Developmental mathematics college students' experiences of mathematical practices in a 4-week summer learning community using local communities of mathematical practice

DEVELOPMENTAL MATHEMATICS COLLEGE STUDENTS’ EXPERIENCES OF MATHEMATICAL PRACTICES IN A 4-WEEK SUMMER LEARNING COMMUNITY USING LOCAL COMMUNITIES OF MATHEMATICAL PRACTICES by Bhupinder Naidu The research literature concerning traditionally aged college mathematics students’ who require remediation, in beginning Algebra topics, states that these students lack confidence in their mathematical skills, have experienced failure and frustration in the past, have low self confidence issues with respect to mathematics and often lack basic studying skills (Hall & Ponton, 2005; Young & Lee, 2002; Zimmerman, 2008). Most research studies on developmental mathematics students have used quantitative methodologies that have not provided the depth or explanation of students’ perspectives of mathematical practices that a qualitative study such as this study provides (Kinney, Stottlemeyer, Hatfield & Robinson, 2004). The purpose of this study was to examine traditionally aged developmental mathematics college students’ experiences of mathematical practices, in a 4-week summer learning community, using a qualitative case study approach (Yin, 2009). This study used the methodological framework of Local Communities of Mathematical Practices (Winbourne & Watson, 1998) to help sort and analyze data, the conceptual theory of situated cognition (Brown & Duguid, 1988), and the theories of communities of practice (Lave & Wenger, 1991), and learning communities (Tinto, 1997). The goals of the study were to inform instructors and administrators as to the contextual factors that allow developmental mathematics college students to be academically successful as evidenced by their mathematical practices (Ball, 2003). The research question for this qualitative, explanatory single case study was: How does participating in a 4-week summer learning community shape developmental mathematics college students’ experiences of mathematical practices? The participants of this case study belonged to one group of four women enrolled in a 4-week summer learning community at a university. I collected data in the form of video and audio tape of classroom interactions, student and instructor personal observations and reflections, and two individual interviews per participant. Analysis of the data revealed that participants’ mathematical practices were shaped in part by: a) the way students identify with mathematics relates to their ‘success’ or ‘failure’ in the mathematics course; b) the students level of participation within the community; c) the students collaboration with purpose, discussion, and reflection gave rise to understanding; d) the students shared repertoire confirmed the consensus of knowledge; e) the students mutual engagement played a large part in their motivation to succeed, and f) the students joint enterprise within the learning community was a significant factor in their learning. Findings suggest that the 4-week summer learning community shaped these developmental mathematics students’ mathematical practices’ by allowing the students to: 1) view themselves as navigating mathematics successfully; 2) create an environment in which to ask questions; 3) connect to the entire community; 4) participate in various activities while in groups; which 5) lead to a self supporting system these students could rely on. This study illuminated for these students that learning is the intersection of activity, concept, and culture (the classroom). DEVELOPMENTAL MATHEMATICS COLLEGE STUDENTS’ EXPERIENCES OF MATHEMATICAL PRACTICES IN A 4-WEEK SUMMER LEARNING COMMUNITY USING LOCAL COMMUNITIES OF MATHEMATICAL PRACTICE by Bhupinder Naidu