Keywords: Standards, ,
Ref: Beth1
Author(s): Masingila, Joanna O.
Date: 1998
Title: Thinking Deeply About Knowing Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 91, 7, 610-614
Reviewer: Beth
Date of Review: 2-24-02
This article was written for the section of “Implementing the Professional Standards for Teaching Mathematics.” The author outlines her case for the necessity of teachers of mathematics to think deeply about “knowing mathematics,” or in other words, “prospective teachers of mathematics need to (a) think deeply about what it means to know mathematics and (b) think deeply about their own understanding of fundamental ideas.” Using her class of prospective secondary math teachers as examples, she presents problems aimed at determining their level of knowing math and being able to effectively communicate mathematical concepts without necessarily using equations. For example, she had them describe how to create an ellipse based on the definition of an ellipse and not the equation. She also has examples using fractions, prime factorization and functions. Overall, the article attempts to show that being able to teach math involves both conceptual and procedural knowledge.
I agree that in order to teach mathematics effectively, you need to be willing to understand it at a deep level. On that note, I like the examples she uses; they force her students, and the reader, to think about how one uses words and analyzes a problem. One of my only questions is how we are to implement the changes necessary for teachers to have the time to develop this deeper knowledge and understanding of math.