Foregrounding and Backgrounding Mathematical Practices to Support English Learners

• In Event: Understanding the Implications of the Common Core Mathematical Practice Standards for English Learners: An Interactive Symposium

Abstract

Objective
This paper investigates how three middle school mathematics teachers developed two of the Mathematical Practices (MPs) of the Common Core State Standards – Mathematics (CCSS-M) (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010) to support English learners’ (ELs’) development of language and mathematics. In particular, this paper attends to the ways participating teachers supported ELs to develop expertise related to MP.1, Make sense of problems and persevere in solving them, and MP.6, Attend to precision, in supporting ELs.

Perspective
ELs need entry to and tools for becoming full-fledged members of the mathematics Discourse (Gee, 1996; Moschkovich, 2002) community, the characteristics and activities associated with being students in a mathematics Discourse (e.g. how to explain their thinking, how they make sense of their own and others’ mathematical work, etc.). Developing mathematics Discourse practices is a way to access and learn both mathematics content and academic language, which is crucial for ELs. This paper utilizes the MPs as key aspects of the classroom mathematics Discourse; the MPs operationalize the Discourse of mathematics classrooms.

Methods
Qualitative methods were used during and following the study to collect and analyze the following data from three teacher participants: interviews, focus groups, and classroom observations. Case study analysis (Yin, 2009) was used to examine how participating teachers developed MP.1 and MP.6 with their ELs. I looked for characteristics identified in the CCSS-M document for these two MPs, such as for students to understand the approaches of others to solving complex problems (MP.1). I then identified such characteristics in teachers’ talk and actions to create cases of each teacher and the two MPs.

Findings
The participating teachers noted and exhibited attention to both MPs in supporting ELs. A key feature for all participants was that they often attended to multiple MPs at once, foregrounding one while backgrounding the other. For example, Teacher 1 used anchor charts, or charts around his room that contained key information about prior topics, to provide ELs access to content so that they could make sense of the tasks they were solving (MP.1). However, his focus was more often on students using the charts to attend to precision (MP.6), such as using the charts to remember how to label units. Another teacher had her students share and explain their thinking with each other during the summary of the lesson. While Teacher 2 focused on having students attend to precision in the summary of the lesson (MP.6), she foregrounded MP.1 by having students explain the correspondence between their multiple representations and by having students understand others’ approaches to solving given tasks. Across these cases, each participant foregrounded and backgrounded the MPs to develop ELs’ academic language, mathematics, and mathematics Discourse.

Significance
As the CCSS-M are implemented, there is a need to provide images of what is possible for other mathematics teachers and to make sense of the affordances and constraints of particular ways of working with the MPs to support ELs.

Author

• Sarah Ann Roberts, University of California - Santa Barbara