Contact the Editor

1 Response to Contact the Editor

1. Zeev Wurman says:

   September 18, 2019 at 3:24 pm

   Dear Editor,

   Yesterday (9/17/19) I have submitted the comment below to the recent AMS blog entry (Pre-Service Mathematics for Elementary (and Secondary) Teachers), yet for some reason it seems to have disappeared into the void. Could you please figure out what has happened? I don’t think I violated any rule with my comment.

   Sincerely, Ze’ev Wurman
   ——————–
   I find the first example of fourth-grade teaching nice and convincing. Learning what to leave out is important in teaching, but it strongly relies on the level of the learner. For accomplished learners, throwing in additional albeit peripheral terms or concepts (correctly defined!) might be fun and broaden the horizon. But don’t try to do it when the the topic is barely introduced.

   I found the number line example and discussion, however, meaningless and lacking purpose. There are many things one can do on a number line, and all of them will give some kind of patterns. Are those patterns meaningful for instruction? Yes, if they can be analyzed and “explained.” Not really, if they serve just to entertain. This example could be the former for students in late middle school to illustrate formulae such as (a+b)(a-b), but is the latter for fourth grade students in here.

   The high school example of graphing, if taught the way described, is indeed deficient. Yet is graphing linear equations commonly taught in such mechanical and mindless way? I doubt it. After all, asking whether a point lies on a line is just another sub-category of teaching linear equations similar to graphing a line using a slope-intercept formula, or deriving the formula of a line crossing two given points. Any half-decent textbook addresses all those sub-categories, and testing for all of them–even in a simple multiple-choice format– is pretty easy and routine. Seems to me the authors here are generalizing based on observing a badly taught class.

   Finally, I do agree that strong focus on terminology and formalism, particularly in early grades, if counter-productive. I also agree that all too often teachers incorrectly feel they are not sufficiently “mathematical” if they do not enforce them. Using common–but precise–jargon-free language in early grades would probably go a long way to curing children from disliking mathematics, and it would be wonderful if schools of education paid attention to it. Unfortunately, it seems few ed-school professors seem actually know, let alone teach, the use of precise but jargon-free mathematical language.

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