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Beware of “Gaps” in Students’ Fraction Conceptions

Patrick L. Sullivan, Joann E. Barnett, and Kurt Killion

Many students have a dominant part-whole conception of fractions. We examine why this is problematic and explore strategies to move students beyond this limitation.

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“Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes

Liza Bondurant and Daniel Reinholz

This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates mixed-reality simulations of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.

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Exploring Grades 3–5 Mathematics Activities Found Online

Lara K. Dick, Amanda G. Sawyer, Margaret MacNeille, Emily Shapiro, and Tabitha A. Wismer

We investigate resources on TeachersPayTeachers and discuss how what is available affects our teaching practices.

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What Can the Realization Tree Assessment Tool Reveal About Explorative Classroom Discussions?

Merav Weingarden and Einat Heyd-Metzuyanim

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.

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Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework

Gwyneth Hughes, Michele B. Carney, Joe Champion, and Lindsey Yundt

Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students’ opportunities to struggle, have been consistently linked to improving students’ mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of professional development (PD) offerings. We describe three examples of how the framework is used to support teacher learning and classroom instructional practice: a state-mandated course, lesson studies, and a large-scale teacher–researcher alliance. Initial findings suggest that consistently emphasizing this framework provides both content and structural guidance during PD development and gives coherence and focus to teachers’ PD experiences.

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Designing Rehearsals for Secondary Mathematics Teachers to Refine Practice

Jared Webb and P. Holt Wilson

ABSTRACT

In this article, we describe rehearsals designed for use in professional development (PD) with secondary mathematics teachers to support them in reimagining and refining their practice. We detail a theoretical framework for learning in PD that informs our rehearsal design. We then share evidence of secondary mathematics teachers’ improvements in classroom practice from a broader study examining their participation in a PD that featured the use of rehearsals and provide examples of the ways two teachers’ rehearsals of the practice of monitoring students’ engagement with mathematics corresponded to changes in their practice. We conclude with a set of considerations and revisions to our design and a discussion of the role of mathematics teacher educators in supporting teachers in expanding their practice toward more ambitious purposes for students’ mathematical learning.

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Puddle Play!

Deanna Pecaski McLennan

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The Power of Sharing the History of Mathematics

Mark Cox

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Math Medley

Dane Camp, John Carter,, and David Masunaga

Song parodies are a fun way to engage others with mathematical topics. The challenge, of course, is finding a song and lyrics that fit just right. While teaching together in Honolulu, we stumbled across a popular song that turned out to be a math parody in disguise! You will notice that we have not changed the words, just how the words were displayed. You might want to try singing this yourself or sing along with the YouTube version: https://youtu.be/d1mqNdZ0obA. What do you notice? What do you wonder?

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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. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.