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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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.
References
Elmore, R. F. (2002). Bridging the gap between standards and achievement: The imperative for professional development in education. Washington, DC: The Albert Shanker Institute.
Fenstermacher, G. D. (1985). Determining the value of staff development. The Elementary School Journal, 85(3), 281–314.
Kohler, F. W., Crilley, K. M., Shearer, D. D., & Good, G. (1997). Effects of peer coaching on teacher and student outcomes. Journal of Educational Research, 90(4), 240–251.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States (2nd ed.). New York: Routledge.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-71207-9_3
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-319-71206-2
Online ISBN: 978-3-319-71207-9
eBook Packages: EducationEducation (R0)