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January 2015, Volume 46, Issue 1

FEATURES

EDITORIAL: Make This Your Year to Review
Cynthia W. Langrall
This editorial explores the importance of field contributions to the peer-review process of JRME.

RESEARCH COMMENTARY: Working at the Boundaries of Mathematics Education and Statistics Education Communities of Practice
Randall E. Groth
Statistics education has begun to mature as a discipline distinct from mathematics education, creating new perspectives on the teaching and learning of statistics. This Research Commentary emphasizes the importance of coordinating perspectives from statistics education and mathematics education through boundary interactions between the two communities of practice. The author argues that such interactions are particularly vital in shared problem spaces related to the teaching and learning of measurement, variability, and contextualized problems.

Two Perspectives on Proportional Relationships: Extending Complementary Origins of Multiplication in Terms of Quantities
Sybilla Beckmann and Andrew Izsák
The authors present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. They argue that (a) the distinction in perspectives is independent from other distinctions in the literature on proportional relationships, including the within measure space versus between measure space ratio distinction; (b) the psychological roots for multiplication suggest the accessibility of the two perspectives to learners; and (c) the fixed numbers of variable parts perspective, though largely overlooked in past research, may provide an important foundation for central topics that build on proportional relationships.

The Development of Children’s Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade
Maria Blanton, Ana Stephens, Eric Knuth, Angela Murphy Gardiner, Isil Isler, and Jee-Seon Kim
A study investigated the impact of a sustained, comprehensive early algebra intervention in third grade. The authors share and discuss students’ responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking.

Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking
Keith R. Leatham, Blake E. Peterson, Shari L. Stockero, and Laura R. Van Zoest
The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. The authors conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what they call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking.

BOOK REVIEW: Learning Important Mathematics From Contextualization and Networked Collaboration—A Review of The SimCalc Vision and Contributions
M. Kathleen Heid
A review of The SimCalc Vision and Contributions: Democratizing Access to Important Mathematics.