## None of Us Stink at Math: Elizabeth Green, Constructing Knowledge, and You

It’s not like clockwork. However, a regular event is to have a high-profile article spur debate … and passion for … specific ‘teaching methods’. The most recent one is an article by Elizabeth Green called “Why Do Americans Stink at Math?” (see http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?ref=magazine&_r=1# ). Well written, understandable … and wrong in all ways that matter.

First, almost all references to ‘math’ in these discussions is actually ‘procedural arithmetic’; yes, we uniformly “stink” at that. I do not see that as a particular problem, since calculating results is no longer considered a human function but is a machine function. Very little of ‘math’ is involved, and none of the important ideas. We need to help writers for the layperson get this right, or risk future generations being doomed by the mythology.

More importantly, this article — like many (even in professional journals) — advocates the use of constructivist models for teaching mathematics. The basic constructivist idea is fine … learning involves constructing knowledge; I use quite a bit of this in my classes, with good results. However, the constructivist model flies in the face of cognitive psychology and decades of research; this model says that students ONLY learn when they construct knowledge by THEMSELVES. (This is ‘radical constructivism; a moderate approach removes the only and says ‘best’.) If you want to explore the details of how constructivism defies research and cognitive psychology, start with this summary: Applications and Mis-Applications of Cognitive Psychology to Mathematics Education (http://act-r.psy.cmu.edu/papers/misapplied.html ) This is one of my favorite articles of all time; nothing seen since its writing would require a change.

The truth is that learning happens in a variety of ways, some in spite of instructional design. As professionals, our job is to design instruction to produce the best quality learning for the most learning. Theory — and research — tells us that this will involve a combination of direction and student struggle. At no time have I seen research support the naive notion that novices can construct valid mathematics on their own OR with loosely guided activities. Although constructivist classes appear to be positive learning environments, that facade does not survive closer examination. Likewise, an “all telling” old-school lecture might have appeal for its clarity of message; this facade also fails when actual learning is examined.

No, we need to resist those telling us that there are simple answers — whether constructivist, Khan Academy, flipped, blended, co-requirsite, accelerated, modularized, or MOOC’d. Solutions involve addressing root problems; we should be more concerned with professional development and engagement than with simple-looking answers.

No, we need to provide a clear message. People in the United States are able to do significant mathematics with reasonable skill; procedural capabilities — arithmetic, algebraic, or other — are not generally present, and the question is “Does that present enough of a problem for us to ‘solve’?” Whether we are talking about ‘real-life’ or academic preparation, we need to focus on major needs of students; this will always result in a complex design, because there are no simple problems. The appearance of simple problems is an illusion caused by multiple salient features being ignored.

All of this is our joint responsibility. I look forward to seeing what YOU can do to help — in your neighborhood, your state, or nationally.

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