Representational technology for learning mathematics: an investigation of teaching practices in Latino/a classrooms

This paper explores representationand language-rich mathematics instruction in two classrooms with low-income Latino/a students. The two classroom teachers were part of a larger study investigating the use of SimCalc in middle school, and their classrooms had learning gains greater than the mean gains for the study overall. Prior analyses documented that these two teachers implemented exemplary classroom discourse practices: they engaged students in discussions with high intellectual work and showed high levels of responsiveness to student statements (Pierson, 2008). Such practices are consistent with both the research on representationally-rich mathematics environments, and instructional practices for students from non-dominant communities. We use transcript excerpts to illustrate these teachers’ practices in detail. We found that these two teachers enacted some similar practices, but they also had different teaching styles, different approaches to connecting representations, and different ways of supporting mathematical discussions. Introduction and Significance As the population of Latino/a students increases in U.S. schools, so do concerns with their needs in mathematics classrooms. One concern is performance on assessments. Only 13% of Latino/a students scored at or above proficient on the 2005 8 grade NAEP exam, compared to 39% of white students and 47% of Asian students (Gándara & Contreras, 2009). Many schools attempt to address these concerns by placing large numbers of Latino/a students in remedial courses designed to address the needs of students who are “at risk,” a decision which may exacerbate the situation. Research shows that the problem lies not in the students but in their access to quality teaching. In general, low-income Latino/a students attend racially segregated poor schools and have little access to the kind of teaching that supports the development of conceptual understanding or academic discourse (Gándara & Contreras, 2009). However, there are examples of classrooms where this is not the case. Quantitative data from the SimCalc study (Vahey, Lara-Meloy, Knudsen, 2009) and qualitative research with this student population has shown that Latino/a students can learn complex mathematics and participate in mathematical discussions (i.e. Moschkovich, 2002) when they have access to quality teaching. In this paper we examine the teaching practices of two teachers, providing a sharp contrast to the perspective that Latino/a students need ‘remedial” teaching. We analyze two instances of mathematics instruction that support conceptual understanding and mathematical discussion as students participate in representation-rich mathematics environments. There is reason to believe that there is consonance between the literature on improving instruction for low-income students from non-dominant linguistic backgrounds and the literature on the use of representationally rich technologies in mathematics (Vahey, Lara-Meloy, & Knudsen, 2009). Both highlight the use of multiple ways to represent ideas, point to supporting students as they make connections among these multiple representations, and point to the importance of language rich practices. However, there has not yet been a systematic attempt to integrate the representational affordances of technology with research on improving mathematics instruction for students from non-dominant linguistic backgrounds. This leaves educators with little guidance on how to use technology for this underserved student population. This paper begins to address this gap by using two lenses to describe the instructional practices of two teachers who were successful in using technology to support students in their primarily high-poverty Latino/a classrooms in learning important conceptual mathematics. We explore the ways in which these successful teachers engaged in practices that were consistent with (or at odds with) research-based recommendations for mathematics instruction that is (a) representation-rich, and (b) supports mathematical discussions.