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.
Beware of “Gaps” in Students’ Fraction Conceptions
Patrick L. Sullivan, Joann E. Barnett, and Kurt Killion
Let’s Give Them Something to Talk About
Nicola M. Hodkowski and Carolyn Carhart-Quezada
Different types of open tasks can be used as a tool to promote rigorous student mathematical discourse and considerations for facilitation.
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.
Adapt It! Adapting Stories and Technology for Engagement in Geometry
Karen L. Terrell, Dennis J. DeBay, and Valerie J. Spencer
A task to develop and provide access to mathematics for all.
Build It! The Rectangle Game
Theresa Wills, Jennifer Suh, Kate Roscioli, Amanda Guzman, Jennifer Everdale, and Sandra Lee
Discover technology-enhanced, game-based tasks and student generalizations.
Discuss It! Collaborating on the Tortoise and Hare Task
K. Ann Renninger, Maria Consuelo De Dios, Annie Fetter, Maeve R. Hogan, Moe Htet Kyaw, Ana G. Michels, Marina Nakayama, Richard Tchen, Stephen A. Weimar, Helena Werneck de Souza Dias, and Feven Yared
The authors share an online collaborative problem-solving activity that integrates support for students’ developing conceptual understanding, focused engagement, and positive feelings of agency and identity.
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.
Designing for Sensemaking of Research: The Mathematics District Leader Research Group
F. Paul Wonsavage
In this article, I share a design-based research intervention meant to help mathematics district leaders build their capacity to engage with research quality. I present my design (i.e., principles, key features, and intervention structure) and elaborate on how the features of the design allowed for mathematics district leaders’ sensemaking of educational research quality, especially regarding the process for collecting data and research implications. I conclude with recommendations for mathematics teacher educators on how they might adapt my design to their contexts.
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.
Using a Practical Measure to Support Inquiry Into Professional Development Facilitation
Hannah Nieman, Kara Jackson, Michael Jarry-Shore, Hilda Borko, Elham Kazemi, Starlie Chinen, Anita Lenges, Zuhal Yilmaz, and Cara Haines
Despite the complexity of facilitating professional development (PD) and growing attention to supporting facilitators, few tools exist for facilitators to engage in ongoing inquiry into their practice. In this article, we offer a practical measure, the Collaborative Professional Development Survey (CPDS), designed to provide facilitators with information about teachers’ perceptions of aspects of the PD learning environment that research indicates matter for teachers’ opportunities to learn. We illustrate how facilitators used the CPDS to support their collective inquiry into facilitation. We also illustrate the social processes that appeared to enable facilitators’ productive use of the CPDS, including a routine to analyze the resulting data, and the orientations that underpinned their analysis. We discuss implications for facilitators’ use of the CPDS.