2008 TERC Math vs. 2008 NMP Math: A Snapshot View

The March 2008 Final Report of the National Mathematics Advisory Panel recognized algebra as the gateway to all higher mathematics. The Panel carefully defined "school algebra" by identifying 27 specific topics, organized into major categories, such as linear equations, quadratic equations, and the algebra of polynomials. The Panel then identified the "critical foundations of algebra." They stressed proficiency with the standard algorithms of whole number arithmetic and proficiency with fractIons. The Panel said students should develop "automatic execution of the standard algorithms." They cautioned that the use of calculators could "impede the development of automaticity."

The TERC 2008 PDF document Early Algebra: Numbers and Operations vaguely defines "algebra" as "a multifaceted area of mathematics content that has been described and classified in different ways."  TERC doesn't identify any specific "algebra" topics.  They do list "four areas" that they believe to be "foundational to the study of algebra," but nothing about mastery of standard arithmetic.  TERC promotes nonstandard methods that attempt to avoid carrying, borrowing, and common denominators.  These are three keys to computational automaticity!   Here are two examples found in TERC 2008 materials.

1) How TERC avoids the concept of borrowing:
                                               3,726
                                             - 1,584
                                               2,000
                                                 200
                                                 -60
                                                   2
                                               2,142

This example of TERC's "Subtracting by Place" method is found in the TERC 2008 5th Grade Student Handbook.  The student somehow knows that 20 - 80 can be written as -60, a negative number, and the student also knows how to compute 2,142 as the sum of positive and negative integers.  TERC avoids the concept of borrowing by assuming knowledge of negative numbers and integer arithmetic.  These two middle school (not 5th Grade) topics are not explicitly mentioned anywhere in the TERC 2008 program materials.

2) How TERC avoids the concept of a common denominator:

Shandra compares 2/5 to 3/8 by arguing "For 3/8, you need another 1/8 to make a half.  For 2/5, you need half of a fifth to make a half.  That's the same as 1/10, so 1/10 is smaller than 1/8, so 2/5 is closer to 1/2.  This means that 2/5 is more."  But how much more? 
If Shandra used 40 as a common denominator and converted 2/5 to 16/40 and 3/8 to 15/40, she would easily see that 2/5 is exactly 1/40 more than 3/8.  Typical for TERC, Shandra's method requires considerable time, significant conscious thought, and fails to give an exact answer.  Converting to a common denominator should become an automatic skill.  This skill is essential for exactly adding, subtracting, and comparing fractions.

Click on 2008 TERC Math vs. 2008 NMP Recommendations for the full report.

Copyright 2008-2011  William G. Quirk, Ph.D.