Abstract
This chapter presents findings on teachers’ and mathematics coaches’ understanding of two mathematical topics: subtraction with regrouping and multi-digit multiplication. These two standard topics in elementary mathematics involve an understanding of the concept of place value. The two topics are purposely chosen because they provide us with a glimpse of respondents’ understanding of a basic mathematical concept (i.e., place value) and its application in two elementary mathematical topics. Newton’s analysis shows that as simple as these two mathematical topics may seem to be, the depth of understanding that is required in order to teach effectively (or teach well) is not as simple as we may think and teachers and mathematics coaches do not necessarily have the depth of content understanding of these two foundational mathematical topics.
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- 1.
This scenario question was used by Liping Ma (1999, p. 1) in her investigation of Chinese and American teachers’ understanding of elementary mathematics topics.
- 2.
This question was adapted from the question that Liping Ma (1999, p. 28) used to investigate Chinese and American teachers’ understanding of elementary mathematics topics.
- 3.
Eighteen elementary and 16 secondary.
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Newton, X.A. (2018). Teachers’ and Math Coaches’ Understanding of Basic Mathematical Ideas. In: Improving Teacher Knowledge in K-12 Schooling. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-71207-9_3
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DOI: https://doi.org/10.1007/978-3-319-71207-9_3
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Publisher Name: Palgrave Macmillan, Cham
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Online ISBN: 978-3-319-71207-9
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