Talk:Word Problems in Math
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Contribution by (DSinCA) (11-3-09)
My sense is that you are over-reaching in some of your claims. For example, when you write "Each discipline develops some special ... symbols," I found myself wondering what the special symbols are in a discipline like English. I agree that the alphabet contains symbols, but use of the alphabet is not specific to English. Perhaps I've misunderstood what you mean by "special." I had never before seen the phrase "content pedagogical knowledge." The phrase that I am familiar with is "pedagogical content knowledge." I do not know why some people are using the former phrase -- whether they are using it to mean something different from "pedagogical content knowledge" (and if so, what it means) or if they mean the same thing by both phrases but on rare occasions have some grammatical reason for changing the order of the words in the phrase (e.g., perhaps they are comparing standard pedagogical knowledge and pedagogical knowledge that's discipline-specific). If you do a Google search, you'll find that "pedagogical content knowledge" is the standard term. My sense is that this is not a phrase used by most educators, but rather is a phrase used by a subset of educational researchers -- those who carry out research on knowledge for teaching. The construct of pedagogical content knowledge refers to knowledge, not methodologies. Not all teachers in a given discipline develop significant pedagogical content knowledge in that discipline. An example of pedagogical content knowledge in mathematics is a sensitivity to the different ways in which the equal sign is used (e.g., in equations to be solved, in identities, and in the definitions of functions). Skilled users of math need to be able to move among these different interpretations, but they don't have to be able to articulate what the different uses are, whereas skilled teachers need to recognize the different uses more explicitly, as these different uses often cause difficulties for students, and because one has a choice about which use to introduce students to first.
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Example: Comment by David Moursund 10/11/09
All math word problems are not created equal. Some are much better teaching and learning aids or vehicles than others. It would be nice to have a large collection of "good" math word problems suitable for use by students with varying levels of math background and math maturity.
