Four Practices That Math Classrooms Could Do without

Abstract

While the big debates about mathematics instruction focus on the question of reform versus back basics, Mr. Fiori would like us consider a different question. Why does school mathematics bear so little resemblance the way practicing mathematicians think? ********** THE MATH classroom is, and probably always will be, a center of controversy. Teachers, mathematicians, and researchers may never come agreement on exactly how their beloved subject is be represented in school. That said, aren't we all making some obvious mistakes? contend that there are some practices, common nearly all math classrooms, that we can all agree simply must be done away with. Here are my four prime candidates. 1. Forty problems a night. Most of my mathematician friends and are only able solve about two problems a year--if we're lucky! Tell a mathematician you've solved even five problems in a single day, and the first thing she will think is, must not have been very interesting Outside of mathematics, does anyone you know ever get 40 things done in a day? Even the mundane problems of our life don't get packaged away that quickly. My daily to lists rarely contain more than eight items, and by the end of the day I'm fortunate if I'm through half of them. Let's cool it with the daily deluge of exercises and reconsider the quality of the problems that can be completed at a rate of 40 per night. 2. The third-person czars of math problems. A strange, anonymous set of people are constantly referred in math classrooms. We frequently hear teachers and students ask such questions as What do you think they mean in problem number 4? or What do they want us write as an answer? The responses follow suit: I think what they're looking for is an expression for x in terms of k. Who are these people? They don't seem be the teacher, and they certainly aren't the students. Are they the authors of the textbook? Or are they the faceless people who invented or discovered mathematics in the first place? How do we know that there are more than one of them? All of these questions leave me in a panic. It can't be healthy for a subject be controlled by a bunch of nameless cronies. Aside from a few pictures, the sidebars, and an occasional name attached a theorem, there are no actual people in math books. This is true of elementary workbooks, high school texts, and even most college mathematics books. …