After reading the article, I would say I agree on using the necessary style most of the time, with limited implementations of arbitrary style to some of the unusual students.
As someone who had been soaked in mathematical terms, definitions, and conventional descriptions for many years, many math teachers who got their qualifications with degrees in related areas can easily take their communication style as second nature. Carrying forward, they overlook the difficulties behind learning the "new language" of math for many beginners or uninterested students. The fact they are used to communicating in formal math language sometimes makes it impossible for these teachers to communicate with students through a beginner's mind, where math should be viewed as applicable tools or new languages to be learned from scratch.
In this sense, the necessary style is good at forcing teachers to review how to converse the images and logics in their head to other minds that require clear definition and descriptions. Familiarizing one self with this style can be beneficial, or even fundamental in teaching math to beginners. There might be some unusual minds who can benefit from arbitrary teaching style, but based of my observation I believe many would appreciate the necessary style.
I really appreciate you highlighted how common it may be for math teachers to forget the difficulty in the language of math rather than the calculations.
ReplyDeleteOne thing you might explore further is how you’d operationalize that in your own classroom — what it actually looks like when you consciously shift out of “expert mode” and into beginner language. You’ve got the insight; now I’m curious how you’d turn it into practice.