Research on teaching mathematics document

May 12th, 2015
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RESEARCH ON TEACHING MATHEMATICS:*MAKING SUBJECT MATTER KNOWLEDGE PART OF THE EQUATION**Deborah Loewenberg BallIntroductionSubject matter understanding and its role in teaching mathematics are the focus of this paper.Although few would disagree with the assertion that, in order to teach mathematics effectively, teachersmust understand mathematics themselves, past efforts to show the relationship of teachers' mathematicalknowledge to their teaching of mathematics have been largely unsuccessful. How can this be? Mypurpose here is to unravel this intuitively indisputable yet empirically unvalidated requirement ofteaching by revisiting what it means to "understand mathematics" and the role played by suchunderstanding in teaching.The thesis of this paper is that teachers' subject matter knowledge interacts with theirassumptions and explicit beliefs about teaching and learning, about students, and about context to shapethe ways in which they teach mathematics to students. There are three parts to the development of thisargument. First, I briefly analyze past investigations of the role of teachers' subject matter knowledge inteaching mathematics. Next, I unpack the concept of subject matter knowledge for teachingmathematics and illustrate what is entailed in finding out what teachers know. The last section presentsthree cases of teaching multiplication and analyzes how each teacher's understanding of mathematicsfigures in her teaching.To provide a context, I b

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