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March 2013, Volume 44, Issue 2

FEATURES

Editorial: JRME—A Stage for Scholarly Discourse
Cynthia W. Langrall, Tami S. Martin, Nerida F. Ellerton, Joshua T. Hertel, and Amanda L. Fain
An editorial that describes the many venues possible for engaging in scholarly discourse and how the field of mathematics education is served when data are shared.

Research Committee: New Assessments for New Standards: The Potential Transformation of Mathematics Education and Its Research Implications
NCTM Research Committee
The current era of common curriculum standards, increased accountability, and rapid expansion of technology within a complex and highly charged political context has influenced changes in assessment practices in mathematics classrooms. This research commentary situates high-stakes assessments in a historical context, discusses recent advances in assessment tools and related technologies, makes recommendations related to future research efforts, and outlines potential challenges and opportunities associated with these recommendations.

Research Commentary: Establishing Mathematics Education as an Academic Field: A Constructive Odyssey
Introduction: Frank K. Lester, Jr; Commentary: Leslie P. Steffe
Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts about his intellectual growth as a researcher, noting that “I have come to the realization that constituting mathematics education as an academic field entails constructing models of mathematical minds that are constructed by students in the context of mathematics teaching, beginning in early childhood and proceeding onward throughout the years of schooling.”

Playing Mathematical Instruments: Emerging Perceptuomotor Integration With an Interactive Mathematics Exhibit
Ricardo Nemirovsky, Molly L. Kelton, and Bohdan Rhodehamel
Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement the authors call perceptuomotor integration. Just as expertise in playing a piano relies on the interanimation of finger movements and perceived sounds, the authors argue that mathematical expertise involves the systematic interpenetration of perceptual and motor aspects of playing mathematical instruments.

Curriculum and Implementation Effects on High School Students’ Mathematics Learning From ... (more)
Douglas A. Grouws, James E. Tarr, Óscar Chávez, Ruthmae Sears, Victor M. Soria, and Rukiye D. Taylan
Curriculum and Implementation Effects on High School Students’ Mathematics Learning From Curricula Representing Subject-Specific and Integrated Content Organizations
This study examined the effect of 2 types of mathematics content organization on high school students’ mathematics learning while taking account of curriculum implementation and student prior achievement. Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.

On Mathematicians’ Proof Skimming: A Reply to Inglis and Alcock
Keith Weber and Juan Pablo Mejía-Ramos
In a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their initial reading of a proof took half as long as their total time spent reading that proof. Authors Keith Weber and Juan Pablo Mejía-Ramos present an analysis of Inglis and Alcock’s data that suggests that mathematicians frequently used an initial skimming strategy when engaging in proof validation tasks. See Inglis and Alcock’s response to Weber and Mejía-Ramos on pages 472-74. A download will include both articles.
Online Addition:
Inglis and Alcock 12FixPlots

Skimming: A Response to Weber and Mejía-Ramos
Matthew Inglis and Lara Alcock
In a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their initial reading of a proof took half as long as their total time spent reading that proof. Authors Keith Weber and Juan Pablo Mejía-Ramos present an analysis of Inglis and Alcock’s data that suggests that mathematicians frequently used an initial skimming strategy when engaging in proof validation tasks. See Inglis and Alcock’s response to Weber and Mejía-Ramos on pages 472—74. A download will include both articles.
Online Addition: Inglis and Alcock 12FixPlots.pdf