Mathematics

In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative  numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction.

Throughout elementary school, students learn about positive numbers and how they fit on a number line. The transition to using negative numbers, after only working with numbers greater than zero for several years, can be difficult for students (Murray 1985). The card game described here was used successfully with fifth graders; through the game, students explore the characteristics of numbers less than zero and how to add positive and negative numbers.

From a social semiotic perspective, students’ use of language is fundamental to mathematical meaning making. We applied thematic analysis to examine students’ use of geometric and contextual ideas while solving a geometry problem that required them to determine the optimal location for a new grocery store on a map of their local community. Students established semantic patterns to connect the problem context to geometry.

Given the current emphasis on the use of transformations for the teaching and learning of geometry, there is opportunity to consider how students’ understanding of geometric transformations can be used to build connections with interrelated concepts. We designed a sequence of three problems, collectively referred to as “the pottery lesson,” to elicit evidence of students’ understanding of reflections. We asked: What conceptions of reflection did students use while working on the pottery lesson?

Providing opportunities for learning through professional development requires the examination of facilitation of sessions with teachers. This study investigates facilitation of professional development to promote teacher learning when using animations and videos in a study group with five teachers. We ask: What practices (and moves within those practices) do the facilitators enact during high-quality conversations and specific to the professional development activities?

The literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments from episodes conducted during a teaching experiment grounded in the activity of iterating estimates of one person's equal share.

When teachers understand the key purposes for having students do mathematical writing, they can use that writing to deepen understanding.

This white paper clarifies different purposes elementary students might write in math class and presents four types of mathematical writing. We define "mathematical writing" as writing that encourages students to engage in mathematical reasoning and communication. Each writing type is defined, samples of student work are provided, and additional instructional considerations are addressed.

The authors report on an immersive mathematics professional development program facilitated by online technology that provides participants with the opportunity to do  mathematics for themselves and to reflect on that experience and its impact on their professional work. In particular, the article describes design principles for creating or running your own such professional development.