|Abstract:||Serving approximately 80% of the one million college students taking pre-college-level mathematics classes, community colleges perform an important function in providing access to advanced coursework and degrees. Low success rates in these classes has led mathematics educators to consider alternative forms of curriculum and instruction for these often required, but non-credit bearing pre-college, or developmental, classes. One emerging reform has pushed for the inclusion of more real-world problem solving and group work in these classes, mirroring reform efforts in K-12 mathematics education (National Council of Teachers of Mathematics, 1989, 2000). Success rates of students in early implementations of this developmental mathematics reform show promising results. However, these studies provided little information about the actual enactment of the curriculum or how developmental students, who have dramatically different demographics and mathematical histories than the K-12 population, experience these classes.
Sitting at the intersection of research on K-12 mathematics education reform and research on developmental mathematics in the community college context, this dissertation sets out to examine how a problem-centered, group-intensive form of instruction plays out with developmental mathematics students at a single community college. Classroom observation data, classroom audio, and both instructor and student interviews were collected in a focus classroom. In addition, survey responses from students in seven Mathematical Literacy classrooms are used to examine the impact of the implementation on students. More specifically, this mixed-methods study: (a) describes what Mathematical Literacy looks like at the classroom level, examining the students’ and instructor’s patterns of engagement with the curriculum over time using an innovative, visual representation of the classroom, (b) examines students’ persistence and affective outcomes using statistical methods, including hierarchical linear modeling, and (c) examines students’ perceptions of the class and how these differ among students and compare with the instructor’s intentions, using open coding and the mixed-method analysis technique of matrices.
Results show that students in the focus classroom had ample opportunity to work within their groups while the instructor operated in a facilitator role. Contrary to many of the reform models implemented at the K-12 level, whole-class discussion was minimal. Instead, students spent the vast majority of class time working collaboratively in their assigned groups, engaging in a comparatively small amount of off-task talk. Those who persisted in the class experienced some positive changes in their attitudes towards mathematics, but benefits were unevenly distributed among this diverse group of students. Differences in the perceptions of the students with positive, neutral, or negative experiences in the class were at least partially rooted in the challenges of having very mathematically diverse students required to work together in groups. although the developmental students’ focused goals and desire for efficiency were strengths in the classroom, they also led to tensions between some of the more and less advanced students within groups.
This study illuminates critical challenges of productively implementing instruction centered around problem solving and group work in developmental mathematics courses. To improve implementation, instructors may need to (a) help students better understand each other’s needs and motivations, (b) support students as they mediate large differences in mathematical backgrounds, and (c) leverage students’ backgrounds and goals when grouping students. More research is needed to uncover productive ways to address these implementation challenges, as well as the academic benefits that can be obtained when doing so.