Modeling through model-eliciting activities : a comparison among students at different performance levels
My dissertation investigated students’ thinking, understanding, and mathematical development when solving mathematics classroom open-ended, real-life context tasks in which they were required to model a solution. Specifically, thought-revealing activities known as Model-Eliciting Activities (MEAs) (Lesh et al., 2000) were used to compare and contrast the reasoning and solutions of 11th grade students at different levels of performance in a northeastern Mexican private institution. Two aspects of student work were analyzed: The quality of the students’ final and intermediate product-solutions and the patterns of group discourse that emerge while they engage such process. Seventy-two students at different level of performance (e.g., low, average, and high performance), as measured by tests and classroom activities, participated in the study. Students formed teams of three members for a total of 24 teams. A case study methodology was used to study three MEAs adapted to the context of the target population. The questions addressed in this research included: To what extent do students’ products and solution processes differ across performance levels (low, average, and high-performance) in Model-Eliciting Activities? What are the mathematical elements, models types, and strategies that students used during the problem-solving process, and how do these differ among students labeled as low, average, and high performance (as measured by classroom’s grades and test scores)? The findings reveal low-performing students’ ability to propose and develop adequate solutions, comparable to the average- and high-performance peers. Furthermore, solutions provided by “average” teams were not so different from the ones provided by the low performers. In addition, although some high-performance teams used more sophisticated elements in their strategies and final and intermediate product-solutions, some teams in this category had incomplete and not well-developed solutions. Finally, transcripts of students’ work and discourse patterns reveal that students engaged in a pattern of argumentation discourse providing claims, evidence, and justifications for their thoughts. In addition, students engaged in describing and explaining type of discourse. Specifically, low-performance teams engaged in an argumentation type of discourse almost double the time in comparison to their average- or high-performance peers. In contrast, average- and high-performance teams engaged mostly in a describing or explaining discourse type, aligning most of the time with each other. In the end, teams at all three performance levels proposed solutions that were adequate and comparable, but also rich and diverse. However, more evidence is needed to test the conjecture that MEAs can indeed level the playing field among students of different levels of achievement.