Integrated Mathematics in LAUSD
Summary
In California, the integrated mathematics option refers specifically to an alternative to the algebra 1, geometry, algebra 2 secondary sequence wherein districts are allowed to provide the same content but in a different sequence over three years. All mathematics programs for K-7 are integrated in that topics from each strand of mathematics are included each year. Because the secondary integrated programs make heavy use of pedagogical approaches often called reform mathematics, these terms have unfortunately been used interchangeably. This confuses the issues.
With respect to the secondary integrated mathematics programs in use in LAUSD:
The content of these courses is not equivalent to the content required by the state standards.
No integrated 1 books were approved by the state under AB2519 – indeed most were not even submitted – as they are unsatisfactory relative to the state learning standards.
The integrated programs cannot be legitimately certified as aligned with the state standards.
Students in these programs learn less mathematics than those in traditional programs.
LAUSD students in integrated mathematics score lower than those in traditional mathematics in grades 8, 9, and 10 on the state standards-based tests according to state records.
This deficit is true for economically disadvantaged students as well as others.
This deficit is true for LEP students as well as others.
This deficit is true for male and female students.
These programs produce students who are less well prepared.
Integrated mathematics has been promoted through LA-SI (the Los Angeles Systemic Initiative, a federally funded project to implement integrated math programs) in schools around the district. Of the eleven schools associated with LA-SI the longest, all but one have experienced decline in SAT participation over the past two years. The average decline is 12% as reported by the IAU (the “Independent Analysis Unit” of LAUSD) to the Board in a report of May 12, 1999.
SAT administration across all LA-SI focal schools is down about 5% while it is up roughly 5% in non-focal schools. The SAT math average in focal schools is 445 while at the non-focal schools have an average of 462.
With respect to reform mathematics, the programs approved by the state for K-8 include a range of reform approaches and frequently note their alignment with NCTM. These approaches will still be available even when programs that fail to align with the standards are avoided.
Integrated Mathematics in LAUSD
Member, LAUSD Mathematics Curriculum Committee
Introduction
Historically, secondary mathematics in California has been taught using the courses algebra 1, geometry, and algebra 2. More recently, some schools have switched to courses that mix these topics across three courses. This is called integrated mathematics and is an optional sequence in the state Mathematics Framework. However, the integrated programs in use differ in many respects beyond the sequence of topic presentation, and thus integrated has taken on other meanings that have to do with pedagogy, presentation style, and other factors.
The new California Mathematics Standards and the Mathematics Framework require a mixture of topics from the strands of mathematics for all students in grades K-7. Districts may use either the traditional or the integrated sequence starting in grade 8. The standards stipulate exactly the same objectives for either sequence – that students learn the required mathematics.
To go along with this option, the standards-based portion of the state testing program (STAR) in mathematics has two choices for grades 8 to 10 – algebra 1, geometry, and algebra 2 or integrated 1, integrated 2, and integrated 3. The two sequences contain exactly the same items overall, but they are assigned in a different sequence across the three years.
Also, in grades 8 to 10, only students enrolled in the corresponding traditional or integrated sequence take the standards-based part of the exam. In grade 11, all students take a cumulative form of the standards-based exam covering all of these topics, regardless of what mathematics courses they have taken.
In general, the performance on these standards-based examinations has been poor. This is expected since students have not previously been expected to meet the new standards throughout their academic careers. Achievement in LA has been poor as well. However, certain comparisons are already possible given the baseline test results from the spring 1999 test administration.
Results for LAUSD
The California data file for these test results gives means for the standards-based mathematics tests in grades 8 to 10 only for those students who are “on-track” for meeting the standards, meaning that they are taking the first year in grade 8, or the second year in grade 9, or the third year in grade 10. Here are the average number of correct answers for all of LAUSD
Results for Economically Disadvantaged Students
The integrated programs also show weaker results for disadvantaged students. The STAR data file does not contain information on ethnic minorities, but it does summarize scores for economically disadvantaged students vs other students. Both groups achieved lower scores with integrated programs. This is not consistent with the idea that the integrated mathematics programs are better for the disadvantaged students. These results are consistent with the idea that the integrated programs lack equivalent mathematical content.
Results for LEP Students
From the state data file, it is also possible to inspect the LAUSD results for limited English proficiency students (LEP) compared to other students. Again, both groups achieved lower scores with integrated programs than with traditional programs across the three grade levels.
Results for Male and Female Students
The state data file breaks down scores by student gender. Again, both groups achieved lower scores with integrated programs than with traditional programs across the three grade levels.
Integrated and Traditional High Schools
It is possible to characterize high schools as traditional or integrated based on the tests taken by the students (counts of tests taken are given even when the scores are not reported). In this example, schools were identified as traditional if at least 75% of these augmented tests were in the traditional sequence, and they were called integrated if at least 75% of the tests were in the integrated sequence. These high schools were then compared on the basis of their average scores for the 11th grade where all students take the same standards-based mathematics exam. The results were:
The Stanford 9 scores for these same high schools give an indication of achievement on a less rigorous assessment. The results using the NPR for the average student at each school are:
LA-SI Schools
The influx of integrated mathematics programs in LAUSD high schools is related to involvement with LA-SI (the Los Angeles Systemic Initiative, a federally funded project to implement integrated math programs). Schools with the longest involvement are Phase I schools. Of the eleven Phase I schools, all but one have experienced decline in SAT participation over the past two years, some rather substantially; 12% is the average reported by the IAU (the “Independent Analysis Unit” of LAUSD) to the Board in a report of May 12, 1999.
According to the IAU numbers, SAT performance across all of the LA-SI Focal schools is down about 5% in the number of takers and has a math average of 445 while the number of takers is up roughly that same 5% at the non-Focal schools with an average of 462. Neither of these numbers is terribly impressive but they suggest a reason why several high schools have abandoned integrated mathematics and are returning to more traditional programs.
The IAU only looked at the two years 1996-1998 but a longer perspective on these LA-SI Phase I schools is informative. Palisades is not on the state’s data base because of its conversion to magnet status but data from the other ten is available on the Internet. That data starts with 1992, the year in which two of them, Roosevelt and Marshall, became pilots for an integrated program called IMP. From 1992 to 1998, the data year of the IAU report, these ten schools dropped an average of 13 points in their SAT math scores while experiencing a 30% overall drop in SAT participation. These numbers compare with the overall statewide math SAT average holding steady at 516 while participation increased by 24%.
Another useful measure of success is the Entry Level Mathematics Exam (ELM) required of students admitted to any CSU campus. The most recent data at that website is for those students admitted sometime during the 1997-8 year. A successful mathematics assessment is an SAT math score of 550 or a passing score on the ELM. For the LA-SI Phase I schools, the collectively failure rate was 78%. This compares with a statewide failure rate of 55%.
Alignment with Standards
The integrated secondary programs in use in LAUSD not only mix up the order of topic presentation, they also reduce the level of mathematics covered. The state has recently approved 5 algebra 1 programs under AB2519, while no integrated 1 programs were approved. In general, the integrated secondary programs were not even submitted because of their lack of alignment with the state standards. The district cannot legitimately certify these integrated programs as being aligned to the state standards.
Reform Methods without Integrated Secondary Programs
Even without these integrated secondary programs, LAUSD students will still have integrated content in grades K-7. Even without these integrated secondary programs, schools will be able to select books with varying degrees of reform mathematics methods at all grade levels. Indeed, the state-approved texts often note their inclusion of these new methods and make reference to the NCTM which is recognized for promoting these methods. Many include leading NCTM members as authors.
LAUSD can comply with state requirements and still encourage classroom teachers to use their own professional judgment in selecting the best methods for meeting the needs of their students. Indeed, this is exactly what is recommended in the state mathematics framework.