# TERC Hands-On Math:  A Snapshot View

### by Bill Quirk  ( wgquirk@wgquirk.com)

Developed by TERC, with funding from the National Science Foundation (NSF),  Investigations in Number, Data, and Space  purports to be “a complete K-5 mathematics curriculum that supports all students as they learn to think mathematically.” The NSF is now spending millions to promote implementation of the TERC program.  School Boards find it difficult to say no. They rationalize: “it’s just a different way to teach elementary math, and the NSF backs it, so how bad can it be?”

This program is very bad because it omits standard computational methods, standard formulas, and standard terminology.  TERC says this is now obsolete, due to the power of \$5 calculators.  They claim their program moves “beyond arithmetic” to offer “significant math,” including important ideas from probability, statistics, 3-D geometry, and number theory.

But math is a vertically-structured knowledge domain.  Learning more advanced math isn’t possible without first mastering traditional pencil-and-paper arithmetic. This truth is clearly demonstrated by the shallow details of the TERC fifth grade program.  Their most advanced “Investigations” offer probability without multiplying fractions, statistics without the arithmetic mean, 3-D geometry without formulas for volume, and number theory without prime numbers.

### TERC Omits All Standard Computational Methods

Consider the “Sample of Ads Investigation,” at the end of the TERC fifth grade.  Students are given a 48-page newspaper and a supply of  “Recording Strips” that are premarked with “familiar fractions,” such as 1/4 and 2/3.  They begin by deciding to sample one-third of the 48 pages.  After using a calculator to divide 48 by 3, they select 16 sample pages and use eyeball estimation to guess the fraction of ads found on each sample page.  Then, using one 3-inch “Recording Strip” for each sample page, students color the fraction of ads, cut out the colored portions, and tape them onto a 48-inch length of adding machine tape, “starting from one end of the tape and putting the pieces right next to each other.”  Students then estimate the fraction of ads for the full 16-page sample by folding the 48-inch strip to estimate the fraction corresponding to the 16 colored-in pieces.

Why not add the 16 fractions and then divide the sum by 16?  TERC students never learn about dividing fractions, and they never learn general methods for adding fractions.  They do learn a hands-on method for adding two proper fractions with denominators less than 7, but this paper-folding method doesn’t work if the denominator of the sum fraction isn’t also less than 7.

### TERC Omits Standard Formulas

For the final fifth grade Investigation in 3-D geometry, TERC students use patterns, scissors, and tape to build prisms, pyramids, cylinders, and cones.  They then attempt to “discover” 3 to 1 volume relationships by pouring rice from one bulging container into another.  Later they find the volume of each paper container by pouring rice from the container into a  plastic measuring tool.

Why not formulas for volume?  TERC says students usually don’t understand formulas and frequently apply them blindly and incorrectly.  So general methods involving standard formulas are not found in TERC math.

### TERC Omits Standard Terminology

TERC recommends natural language, not standard terminology.    For statistics they say “we have found useful such words as clumps, clusters, bumps, gaps, holes, spread out, and bunched together.”   For “the  mathematics of change” they recommend “grow, shrink, faster, slower, steep, flat, slow, steady, speed up, slow down, grows steadily, grows faster and faster, grows slower and slower, shrinks steadily, shrinks slower and slower, shrinks faster and faster, grows and then shrinks, oscillates between growing and shrinking.”  TERC appears to believe that these subjective terms are related to calculus.

TERC has redefined the meaning of “think mathematically” and painted a false picture of elementary mathematics.  It’s all very hard to believe, but it’s sadly true.

For a detailed analysis of TERC math, click on

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Copyright 2002-2005 William G. Quirk, Ph.D.