Knowledge of Subject Easily Trumps “Good Pedagogy”

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Picking on a small excerpt from any author’s work is easy to do. Liping Ma wrote an excellent book titled Knowing and Teaching Elementary Mathematics where she compares mathematical understanding among U.S. and Chinese elementary school teachers as it relates to classroom teaching practices.

Liping became an elementary school teacher as a consequence of the cultural revolution. She ended up in a mathematics doctoral program at Stanford University in the United States. She did postdoctoral work at Berkeley and her dissertation constitute the substance of her magnum opus Knowing and Teaching Elementary Mathematics.

I interpret her work as a very just criticism of teachers who only have a superficial knowledge of procedures and rules. A concrete example of only having superficial knowledge of a procedure would be the calculus teacher who knows to instruct his students to set the derivative equal to zero to locate maximum or minimum values of a function, BUT does not realize these are the locations of horizontal tangent lines on the graph of the function. This sort of thing is all too common in USA schools!

The picture you see below is the title of a section in her book where she actually has to pose the ludicrous question : Can pedagogical knowledge make up for ignorance of the concept? Translated in a much less civilized manner: Can a Dumbass with good teaching skills still teach a subject he does not know?

The answer, of course, is Hell No! Liping Ma, politely, collected data to answer a question with an obvious answer. A sad state of affairs in the United States is there are countless teachers who are “well-trained and certified , i.e have good pedagogical practices” , but do not have an acceptable understanding of the subject matter they are teaching. No amount of Pedagogical Acumen can make up for Content Ignorance.

Knowing and Teaching Elementary Mathematics
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