The "Parrot Math" Attack on Memorization

By Bill Quirk

Constructivist math educators regularly cite  Parrot Math  by Thomas C. O'Brien.  Although this paper promotes constructivist  "activity-based" learning over direct instruction, it's primary claim to fame is the open hostility to memorization.  Professor O'Brien rejects "memorization and parrot-like drill " in favor of "children's invented strategies." He references a paper by Kamii and Dominick as evidence of "considerable research" showing that mastery of the standard algorithms of arithmetic is harmful for children.  [See The Bogus Research in Kamii and Dominick's Harmful Algorithms Papers

Understanding and Thinking Depend Fundamentally on Remembered Content Knowledge

Constructivist math educators reject memorization and practice and thereby severely limit the student's ability to remember specific math facts and skills.  They say they want to maximize "understanding" and develop "powerful thinking skills," but appear blind to the fact that both understanding and thinking depend fundamentally on remembered content.  Knowledge must first be loaded into the brain before it can connected to other knowledge and "understood." Explicit memorization is sometimes the most efficient way to get it there.  Without specific remembered math facts and skills, students must regularly revisit previously covered content ("spiral back") and rely on general content-independent skills, such as the NCTM problem-solving strategies:  1. use manipulative materials, 2. trial and error, 3. make a list, 4. draw a diagram, 5. look for a pattern, 6. act out a problem, and 7. guess and check. 

K-12 math is the first man-made knowledge domain where 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 sound methods of knowledge transmission, the student is led, step-by-step, to remember more and more specific math facts and skills, continually moving higher and higher in the vertically 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.  Although the specific facts, skills, and organizing principles differ from domain to domain, genuine domain experts must necessarily remember a vast amount of specific information that is narrowly relevant to their targeted knowledge domains, frequently without the possibility of transfer to other domains.  

The Power of Automaticity

It is a profoundly erroneous truism ... that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. - Alfred North Whitehead

Constructivists fail to understand that it's 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. For example, a key idea of the standard algorithms of arithmetic is that multi-digit calculations are reduced to single-digit calculations. If children don't have instant recall of the single-digit number facts, they aren't equipped with the essential pre-knowledge for easily carrying out multi-digit computations. For more about the power of automaticity, see The Bogus Research in Kamii and Dominick's Harmful Algorithms Papers.

Activity-Based Learning

Thomas C. O'Brien and his constructivist colleagues are not offering a different way to teach traditional K-12 math content.  They are discarding most of this content, including all of standard arithmetic. In Parrot Math  Professor O'Brien promotes "activity-based" learning, but doesn't give any examples. He misses a nice opportunity when he spends two pages discussing "the handshake problem," but offers nothing about how to solve this problem.  To learn about the historic importance of this interesting problem, see How Many Handshakes in How the NCEE Limits Elementary School Math, Chapter 2 in How the NCEE Redefines K-12 Math.   .  

To better understand "activity-based" learning, see the examples in Chapters 2, 3, and 4 of How the NCEE Redefines K-12 Math  Also see Chapter 1,  A Summary View of NCEE Math and notice that most of traditional K-12 math content is missing.

Copyright 2013 William G. Quirk, Ph.D.