Implementing Standards-Based Mathematics: Toward Improving Conceptual Understanding of Key Ideas of Linear Functions for Middle School Immigrant Students

Abstract

Mathematics education research on immigrant students indicates that schools are often not prepared to support students with cultural and language barriers (Campbell, Adams, & Davis, 2007; Civil 2014). This descriptive case study documents the ways in which middle school immigrant students demonstrated understanding of key ideas of linear functions prior to and after participation in an eight-week Constructivist Teaching Experiment (CTE) (Cobb & Steffe, 2011; Cohen, Manion & Morrison, 2011). The purpose of this study is to show that all students-- regardless of their English language or mathematical proficiency ratings-- can learn mathematics with conceptual understanding (Hansen-Thomas, 2009; Silver & Stein, 1996; Whitney, 2010). Results prior to the CTE indicated the following. First, middle school immigrant students answered a majority of questions correctly without justifying when it was not required on the pre-assessment. And second, pre-assessment questions influenced the ways that middle school immigrant students communicated and used representations. Results after the CTE revealed three major findings. One, all middle school immigrant student participants increased their conceptual understanding on the post-assessment. Two, post-assessment questions with a real-life situation that asked for multiple representations influenced the ways that middle school immigrant students communicated and used representations. Three, all students filled in procedural and conceptual gaps after listening to peer presentations, individually and as a team. In summary, positive outcomes were associated with student-centered and problem-centered mathematics instruction that aligned with equity goals (National Council of Teachers of Mathematics, 2000).