Topic: How to deal with TERC's
Investigations K-6 Math Program

I’m
not a fan of TERC math. I believe it’s
an insult to the intelligence of the average child. ’ll begin with an
outline of the problem, and then I’ll discuss solution strategies. There are many ideas to cover, so I’ll
be
reading from prepared notes to limit this to 15 minutes.

TERC
claims to offer a “standards-based” approach for elementary math
education.
The standards referenced are those of the NCTM, the National Council of
Teachers of Mathematics. The term standards is a bit misleading, since
the
NCTM standards are primarily about the NCTM’s philosophy of math
education.

TERC uses the term Investigations for their discovery-learning activities. It’s assumed that children can naturally discover math as they carry out investigations with their peers. TERC’s materials for teachers have detailed scripts for how to direct investigations, but there are no clearly stated prerequisites or learning objectives for these investigations. Although there are extensive materials for teachers, there are no student textbooks. Students needing help are to look to their peers, not their parents, and not even their teachers.

Standards-based programs also embraces ideas from child psychology. TERC’s lead developer has a Ph.D. in child psychology and no credentials in math. From the progressive child psychology perspective, learning should always be a happy experience, and children shouldn’t be stressed. Progressive educators use the phrase “developmentally appropriate.” They mean that each child should be allowed to learn at their own pace. A child shouldn’t be pushed.

Putting it together we have: Children are to expected to discover math as a byproduct of playing games and carrying out group activities. Teachers can’t directly teach standard elementary math. Learning must be fun. Now, it’s really not possible to learn much this way. TERC gets around this by changing elementary math education in three fundamental ways.

First Fundamental Change: They’ve eliminated standard elementary math content. Standard language, standard computational methods, and standard formulas are all out. They justify eliminating standard arithmetic by claiming that it’s obsolete due to the power of calculators. This alone eliminates 80% of traditional elementary math content. The little that is learned isn’t traditional elementary math. With no student textbooks and non-standard content, it’s very difficult for parents to help their children.

Second Fundamental Change: Because children can’t be stressed, memorization and practice are ruled for TERC math. But “mastery" of any subject matter requires a process that loads subject matter details into the brain. Once details are in the brain, they can be connected to other details and "understanding" gradually evolves. TERC fails to understand that it's often desirable to move to automatic use of knowledge. The mind must be free to think at higher levels of complexity, without consciously revisiting underlying details. Memorization and practice are the two main strategies for helping us remember information, But TERC rejects the importance of both. So TERC students won't even remember the minimal TERC content.

Third Fundamental Change: TERC claims to emphasize problem solving and conceptual understanding, but they have redefined the meaning of these phrases. Real math problem solving involves applying one or more remembered math facts or skills. But with so little content, and no methods to help the student remember, there’s not much knowledge in the brain to apply. So TERC has redefined math problem solving to mean using one or more content-independent techniques: Make a list, draw a picture, look for a pattern, act it out, use trial and error, or guess and check. Real math understanding is about seeing connections between math ideas.

TERC has redefined understanding to mean demonstrate using hands-on materials. TERC strongly rejects the idea that children must eventually migrate from hands-on to abstract thinking TERC fails to recognize the vertically-structured nature of the math knowledge domain. Standards-based programs claim to emphasize connections, but they don’t see how mathematical ideas are connected. Knowledge of addition is necessary for learning multiplication, knowledge of multiplication is necessary for learning division, knowledge of division is necessary for learning about fractions, and all are needed for algebra..

It all starts with mastery of single digit number facts. Mastery means to know these facts automatically, without conscious thought. Mastery of multdigit computation requires prior mastery of single digit number facts. Mastery of operations with fractions also requires prior mastery of single digit number facts.

Designers of
good,
content-based math programs understand the necessity of carefully
sequencing
material relative to the vertically-structured nature of the math
knowledge
domain. Coupled with strategies for
remembering what’s already been learned (memorization and practice),
students
in such content-based programs learn more and more quickly, as they
migrate up
the math learning curve. Singapore Math is an excellent example.
You can’t learn
algebra if you haven’t first mastered standard arithmetic, and algebra
is the
gateway to higher math.

By standard arithmetic we mean the standard
procedures for
adding, subtracting, multiplying and dividing whole numbers, fractions,
and
decimals. Long division is the most difficult example. But there is not
one
instance where TERC recommends that students master a standard
computational method. TERC is openly
hostile to such methods. The
problem here goes far beyond the failure to prepare for algebra.

Math is the
first man-made knowledge domain where American children build a
remembered
knowledge base of domain-specific content, with each child gradually
coming to
understand hundreds of specific ideas that have been developed and
organized by
countless contributors over thousands of years. With teachers who know
math and
sound methods of knowledge transmission, the child is led,
step-by-step, to
remember more and more math, continually moving deeper and deeper into
the
structured knowledge domain that comprises traditional K-12
math. This
first disciplined knowledge-building experience is a key enabler,
developing
the memorizing and organizing skills of the mind, and thereby helping
to
prepare the individual to eventually build remembered knowledge bases
relative
to other knowledge domains in the professions, business, or personal
life.

:TERC claims that TERC students outperform
students in
traditional elementary math programs.
But this is only possible if the tests are limited to the
minimal TERC
content, or parents have supplemented by engaging tutors or teaching
their own
children. You will be told that TERC
math is necessary to prepare students for the Connecticut Mastery Tests. This isn’t true. The most difficult
(released) 8th grade question for fractions, asks the student to
compute 1/4 + 3/8. Another question asks the student to
choose the number that's between 1/4 and 3/4. The candidates are
3/8, 5/8, 7/8, and 13/16. What's the correct answer?
They say 5/8. Guess they meant the largest right answer.

Why have
they done this? Standard-based math is
also about social goals.
The equity principle is the first principle in Principles and Standards
for
School mathematics, the latest version of the NCTM standards. The
equity
principle is about equality of results, not equality of opportunity.
Steven
Lienwand, former lead math consultant for the State of Connecticut says
that
traditional math is only for the elite 20% of students. TERC’s
progressive math
educators believe they are serving the needs of the other 80%. They’ve
limited
content to what they think is needed for everyday life, not to prepare
for more
advanced learning.

March 14, 2006 Update: See Finding Ground in K-12 Mathematics for important new information. TERC doesn't meet any of these common ground agreements!

The content found
in
Singapore math is also an excellent guide. Show them the kind of
problems you
want your children to solve. The
California Framework and Singapore math are both good sources for
examples. Also, see David Klein’s lists
at http://www.csun.edu/~vcmth00m/5th.pdf
You might construct sample
tests. You want your children to be able to pass such a test by the end
of the
5^{th} grade. The major, summary learning expectation is
mastery of the
standard methods for the addition, subtraction, multiplication, and
division
for whole numbers, decimals, and fractions

Point out that the content you consider essential
is usually
not covered, or covered in too shallow a fashion in TERC math. Point
out that
you believe that TERC is very wrong in their open hostility to anything
standard. Non-standard methods have no
lasting value. The time spent is a
diversion from important learning objectives.
It’s a zero sum game.

According to the State of Connecticut, parents are
responsible for the education of their children. So
you and the greater community of Region 4 should decide __what __should
be taught. The teachers have been hired
because of supposed expertise in __how __to teach what the public
wants
taught. If teachers are allowed to
decide what to teach, what prevents them from selecting material that
requires
little effort on their part.

Point out
that TERC math puts the responsibility on students to teach themselves,
relying
primarily on input from their peers, not teachers. There are many
people in
Region 4 who know more math than the typical elementary math teacher in
Essex. Such people should have a role in
determining what should be taught. No, you don’t want rote memorization
of
standard procedures. You want your
children to master such procedures and learn how to correctly use them
to solve
problems.