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Mathematical Habits of Mind for Teaching

Abstract

This paper addresses the following claim(s):

"Rather than claims and conjectures, we have questions. For example, for decades, researchers have claimed that strong teacher content knowledge is a prerequisite for increased student achievement. Over the years, the claim has been refined, both in the nature of the specialized content knowledge used by teachers and in the characterization of genuine student achievement. Focus on Mathematics (and before it, PROMYS for Teachers) is built on the premise that an immersion experience in mathematics and participation in a mathematical community that involves practicing mathematicians helps teachers develop the habits of mind that are common among mathematicians, and we have some evidence that this is the case. But the question remains: how do these habits of mind get customized and used in the profession of secondary teaching? We have some conjectures and even some hopes, but no solid answers. The goal of our Phase II research study is to look more deeply into the effects of "thinking like a mathematician'' on the work of middle and high school teachers (see [20] for an example of this)."