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March 2010, Volume 41, Issue 2

FEATURES

Editorial: Where's the Math (in Mathematics Education Research)?
M. Kathleen Heid
Twenty-five years ago, a fast-food TV ad initiated a catchphrase, “Where’s the beef?” The phrase evolved into a way to question the amount or substance of an idea or product. It is now time for the phrase to make its way into discussions about mathematics education research.

Nonstandard Student Conceptions About Infinitesimals
Robert Ely
A case study of an undergraduate calculus student’s nonstandard conceptions of the real number line. Interviews with the student reveal robust conceptions of the real number line that include infinitesimal and infinite quantities and distances. Similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated by the formalization of infinitesimals in A. Robinson’s nonstandard analysis. These similarities suggest that these student conceptions are not mere misconceptions, but are nonstandard conceptions, pieces of knowledge that could be built into a system of real numbers proven to be as mathematically consistent and powerful as the standard system.

Using Propensity Scores to Reduce Selection Bias in Mathematics Education Research
Suzanne E. Graham
This article describes general principles underlying propensity score methods and illustrates their application to mathematics education research using 2 examples investigating the impact of problem-solving emphasis in mathematics classrooms on students’ subsequent mathematics achievement and course taking. Selection bias is a problem for mathematics education researchers interested in using observational rather than experimental data to make causal inferences about the effects of different instructional methods in mathematics on student outcomes. Propensity score methods represent 1 approach to dealing with such selection bias. Limitations of the method are discussed.

Professional Noticing of Children’s Mathematical Thinking
Victoria R. Jacobs, Lisa L. C. Lamb, and Randolph A. Philipp
The construct professional noticing of children’s mathematical thinking is introduced as a way to begin to unpack the in-the-moment decision making that is foundational to the complex view of teaching endorsed in national reform documents. The authors define this expertise as a set of interrelated skills including (a) attending to children’s strategies, (b) interpreting children’s understandings, and (c) deciding how to respond on the basis of children’s understandings. The findings help to characterize what this expertise entails; provide snapshots of those with varied levels of expertise; and document that, given time, this expertise can be learned.