Meeting With Parents in Region 4 - Chester - Deep River - Essex

Topic: How to deal with TERC's Investigations K-6 Math Program
Date: March 4, 2004  plus Important March 14, 2006 Update
Speaker:  William G. Quirk, Ph.D.

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 constructivism for their interpretation of this philosophy. This is a blend of ideas from sociology, child psychology, and old-fashion progressive education. Progressive educators reject teacher-centered knowledge transmission. Since the time of Rousseau, progressive educators have believed that children can discover what’s important for them to know if they are placed in the right environment. This is the underlying philosophy behind whole language. The real world is considered the ideal learning environment.  That’s why there’s such an interest in projects outside of the classroom.

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.

This program isn’t for college-bound children.  It doesn’t even prepare them for genuine high school level math. What Can Parents Do ? Be very specific about what you want your children to learn. Construct a list of specific learning expectations.  If you want specific, grade-by-grade learning expectations, a good current reference is chapters 2 and 3 of the Mathematics Framework for California Public Schools.   This framework is available on the internet, and can be purchased for about $25 plus S&H. 

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 5th 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.