Abstract
In this article, we describe a framework and instrument for measuring the mathematical quality of mathematics instruction. In describing this framework, we argue for the separation of the mathematical quality of instruction (MQI), such as the absence of mathematical errors and the presence of sound mathematical reasoning, from pedagogical method. We argue that conceptualizing this key aspect of mathematics classrooms will enable more clarity in mathematics educators’ research questions and will facilitate study of the mechanisms by which teacher knowledge shapes instruction and subsequent student learning. The instrument we have developed offers an important first step in demonstrating the viability of the construct.
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Notes
Atweh et al. (2003) observe that during the last two decades reform ideas in the U.S. and England travelled as far as Australia and some East Asian countries. Other scholars also trace the impact of reform ideas—and particularly the four process standards outlined in the NCTM 1989 document (i.e., problem solving, communication, reasoning, and connections)—on the mathematics education of countries in Europe and the Middle East (cf. Amit and Fried 2002; Boaler 2002; Christou et al. 2009; Jones et al. 2002; Tirosh and Graeber 2003).
The glossary, giving the criteria for our codes, can be found at: www.sitemaker.umich.edu/lmt.
In the measurement community, constructs refer to the underlying trait or phenomena one wishes to measure; scales are the tools for measuring constructs.
We are currently piloting a set of codes that capture student’s interactions with mathematical content—for instance, whether they provide mathematical explanations, ask mathematical questions, or make mathematical claims.
The explicit talk about the meaning and use of mathematical language code only has two options: “present” or “not present.”
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Acknowledgments
This research was funded by NSF grants REC-0207649, EHR-0233456, and EHR-0335411.
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During the time this article was written, the Learning Mathematics for Teaching project consisted of Heather C. Hill, Deborah Loewenberg Ball, Hyman Bass, Merrie Blunk, Katie Brach, Charalambos Y. Charalambous, Yaa Cole, Carolyn Dean, Seán Delaney, Sam Eskelson, Imani Masters Goffney, Jennifer M. Lewis, Geoffrey Phelps, Laurie Sleep, Mark Thames and Deborah Zopf.
Appendix A
Appendix A
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1.
Imagine that you are working with your class on multiplying large numbers. Among your students’ papers, you notice that some have displayed their work in the following ways:
Which of these students would you judge to be using a method that could be used to multiply any two whole numbers? (Fig. 2).
Three solutions to 35 × 25
Method would work for all whole numbers | Method would NOT work for all whole numbers | I’m not sure | |
|---|---|---|---|
(a) Student A | 1 | 2 | 3 |
(b) Student B | 1 | 2 | 3 |
(c) Student C | 1 | 2 | 3 |
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Learning Mathematics for Teaching Project. Measuring the mathematical quality of instruction. J Math Teacher Educ 14, 25–47 (2011). https://doi.org/10.1007/s10857-010-9140-1
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DOI: https://doi.org/10.1007/s10857-010-9140-1