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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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Making Black Girls Count in Math Education

Nicole M. Joseph

The author shares an experience she had as a mathematics learner, which became the catalyst for her work as a mathematics education researcher. She discusses the issues that Black girls face in our math classrooms and offers potential solutions for partnering with Black girls.

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Exploring Young Children’s Math Thinking in Sandcastle Building

Hannah Tan and Cynthia Lim

Children explore concepts of capacity and height measurement through sand play in nursery class.

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Ways to Help Students Become Powerful Mathematical Thinkers

Alan H. Schoenfeld

Ear to the Ground features voices from several corners of the mathematics education world.

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Construct It! Triangle Puzzle Challenges

Enrique Ortiz

This article presents an original puzzle that supports students’ development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought.

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Model It! Building and Sustaining Cultural Traditions with Ethnomodeling

Siddhi Desai and Farshid Safi

This geometric transformation-focused ethnomodeling respects individual and collective community experiences and moves toward educational experiences that acknowledge and celebrate the multidimensional aspects related to identity.

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Characterizing Secondary Teachers’ Structural Reasoning

Stacy Musgrave, Cameron Byerley, Neil Hatfield, Surani Joshua, and Hyunkyoung Yoon

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

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Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers

Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin

In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.

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“Mathematics: The Universal Language?”

Sharon B. Hoffert and Introduction by: Candies Cook

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

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Translanguaging Pedagogy in Elementary Mathematics

Tara M. Willging and Luciana C. de Oliveira

A monolingual English-speaking teacher reflects on her experiences practicing a translanguaging stance in first grade with two multilingual learners and provides a set of guiding principles.