## 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.