The impact of small-group mathematical modeling activities on students' understanding of linear and quadratic functions

Mathematical modeling education has received renewed attention over the past decade due to mathematics educators' interest in developing and implementing curricular and pedagogical approaches that enhance how students perceive, learn, and apply mathematics. Situated within the modeling-as-vehicle perspective, this study explored how mathematical modeling contributes to community college students' mathematical learning and mathematical beliefs.;This study had three main goals. First, to develop mathematical modeling activities that emphasize model development, prompt students to utilize their knowledge of linear and quadratic functions, and enhance students' conceptual and procedural understanding of linear and quadratic functions. Second, to examine the impact of small-group modeling activities on student's conceptual and procedural understanding of linear and quadratic functions and students' beliefs about mathematics. Third, to investigate students' mathematical cognition as they engage in modeling activities and identify generic and activity-specific blockages that inhibited students from completing steps in a modeling process.;This mixed methods study occurred at an urban community college in the Northeast. Using a quasi-experimental design, the study compared the cognitive and affective outcomes of students in a traditional intermediate algebra course augmented with small-group modeling activities with the outcomes of students in a traditional intermediate algebra course. A qualitative analysis was conducted to explore students' modeling behaviors, mathematical cognition, and perceptions of modeling. Data collection instruments included the Indiana Mathematics Beliefs Scales and researcher-designed mathematics pre- and post-tests.;The modeling activities did not significantly impact students' overall procedural and conceptual understanding of linear and quadratic functions or students' attainment of specific linear and quadratic function learning outcomes. The study found inconclusive results regarding the effect of the modeling activities on students' mathematical beliefs. Qualitative analysis indicated that students had difficulty solving modeling problems due to a lack of model development competencies. These included understanding and identifying relevant mathematical features of a contextual situation, translating from contextual representations to symbolic representations, and mathematizing situation models.;This study discussed important considerations of modeling within community college mathematics courses and offered insights on directions for new research on modeling in community college mathematics courses.