plus. We’re pro-choice,” said Ellen Poglits of West Bloomfield. “If the west side of the district has a choice over math programs, we don’t understand why we don’t have the choice on the east side.”

Until this year, Andover High School students were allowed to transfer to Lahser if they wanted traditional math. Now, with enrollments skewed at the high schools for other reasons, the district ended the practice.

Lynne Portnoy is one of about a dozen parents circulating petitions asking the board to offer a dual track at Andover, as well as at all three middle schools. They say the board has refused to discuss the request with them until some unspecified later date.

“I have a fifth-grader. I don’t know what program is going to be better for him when he gets to high school. What I want is the choice,” Portnoy said.

To punctuate her concerns, Portnoy points to students like Jamie Chioini, a Lahser sophomore who transferred from Andover last year after deciding that Core-Plus had left her deficient in simple computational skills.

“I became so dependent on the calculator that I forgot how to calculate simple fractions,” she told the school board Tuesday. “What are Core-Plus students going to do when they take math in college? They can’t start over like I did.”

The Bloomfield Hills and West Bloomfield school boards held a joint public meeting about math reform in October, mostly because of growing concerns over Core-Plus. Both offer the program, which was developed at Western Michigan University and is in its fifth year of testing throughout the country.

Since then, West Bloomfield’s board has held its own follow-up meeting to discuss the issue with parents, then formed a math committee to look at ways to adjust Core-Plus to assuage parents’ concerns.

West Bloomfield schools Communications Director Steve Wasco said controversy mostly dissipated as parents saw that their concerns were being addressed.

Bloomfield Hills parents say their board could learn from the approach.

“It’s almost as if they look at the parents and say, ‘We know what’s best for you,’ ” Portnoy said.

Barb Browne, Bloomfield Hills schools spokeswoman, said the board is simply trying to take in all available information before making up its mind. “That’s why we’re bringing in experts. We want to be sure that everyone — the board, as well as the parents — are fully informed.”

But parents say the only information they’re given supports Core-Plus.

“There are lots of people who will back it up and say it’s good. But unless you’ve got some good, hard data, are you willing to risk your child’s math future on the fact that four or five educators think it’s good? I’m not,” Poglits said.

The district’s next information session is scheduled for 7:30 p.m. Wednesday, when a University of Michigan math professor, Pat Shure, will give the university’s outlook on math reform. The session will be in the Andover High School cafeteria, 4200 Andover Road.

A meeting of Parents for Excellence in Math Education is scheduled for 7:30 p.m. Jan. 27 at Temple Beth El, Handleman Hall, 7400 Telegraph Road, Bloomfield Township.

Tracy Van Moorlehem can be reached at 1-313-223-4534 or by E-mail at vanmoo@det-freepress.com

NYC MATH WARS
NYC Honest Open Logical Debate (NYC HOLD)On Math Reform
Elizabeth Carson

November 27, 2000

New York, NY. NYU mathematicians speak out against controversial new math programs being taught in NYC’s premiere School District 2 in Manhattan. Community School Board 2 will hear the professors’ preliminary report at the calendar meeting on Tuesday, November 28, 6:30 pm at 333 7^{th Ave, Seventh Floor.}

^{A groundswell of parent concern over how math is being taught in District 2 schools led to a front page New York Times article last spring, “The New, Flexible Math Meets Parent Rebellion.” CBS Weekend News brought national attention to the local struggle last May in the segment, “New, New Math = Controversy.”}

^{District 2 parents have now gained the support of mathematicians at NYU and the University of Rochester in grieving their concerns to District officials. The professors are scheduled to take part in a Math Forum sponsored by Community School Board 2 scheduled for March 1, 2001.}

^{The controversy in District 2 has gained the attention of Schools Chancellor Harold O. Levy and members of his recently established Commission on Mathematics Education charged with investigating how math is being taught in schools across the city.}

^{District 2 pilots the latest wave of experimental math programs, called the “new, new math,” echoing an earlier failed reform in the 60’s called “new math.” Memorization of math facts is no longer emphasized. Children are encouraged to use language to describe solutions and the way they feel about math.}

^{Community response in NYC and across the country has erupted in what have become known as the “math wars.” Critical parents, joined by mathematicians and scientists advocate clarity and balance in math reform: urging the inclusion of grade by grade goals, explicit teaching of standard procedures, basic skill building and rigor along with the inclusion of some of the creative exercises in the new programs. The pendulum has swung too far and must be corrected.}

^{One parent, Mark Schwartz, in testimony last year before the House Education and Workforce Committee stated: “If medical doctors experimented with our kids in the same fashion school districts do they would be in jail.” The hearings were held to review the US Department of Education’s endorsement of 10 of the experimental programs.}

^{Over 200 of the nation’s top mathematicians, including seven Nobel Laureates,} winners of the Fields Medal ^{the department heads at more than a dozen universities including Caltech, Stanford and Yale, responded to the federal endorsements with an open letter of protest to Secretary of Education Richard Riley, published in the Washington Post in November, 1999.}

^{“These programs are among the worst in existence,” said David Klein, a Cal State Northridge professor who was one of the letter’s authors. “To recommend these books as exemplary and promising would be joke if it weren’t so damaging.” Several of the cited programs, Interactive Mathematics Project (IMP),Connected Mathematics Project (CMP) and Everyday Mathematics are now being used in NYC schools.}

^{The new wave of math reform is based on a “constructivist” teaching philosophy; emphasizing creative exercises, hands-on projects and group work, with far less attention given to basic skills. Students are asked to ‘construct’ their own solutions. The use of calculators is encouraged. Teachers are instructed to serve as “facilitators” and are discouraged from explaining to students the standard solutions of basic arithmetic. Practice and drill have been eliminated. In higher grades algebra is de-emphasized. Many of the programs have no textbooks.}

^{Members of Chancellor Levy’s Math Commission will consider the new programs, which are being used in over 60% of NYC schools, including roughly 50 of the city’s weakest, which comprise the Chancellor’s District . Plans are set to expand implementation into more schools. One of the most controversial programs, the Interactive Mathematics Project (IMP), will be mandated in Bronx High Schools beginning next year.}

^{Professor Richard Askey, who holds an endowed chair in math at the University of Wisconsin, explained his motives in co-authoring the protest letter to Secretary Riley, “I’m hoping to provide ammunition for teachers who are under pressure to adopt some of these programs.”}

^{High math scores remained stable in some of the privileged District 2 schools, last year; though some schools’ scores dropped significantly. Across the rest of the city, 75% of eighth grade students failed the state math test ; 66% failed the city math tests. Answers are critical at a time when graduation requires students pass a new math Regents exam.}

^{It was the introduction of Connected Mathematics Project (CMP) and Investigations in Number Data and Space (TERC), two of the District 2 programs, that sparked the initial parent revolt that led to the California Math Wars.} Six parents in Plano,Texas have filed suit in federal court against their local school district after parent requests for an alternative to CMP were denied. ^{A nuclear physicist in Okemos Michigan led the local campaign against CMP. The use of TERC in one school system in Massachusetts prompted members of the Harvard Mathematics Department to issue a public protest. Parents in Reading Massachusetts fought the adoption of Everyday Math.}

^{The “new, new math” programs are based on the 1989 National Council of Teachers of Mathematics (NCTM) Standards. Frank Allen, past president of the NCTM and Emeritus professor of Mathematics at Elmhurst College comments: “NCTM leaders must admit that they have urged the application, on a national scale of highly controversial methods of teaching before they have been adequately debated or understood and before researchers have verified them by well-controlled and replicated studies.”}

^{=============}

November 27, 2000

To: Harold O. Levy, Chancellor

Dr Judith Rizzo, Deputy Chancellor for Instruction

Burton Sacks, Chief Executive for Community School District Affairs

Dr Irving Haimer, Member, Board of Education, Manhattan Representative

Trudy Irwin, Director of Education, Office of the Manhattan Borough President

From: NYC HOLD, Steering Committee

Re: Community School Board 2 Calendar Meeting November 28, 2000

We respectfully invite you to attend the calendar meeting of Community School Board 2 in Manhattan scheduled for Tuesday November 28, beginning at 6:30 pm. During the public session the Board will hear comment on District 2’s K-12 math programs. Distinguished faculty of the Courant Institute of Mathematical Sciences at New York University and concerned parents plan to speak.

The District’s mathematics reform is one component of the systemic instructional reform initiated by Anthony Alvarado in the previous decade. District 2 prides itself in being a leader in education reform in New York City. Our District piloted the New Standards Performance Standards in Mathematics which were adopted city-wide last year.

The implications of the relative success of our District’s math reform for the entire NYC school system should be evident.

In our District, parent concern with their children’s progress in mathematics is escalating; worries are being strongly voiced about aspects of the new math programs just as full implementation takes hold. School year 1999-2000 marked the first year the new K- 8 programs, Investigations in Number Data and Space (TERC) and Connected Mathematics Project (CMP) were mandated.

Parents are tutoring in record numbers. For many of their children, the new constructivist programs fail to provide a sound foundation in basic arithmetic. Parents recognize the value of the new programs’ creative, hands-on classroom and homework activities. However, many question the extensive time devoted to such activities, ostensibly at the expense of explicit teaching of the standard procedures and practice of skills. The absence of textbooks has exacerbated the situation.

Concerned parents have reached out to the NYU mathematics community in District 2 for analysis and opinion of our programs in hopes of finding ways to amend or extend the implemented programs to reach a better balance in the math instruction.

There are clearly implications in the course the District 2 community takes for the work of the newly appointed Commission on Mathematics Education to review math programs city-wide. We hope our experiences in District 2 can contribute to the assessment of the Committee.

Parents, teachers and administrators in District 2 share a well earned pride in our exemplary schools and strong educational community. Parents see on a daily basis, through their children’s work and enthusiasm for learning, the results of the skill and commitment of the teaching staff and administrators in our schools. Parents appreciate the formidable challenges district administrators face in guiding systemic reform in a large and diverse community school district.

We look forward to an ongoing and meaningful partnership in District 2.

We sincerely hope you will take an interest in our concerns and efforts to advance the course of math education for our children.

Sincerely,

Steering Committee
NYC HOLD

Elizabeth Carson
Christine Larson
Garry Dobbins
Margaret Hunnewell
Mary Somoza, Member, CSB #2
Granville Leo Stevens, Esq
Maureen McAndrew, DDS
Michael Weinberg

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No Such Thing As Malpractice In Edu-Land
– DEBRA J. SAUNDERS
Friday, February 4, 2000

LAST OCTOBER, the U.S. Department of Education released a list of 10 math programs which department educrats considered “exemplary” or “promising.” It would have been more accurate to rate the 10 programs as “trendy” or “math-lite.” Some 200 appalled mathematicians and scientists — including three Nobel laureates — ran an ad in the Washington Post calling on Secretary Richard Riley to rescind the seal of approval.

On Wednesday, two House Education subcommittees held a hearing on the issue. Educrats defending the Top Ten talked about process. Critics of the trendy new-new math talked about results.

Susan Sarhady, a parent from Plano, Texas, knows what the middle-school Connected Mathematics program — rated “exemplary” — did for her community. Some high-achieving students didn’t test well in math. Parents were baffled by assignments, like the tossing of marshmallows to see how many landed on their ends or their sides. Her friend Kathy bought a traditional math textbook and started spending a half hour every night with her son to make sure he didn’t miss math he would later need. Kathy found it galling that if her son scores well, Connected Math will get the credit.

Rachel Tronstein, a University of Michigan freshman, was enrolled in an accelerated Core Plus program — also “exemplary” — at Andover High School in Michigan. When she attended Stanford University’s summer session in 1998, she took the pre- calculus course after taking pre-calculus in Core Plus. She said, “the vast majority of material in that course was material to which I had never been exposed.”

Stanford mathematics professor R. James Milgram explained that he became interested in K-12 math curricula when he noticed that highly motivated math students couldn’t do well in their college math classes because they had received a “third-rate education.”

In 1989, the National Council of Teachers of Mathematics released the trendy math standards — which eschewed traditional math in favor of group work and discovery learning — which were the basis for the Department of Educrats’ Top Ten. By 1989, California schools had started using at least three trendy programs that were written to in conjunction with the new pedagogy. Milgram noted that since 1989, the percentage of California State University students — who are restricted to the top 30 percent of state high school graduates — who were required to take remedial math has more than doubled from 23 percent in 1989, to 55 percent.

Linda Rosen of the Department of Education argues that 23 percent is not exactly a number to brag about. And: “These new materials have only been out” for two to three years. She has a point. In 1989, participation in new-new math was uncommon. Since then, not every school has gone fuzzy, although many have.

California led the nation in the rush to dumb down math. The state’s 1985 math framework began the slide and the 1992 framework mastered it. Teachers who followed the framework adopted the math- lite approach years ago. Five years ago, the dissident math group Mathematically Correct was born when parents angry about the “exemplary” College Preparatory Mathematics realized the problem wasn’t just in their three school districts, but had become widespread.

Fact is, remedial math at CSU has more than doubled since 1989. Fact is, no one knows how many schools use new-new math because that is the rare education statistic which state and federal bureaucrats don’t collect.

Get the feeling they don’t want to know?

Michigan parent Mark Schwartz testified, “If medical doctors experimented with our kids in the same fashion school districts do, they would be in jail.” In edu- land, they get named to a on a panel that chooses pet math programs.

 

Page A – 25
URL: http://sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/2000/02/04/ED101353.DTL

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©2005 San Francisco Chronicle

NYC MATH WARS
NYC Honest Open Logical Debate (NYC HOLD)On Math Reform
Elizabeth Carson

November 27, 2000

New York, NY. NYU mathematicians speak out against controversial new math programs being taught in NYC’s premiere School District 2 in Manhattan. Community School Board 2 will hear the professors’ preliminary report at the calendar meeting on Tuesday, November 28, 6:30 pm at 333 7^{th Ave, Seventh Floor.}

^{A groundswell of parent concern over how math is being taught in District 2 schools led to a front page New York Times article last spring, “The New, Flexible Math Meets Parent Rebellion.” CBS Weekend News brought national attention to the local struggle last May in the segment, “New, New Math = Controversy.”}

^{District 2 parents have now gained the support of mathematicians at NYU and the University of Rochester in grieving their concerns to District officials. The professors are scheduled to take part in a Math Forum sponsored by Community School Board 2 scheduled for March 1, 2001.}

^{The controversy in District 2 has gained the attention of Schools Chancellor Harold O. Levy and members of his recently established Commission on Mathematics Education charged with investigating how math is being taught in schools across the city.}

^{District 2 pilots the latest wave of experimental math programs, called the “new, new math,” echoing an earlier failed reform in the 60’s called “new math.” Memorization of math facts is no longer emphasized. Children are encouraged to use language to describe solutions and the way they feel about math.}

^{Community response in NYC and across the country has erupted in what have become known as the “math wars.” Critical parents, joined by mathematicians and scientists advocate clarity and balance in math reform: urging the inclusion of grade by grade goals, explicit teaching of standard procedures, basic skill building and rigor along with the inclusion of some of the creative exercises in the new programs. The pendulum has swung too far and must be corrected.}

^{One parent, Mark Schwartz, in testimony last year before the House Education and Workforce Committee stated: “If medical doctors experimented with our kids in the same fashion school districts do they would be in jail.” The hearings were held to review the US Department of Education’s endorsement of 10 of the experimental programs.}

^{Over 200 of the nation’s top mathematicians, including seven Nobel Laureates,} winners of the Fields Medal ^{the department heads at more than a dozen universities including Caltech, Stanford and Yale, responded to the federal endorsements with an open letter of protest to Secretary of Education Richard Riley, published in the Washington Post in November, 1999.}

^{“These programs are among the worst in existence,” said David Klein, a Cal State Northridge professor who was one of the letter’s authors. “To recommend these books as exemplary and promising would be joke if it weren’t so damaging.” Several of the cited programs, Interactive Mathematics Project (IMP),Connected Mathematics Project (CMP) and Everyday Mathematics are now being used in NYC schools.}

^{The new wave of math reform is based on a “constructivist” teaching philosophy; emphasizing creative exercises, hands-on projects and group work, with far less attention given to basic skills. Students are asked to ‘construct’ their own solutions. The use of calculators is encouraged. Teachers are instructed to serve as “facilitators” and are discouraged from explaining to students the standard solutions of basic arithmetic. Practice and drill have been eliminated. In higher grades algebra is de-emphasized. Many of the programs have no textbooks.}

^{Members of Chancellor Levy’s Math Commission will consider the new programs, which are being used in over 60% of NYC schools, including roughly 50 of the city’s weakest, which comprise the Chancellor’s District . Plans are set to expand implementation into more schools. One of the most controversial programs, the Interactive Mathematics Project (IMP), will be mandated in Bronx High Schools beginning next year.}

^{Professor Richard Askey, who holds an endowed chair in math at the University of Wisconsin, explained his motives in co-authoring the protest letter to Secretary Riley, “I’m hoping to provide ammunition for teachers who are under pressure to adopt some of these programs.”}

^{High math scores remained stable in some of the privileged District 2 schools, last year; though some schools’ scores dropped significantly. Across the rest of the city, 75% of eighth grade students failed the state math test ; 66% failed the city math tests. Answers are critical at a time when graduation requires students pass a new math Regents exam.}

^{It was the introduction of Connected Mathematics Project (CMP) and Investigations in Number Data and Space (TERC), two of the District 2 programs, that sparked the initial parent revolt that led to the California Math Wars.} Six parents in Plano,Texas have filed suit in federal court against their local school district after parent requests for an alternative to CMP were denied. ^{A nuclear physicist in Okemos Michigan led the local campaign against CMP. The use of TERC in one school system in Massachusetts prompted members of the Harvard Mathematics Department to issue a public protest. Parents in Reading Massachusetts fought the adoption of Everyday Math.}

^{The “new, new math” programs are based on the 1989 National Council of Teachers of Mathematics (NCTM) Standards. Frank Allen, past president of the NCTM and Emeritus professor of Mathematics at Elmhurst College comments: “NCTM leaders must admit that they have urged the application, on a national scale of highly controversial methods of teaching before they have been adequately debated or understood and before researchers have verified them by well-controlled and replicated studies.”}

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November 27, 2000

To: Harold O. Levy, Chancellor

Dr Judith Rizzo, Deputy Chancellor for Instruction

Burton Sacks, Chief Executive for Community School District Affairs

Dr Irving Haimer, Member, Board of Education, Manhattan Representative

Trudy Irwin, Director of Education, Office of the Manhattan Borough President

From: NYC HOLD, Steering Committee

Re: Community School Board 2 Calendar Meeting November 28, 2000

We respectfully invite you to attend the calendar meeting of Community School Board 2 in Manhattan scheduled for Tuesday November 28, beginning at 6:30 pm. During the public session the Board will hear comment on District 2’s K-12 math programs. Distinguished faculty of the Courant Institute of Mathematical Sciences at New York University and concerned parents plan to speak.

The District’s mathematics reform is one component of the systemic instructional reform initiated by Anthony Alvarado in the previous decade. District 2 prides itself in being a leader in education reform in New York City. Our District piloted the New Standards Performance Standards in Mathematics which were adopted city-wide last year.

The implications of the relative success of our District’s math reform for the entire NYC school system should be evident.

In our District, parent concern with their children’s progress in mathematics is escalating; worries are being strongly voiced about aspects of the new math programs just as full implementation takes hold. School year 1999-2000 marked the first year the new K- 8 programs, Investigations in Number Data and Space (TERC) and Connected Mathematics Project (CMP) were mandated.

Parents are tutoring in record numbers. For many of their children, the new constructivist programs fail to provide a sound foundation in basic arithmetic. Parents recognize the value of the new programs’ creative, hands-on classroom and homework activities. However, many question the extensive time devoted to such activities, ostensibly at the expense of explicit teaching of the standard procedures and practice of skills. The absence of textbooks has exacerbated the situation.

Concerned parents have reached out to the NYU mathematics community in District 2 for analysis and opinion of our programs in hopes of finding ways to amend or extend the implemented programs to reach a better balance in the math instruction.

There are clearly implications in the course the District 2 community takes for the work of the newly appointed Commission on Mathematics Education to review math programs city-wide. We hope our experiences in District 2 can contribute to the assessment of the Committee.

Parents, teachers and administrators in District 2 share a well earned pride in our exemplary schools and strong educational community. Parents see on a daily basis, through their children’s work and enthusiasm for learning, the results of the skill and commitment of the teaching staff and administrators in our schools. Parents appreciate the formidable challenges district administrators face in guiding systemic reform in a large and diverse community school district.

We look forward to an ongoing and meaningful partnership in District 2.

We sincerely hope you will take an interest in our concerns and efforts to advance the course of math education for our children.

Sincerely,

Steering Committee
NYC HOLD

Elizabeth Carson
Christine Larson
Garry Dobbins
Margaret Hunnewell
Mary Somoza, Member, CSB #2
Granville Leo Stevens, Esq
Maureen McAndrew, DDS
Michael Weinberg