# Journal for Research in Mathematics Education

An official journal of the National Council of Teachers of Mathematics (NCTM), JRME is the premier research journal in mathematics education and is devoted to the interests of teachers and researchers at all levels--preschool through college.

## Using Moment-by-Moment Reading Protocols to Understand Studentsâ€™ Processes of Reading Mathematical Proof

This article documents differences between novice and experienced undergraduate studentsâ€™ processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novicesâ€™ reading differed from that of their experienced peers: alternative task models, accrual of premises, and warranting. Alternative task models refer to the types of goals that students set up for their reading of the text, which may differ from identifying and justifying inferences. Accrual of premises refers to the way novice readers did not distinguish propositions in the theorem statement as assumptions or conclusions and thus did not use them differently for interpreting the proof. Finally, we observed variation in the type and quality of warrants, which we categorized as illustrate with examples, construct a miniproof, or state the warrant in general form.

## Undergraduate Studentsâ€™ Combinatorial Proof of Binomial Identities

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were important for their success with establishing combinatorial arguments; in particular, the students demonstrated referential symbolic reasoning within an enumerative representation system, and as the students engaged in successful combinatorial proof, they had to coordinate reasoning within algebraic and enumerative representation systems. We illuminate features of the studentsâ€™ work that potentially contributed to their successes and highlight potential issues that students may face when working with binomial identities.

## The Cultural Production of Racial Narratives About Asian Americans in Mathematics

Although considerable literature illustrates how studentsâ€™ experiences and identities are racialized in mathematics education, little attention has been given to Asian American students. Employing ethnographic methods, this study followed 10 immigrant Chinese-heritage families to explore how the racial narrative of the model minority myth was locally produced in mathematics education. We draw on constructs of racial narratives and cultural production to identify the local production of the narrative Asians are smart and good at math during Kâ€“12 schooling. Specifically, the Asian American students (re)produced racial narratives related to three cultural resources: (a) Their immigrant parentsâ€™ narratives about the U.S. elementary school mathematics curriculum; (b) the school mathematics student tracking system; and (c) studentsâ€™ locally generated racial narratives about what being Asian means.

## Acknowledgment

The Journal for Research in Mathematics Education is published online five times a year—January, March, May, July, and November—at 1906 Association Dr., Reston, VA 20191-1502. Each volume’s index is in the November issue. JRME is indexed in Contents Pages in Education, Current Index to Journals in Education, Education Index, Psychological Abstracts, Social Sciences Citation Index, and MathEduc.

An official journal of the National Council of Teachers of Mathematics (NCTM), JRME is the premier research journal in mathematics education and is devoted to the interests of teachers and researchers at all levels--preschool through college. JRME presents a variety of viewpoints. The views expressed or implied in JRME are not the official position of the Council unless otherwise noted.

JRME is a forum for disciplined inquiry into the teaching and learning of mathematics. The editors encourage submissions including:

• Research reports, addressing important research questions and issues in mathematics education,
• Brief reports of research,
• Research commentaries on issues pertaining to mathematics education research.

Editorial Board

The JRME Editorial Board consists of the Editorial Team and Editorial Panel.  The Editorial team, led by JRME Editor Patricio Herbst, leads the review, decision and editorial/publication process for manuscripts.  The Editorial Panel reviews manuscripts, sets policy for the journal, and continually seeks feedback from readers. The following are members of the current JRME Editorial Board.

Editorial Staff

 Patricio Herbst University of Michigan; Editor Sandra Crespo Michigan State University; Associate Editor Percival Matthews University of Wisconsin - Madison; Associate Editor Erin Lichtenstein University of Michigan; Assistant Editor Michael Ion University of Michigan; Editorial Assistant Daniel Chazan University of Maryland; Research Commentary Editor

Editorial Panel

 Nicole M. Joseph Vanderbilt University; Chair Jennifer Suh George Mason University; Board of Directors Liason Jonathan D. Bostic Bowling Green State University Tutita Casa University of Connecticut Teddy Chao Ohio State University Toya Frank George Mason University Amanda Jansen University of Delaware Karl Kosko Kent State University Ami Mamolo Ontario Tech University Kate Melhuish Texas State University Eva Thanheiser Portland State University Jamaal Young Texas A&M University William Zahner San Diego State University David E. Barnes NCTM, Reston, Virginia; Staff Liaison

 Lara Alcock England Sigrid Blömeke Norway Ghislaine Gueudet France Oh Nam Kwon South Korea Thomas Lowrie Australia

 David E. Barnes Associate Executive Director Ken Krehbiel Executive Director Scott Rodgerson Director of Publications and Creative Services Tristan Coffelt Production Manager

The editors of the Journal for Research in Mathematics Education (JRME) encourage the submission of a variety of manuscripts. Manuscripts must be submitted through the JRME Online Submission and Review System

Research Reports

JRME publishes a wide variety of research reports that move the field of mathematics education forward. These include, but are not limited to, various genres and designs of empirical research; philosophical, methodological, and historical studies in mathematics education; and literature reviews, syntheses, and theoretical analyses of research in mathematics education. Papers that review well for JRME generally include these Characteristics of a High Quality Manuscript. The editors strongly encourage all authors to consider these characteristics when preparing a submission to JRME

The maximum length for Research Reports is 13,000 words including abstract, references, tables, and figures.

Brief Reports

Brief reports of research are appropriate when a fuller report is available elsewhere or when a more comprehensive follow-up study is planned.

• A brief report of a first study on some topic might stress the rationale, hypotheses, and plans for further work.
• A brief report of a replication or extension of a previously reported study might contrast the results of the two studies, referring to the earlier study for methodological details.
• A brief report of a monograph or other lengthy non-journal publication might summarize the key findings and implications or might highlight an unusual observation or methodological approach.
• A brief report might provide an executive summary of a large study.

The maximum length for Brief Reports is 5,000 words including abstract, references, tables, and figures. If source materials are needed to evaluate a brief report manuscript, a copy should be included.

Correspondence regarding manuscripts for Research Reports or Brief Reports should be sent to:

Patricio Herbst, JRME Editor, jrme@nctm.org

Research Commentaries

JRME publishes brief, peer-reviewed commentaries on issues pertaining to mathematics education research. Research Commentaries differ from Research Reports in that their focus is not to present new findings or empirical results, but rather to comment on issues of interest to the broader research community.  Commentaries are intended to engage the community and increase the breadth of topics published in JRME

Topics for this section may include, but are not restricted to:

• Discussion of connections between research and Principles to Actions
• Commentaries on research methods
• Discussions of connections between research, policy, and practice
• Analyses of trends in policies for funding research
• Examinations of evaluation studies
• Critical essays on research publications
• Commentaries or interpretations of previously published research in JRME that bring insights from an equity lens
• Exchanges among scholars holding contrasting views about research-related issues

The maximum length for Research Commentaries is 5,000 words including abstract, references, tables, and figures.

Correspondence regarding Research Commentary manuscripts should be sent to:

Daniel Chazan, JRME Research Commentary Editor, dchazan@umd.edu

Tools for Authors

The forms below provide information to authors and help ensure that NCTM complies with all copyright laws

Student Work Release