Friday, May 13, 2011

The Constructivist School of Thought

Parents from my daughter’s school and our local park often ask me what are the philosophical and scientific underpinnings of the so-called “Constructivist” school of thought. It seems odd to them that these reformists could be so misguided in their beliefs and yet be so successful in the “math wars”. After all it has been almost three decades since their agenda has taken hold – certainly since the “NCTM standards” were nationally implemented in the early 1990s. Surely, these parents believe, the reformists must be onto something good and must have the best of intentions in mind. In other words, there must be significant research proving their agenda correct and the leaders of the education community must know better what is best for our children’s education than mere parents or teachers bent on old-school traditionalism…

I appreciate these questions because I battled with them myself (and still do on many issues). It does seem unbelievable that the reformists would be so misguided for so long and yet still be all around… but after having read many papers, reports, surveys, etc. not only am I more skeptical of the constructivist philosophy but I am now suspicious of and opposed to their opaque agenda. Their willful disregard for all expert opinions and empirical evidence militating against their programs is borderline criminal and definitely unethical in my book. While another post will address why I think the reformists have and still thrive despite their horrendous track record, this post presents the Constructivists’ main arguments and the next post will offer the case against.

This presentation relies on a paper by Constance Kamii published in The Constructivist in 1997 and titled “52 X 8: The Importance of Children's Initiative”. Please note there are many more primary sources interested readers should review. I selected this one because it neatly summarizes the main points but mainly because it was regularly distributed in the early 2000s by Manhattan District 2 Math Director Lucy West to parents at information meetings held by Ms. Karen Feuer, President of Community School Board 2, to educate school parents on the philosophy of TERC Investigations.

Today, and this is the interesting part, Ms. Feuer is principal of PS110, my daughter’s school, and Mrs. Lucy West has just been hired as our math consultant to supplement our Everyday Mathematics curriculum with another reform math program called Math in the City. How interesting can it get? The same cast of characters, in different roles 12 years later, and still promoting the same reform math programs… in fact, promoting new math reform programs to “supplement” older math reform programs… can you square that circle?

The reformist school of thought is generally called “Constructivist”… because it is largely based on Jean Piaget’s theory of constructivism which holds that children are better wired to arrive at or “construct” their own solutions to problems rather than being passive recipients of direct instructions from a teacher standing at the blackboard ruler in hand…

As Ms. Kamii says (pp. 7-13):

Piaget showed that children acquire logico-mathematical knowledge not by internalizing rules from the outside but by constructing relationships from within, in interaction with the environment.”


Children’s minds do not work in the fragmented manner by which textbook writers organize their texts. Children go much farther and more naturally, with greater joy, if they are encouraged to pose their own questions and answer them in their own way.”

Thus the question becomes how do teachers foster children’s inherent ability to construct their own solutions? Ms. Kamii lists the 3 main constructivist steps:

1)       “… by picking up on what they say... the questions they ask are more developmentally appropriate than those found in textbooks… because they come out of their level of thinking.”

2)       “… by refraining from teaching conventional algorithms and, instead, encouraging children to invent their own procedures for solving problems. Algorithms force children to give up their own thinking.

Here it’s important to note that the authors say “the only children who have not been crippled by conventional algorithms are the brightest, most advanced minority in each class, who could make sense of the algorithms.” This advanced minority, for the authors and the reformists in general, is male, white or Asian. As we will see in another post, this is important to understand because it explains why reformists benefit from such wide political support

3)       “… by refraining from saying that an answer is correct or incorrect and, instead, encouraging children to agree or disagree among themselves. When the teacher decrees that an answer is correct, all thinking and all initiative stop.

And there you have it… the three guiding principles of the constructivist school of thought that stand diametrically opposite of what most of us learned and how we were taught in school. Not that that is necessarily bad in and of itself… yet the fact that it seeks to destroy what has been tested and fine-tuned over centuries of teaching with good results seems counter-productive and irresponsible, especially in light of the disastrous math test results and international rankings this generation of students has achieved under this reform.

Clearly something is not working as planned: 30 years and bad results should provide ample evidence that its time to stop this experiment and change course… but it doesn’t. In fact, the reformists have more power and influence than ever. Why? That is the real question.

My next post will present the case against Constructivism.


  1. Are you advocating a complete return to algorithms? Surely, it has its failings. Prior to reform math the USA's world ranking in mathematics was far from impressive. I'm not an expert but the three guiding principles above seem reasonable. What about a third choice? I wonder if there's a compromise between the two that would be more effective.

  2. Anonymous,

    Yes I am in favor of direct instruction and the four standard algorithms. Please read my new posts on these 2 issues.

  3. This post confuses Discovery with Constructivism. We all construct knowledge, whether the teaching method is direct or discovery. Direct instruction is just more efficient. The drawback with direct instruction is not the method but whether the person teaching has the depth of knowledge to help students construct deep enough understanding. The drawback with discovery is the same as for direct instruction, but also is inefficient. But in either case, knowledge (correct or incorrect) is still constructed.

  4. Sally,

    According to my reading of the literature, most “reform math” programs (Discovery Learning, Problem-Solving Learning, etc.) have been lumped together under the “Constructivist” umbrella as a simple method of categorizing them in opposition to the more traditional programs emphasizing direct instruction, memorization of facts and procedures, mastery-first, sequencing, etc.

    Are you saying that Discovery Learning and Constructivism do not promote similar pedagogical methods? Are you also implying that Direct Instruction methods are a subset of Constructivism because “we all construct knowledge” irrespective of teaching method?