Mathematics

In this article, we describe the experiences of three Elementary Mathematics Specialists (EMS) who were part of a larger project investigating the impact of EMS certification and assignment (self-contained or “departmentalized”) on teaching practices and student achievement outcomes. All three of the teachers were “departmentalized,” in the sense that each was responsible for teaching mathematics to at least two groups of students, and accordingly, did not teach all subjects as would a typical self-contained elementary teacher.

Researchers and educators agree: Children demonstrate a clear readiness to engage in science, technology, engineering, and math (STEM) learning early in life. And, just as with language and literacy, STEM education should start early in order to maximize its benefits and effectiveness. So why is STEM not woven more seamlessly into early childhood education? What can we do – in the classroom, in homes, in museums, in research labs, and in the halls of legislating bodies – to ensure that all young children have access to high-quality STEM learning early in life?

This study investigates the models of elementary content specialization (ECS) in elementary mathematics and science and the affordances and constraints related to ECS—both generally and in relation to specific models. Elementary content specialists are defined as full-time classroom teachers who are responsible for content instruction for two or more classes of students. The sample consists of 34 elementary content specialists in math and/or science, as well as a matched comparison group of self-contained classroom teachers.

Noticing students' mathematical thinking is a key element of effective instruction, but novice teachers do not naturally engage in this practice. Prospective secondary school mathematics teachers were engaged in an intervention grounded in analysis of minimally edited video from local secondary school mathematics classrooms; the goal was to support their ability to notice important student thinking within the complexity of instruction.

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.