Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist matsshematics teacher educators in designing their courses to maximize their instructional time.
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Evthokia Stephanie Saclarides, Brette Garner, Gladys Krause, Claudia Bertolone-Smith, and Jen Munson
A. Susan Gay, Jeanine Haistings, and Jason L. Rucker
The authors describe a fourth-grade lesson that promotes understanding of angle as a dynamic figure through use of a real-world tool used by physical therapists to measure joint motion.
Susanne Prediger, Kirstin Erath, Henrike Weinert, and Kim Quabeck
Empirical evidence exists that enhancing students’ language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (N = 589) investigates differential effects for these extended target groups, comparing two language-responsive interventions (with or without vocabulary work) and a control group. The regression analysis reveals that all students significantly deepened their conceptual understanding in both interventions. Unlike what was anticipated, multilingual students’ growth of conceptual understanding had no significant additional benefit from integrated vocabulary work. These findings call for promoting language-responsive mathematics instruction for all students and for using a discursive rather than a vocabulary focus.
Cynthia E. Taylor, Christa Jackson, and Kelley Buchheister
A third grade teacher uses the What component in the What-How-Who structure to create a mathematical task from a culturally rich book.
Luz A. Maldonado Rodríguez, Naomi Jessup, Marrielle Myers, Nicole Louie, and Theodore Chao
Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by , ) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.
Daniel Frischemeier
Bar graphs are fundamental to display distributions of categorical variables in primary school. Here is an approach using TinkerPlots™ to create bar graphs on different representation levels in small and large data sets.
Mindy Kalchman
Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.
Madelyn W. Colonnese
A teacher implements this type of personal prose in the classroom to help students make sense of fractions and communicate ideas.
Sandra Vorensky
Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.
Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen
An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.
