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Ashley Reiter, Maine School of Science and Mathematics, 77 High Street Limestone, ME 04750, reitera@mssm.lcs.k12.me.us
Although most students "learn to read" during their first year of primary school, or even before, reading is a skill which continues to develop through primary, secondary and post-secondary school, as the reading material becomes more sophisticated and as the expectations for level of understanding increase. However, most of the time spent deliberately helping students learn to read focuses on literary and historical texts. Mathematical reading (and for that matter, mathematical writing) is rarely expected, much less considered to be an important skill, or one which can be increased by practice and training.
Even as an undergraduate mathematics major, I viewed mathematical reading as a supplementary way of learning--inferior to learning by lecture or discussion, but necessary as a way of "filling in the gaps." Not until graduate school was I responsible for reading new material at a high level of comprehension. And, as I began to study primarily written mathematics (texts and articles) rather than spoken mathematics (lectures), I discovered that the activities and habits needed to learn from written mathematics are quite different from those involved in learning from a mathematics lecture or from those used in reading other types of text. As I consciously considered how to read mathematics more effectively and to develop good reading habits, I observed in my undergraduate students an uneasiness and lack of proficiency in reading mathematics.
In response to this situation, I wrote for my students (mostly math majors in Introductory Abstract Algebra at the University of Chicago) two handouts, one on reading theorems and the other on reading definitions. These describe some of the mental activities which help me to read mathematics more effectively. I also gave a more specific written assignment, applying some of these questions to a particular section of assigned reading. My hope was that, as they were forced to actively engage in reading, they would discover that reading mathematics could be a profitable pursuit, and that that they would develop habits which they would continue to use.
More than one such written exercise is needed to significantly affect the way that students view reading. While the students seemed to understand the types of questions that are helpful, they needed some practice in carrying these out, and even more practice using these activities in the absence of a written assignment.
A few questions to consider are:
Ask yourself (or the book) a few questions:
Let's apply this to an example, abelian groups:
Back to beginning of article Reading Theorems
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