Translating Learning Trajectories Into Useable Tools for Teachers

Abstract

Mathematics teacher educators play a critical role in translating research findings into frameworks that are useful for mathematics teachers in their daily practice. In this article, we describe the development of a representation that brings together four research-based learning trajectories on number and operations. We detail our design process, present the ways in which we shared this representation with teachers during a professional development project, and provide evidence of the ways teachers used this translation of research into a pedagogical tool to make sense of students' mathematics. We conclude with revisions to the representation based on our analysis and discuss the role of mathematics teacher educators in translating research findings into useful tools for teachers.

Enhancing Noticing: Using a Hypothetical Learning Trajectory to Improve Pre-service Primary Teachers’ Professional Discourse

“…On the other hand, teachers may find it easier to notice relevant instructional details when given a focus point (Choy, Thomas, & Yoon, 2017). Therefore, structured frameworks, such as hypothetical learning trajectories, could provide pre-service teachers with a way to focus their attention on students' thinking (Edgington, 2014;Edgington, Wilson, Sztajn, & Webb, 2016).…”

“…Nickerson et al (2017) claimed that "meaningfully analysing responses of interpreting and deciding how to respond to students' mathematical ideas requires knowledge of students' possible learning trajectories" (p. 393). For example, with the aim of developing learning activities to support students in constructing more sophisticated ways of reasoning, pre-service teachers can use hypothetical learning trajectories to focus their attention on how students think about a target concept (Edgington, 2014;Edgington et al, 2016). In some ways, a hypothetical learning trajectory functions as a kind of roadmap to support teachers in identifying learning goals, interpreting students' mathematical thinking and responding with appropriate instruction (Sztajn, Confrey, Wilson, & Edgington, 2012).…”

“…As highlighted by Edgington et al (2016), hypothetical learning trajectories can provide pre-service teachers with a specific language to describe students' thinking. This language can allow pre-service teachers to create a system for picking out, classifying and naming elements of students' thinking (Wells, 1999) that can help them to identify, interpret and make instructional decisions.…”

A Learning Trajectory as a Scaffold for Pre-service Teachers’ Noticing of Students’ Mathematical Understanding

“…One of the objectives of research on learning trajectories is to make LTs into usable tools for teachers (Daro et al, 2011). To do so, mathematics teacher educators must "use their understandings of the goals and context of both the research and teaching communities to represent findings from research in ways that are meaningful and useful for teachers" (Edgington et al, 2016). This way of working (transforming learning trajectories into usable tools for teachers) has special implications in our present context in which PTs have little opportunity to put their theoretical knowledge into practice in teaching situations.…”

Investigación en educación matemática : [actas del XXI Simposio de la Sociedad Española de Investigación en Educación Matemática : Zaragoza, 6-9 de septiembre de 2017]

“…Estos estudios han mostrado que esta competencia puede ser desarrollada por los estudiantes para maestro en los programas iniciales de formación, aunque esta no es una tarea sencilla sin unas referencias que guíen qué y cómo mirar (Levin, Hammer y Coffey, 2009;Schack et al, 2013;Tyminsky, Land, Drake, Zambak y Simpson, 2014;Wilson, Sztajn, Edgington, y Confrey, 2014). En este sentido, investigaciones recientes han mostrado que las trayectorias de aprendizaje de los conceptos matemáticos son un instrumento capaz de ayudar a los maestros a focalizar la atención sobre aspectos relevantes en las respuestas de los estudiantes e interpretar su pensamiento matemático (Edgington, Wilson, Sztajn, y Webb, 2016;Sztajn, Confrey, Wilson y Edgington, 2012;.…”