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November 2012, Volume 43, Issue 5

FEATURES

Some Thoughts on the Importance of the Community and on the Challenge of Identifying Great Research Challenges in Mathematics Education
M. Kathleen Heid
The importance of advancing the field of mathematics research is explored.

Aspects of Students’ Reasoning About Variation in Empirical Sampling Distributions
Jennifer Noll and J. Michael Shaughnessy
Sampling tasks and sampling distributions provide a fertile realm for investigating students’ conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Results suggest that teachers explicitly need to focus on multiple aspects of distributions, especially on variability, to enhance students’ reasoning about sampling distributions.

The Splitting Group
Anderson Norton and Jesse L. M. Wilkins
Piagetian theory describes mathematical development as the construction and organization of mental operation within psychological structures. Research on student learning has identified the vital roles 2 particular operations—splitting and units coordination—play in students’ development of advanced fractions knowledge. This article demonstrates the utility of modeling students’ development with a structure that is isomorphic to the positive rational numbers under multiplication—the splitting group.

Knowledge of Algebra for Teaching: A Framework of Knowledge and Practices
Raven McCrory, Robert Floden, Joan Ferrini-Mundy, Mark D. Reckase, and Sharon L. Senk
Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, an analysis of video, interviews with teachers, and an analysis of textbooks, the authors define categories of knowledge and practices of teaching for understanding and assessing teachers’ knowledge for teaching algebra. They argue that the combination of categories and practices must be covered in assessments of teacher knowledge, if the assessments are to be used in research that investigates the presumed links among teachers’ content preparation, their knowledge, their practice, and student learning.

Making Connections Among Student Learning, Content, and Teaching: Teacher Talk Paths in Elementary Mathematics Lesson Study
Aki Murata, Laura Bofferding, Bindu E. Pothen, Megan W. Taylor, and Sarah Wischnia
The authors investigated how elementary teachers in a mathematics lesson study made sense of student learning, teaching, and content, as related to using representations in teaching multidigit subtraction, and how changes occurred over time in their talk and practice.

Enhancing Students’ Mathematical Learning Through Focused Teacher Growth: A Review of Promoting Purposeful Discourse...
P. Janelle McFeetors
A review of Promoting Purposeful Discourse: Teacher Research in Mathematics Classrooms, edited by Beth Herbel-Eisenmann and Michelle Cirillo.

Acknowledgment

Individuals who have served as reviewers and guest editors for manuscripts submitted in 2011 are publicly acknowledged.

Index for JRME Volume 43

The index for JRME, volume 43, encompasses January, March, May, July, and November 2012 issues.