Attending to Uncertainty in the Design and Implementation of DGE Tasks to Engage Mathematics Students in Productive Struggle

Open Access
- Author:
- Jairam, Ashley Esther
- Graduate Program:
- Curriculum and Instruction
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 15, 2020
- Committee Members:
- Rose Mary Zbiek, Dissertation Advisor/Co-Advisor
Rose Mary Zbiek, Committee Chair/Co-Chair
Andrea Vujan Mccloskey, Committee Member
Susan Mary Land, Committee Member
Mihran Papikian, Outside Member
Kimberly Anne Powell, Program Head/Chair - Keywords:
- Productive Struggle
Uncertainty
Dynamic Geometry Environment
Secondary Mathematics
Mathematical Tasks - Abstract:
- Struggling with mathematics is important for several reasons. According to learning theorists and empirical studies, the act of struggling can help students learn mathematics. Also, several important mathematics education documents advocate that students should engage in struggle as part of the problem-solving process. In addition, being able to struggle and persevere through struggle when solving problems is an essential skill for graduates to have as they pursue future employment. However, it may not be clear to mathematics teachers how to engage students in struggle and make and keep that struggle productive. Creating uncertainty for students could possibly be a means for engaging students in productive struggle, because of the close relationship between uncertainty and struggle. This study sought to engage students in productive struggle by engaging them in dynamic geometry tasks that elicit uncertainty. Dynamic geometry environments were chosen for their usefulness in creating and resolving uncertainties due to their exploration and feedback features. Eight mathematical tasks were chosen, modified, or designed in such a way as to elicit uncertainty. Uncertainty was to be created in two ways in the tasks, through competing claims and unknown paths/questionable conclusions. Classroom observations were conducted to observe secondary geometry students working on these tasks using the dynamic geometry environment, GeoGebra. This data was analyzed in such a way as to determine answers to the following questions: (a) Did the task create uncertainty?, (b) Did the uncertainty lead to struggle?, (c) What parts of the struggle were productive and what parts of the struggle were not productive?, and (d) What supported or hindered students’ productive struggle? The tasks did create uncertainty, but this uncertainty did not always lead to students engaging in productive struggle. Even when students were faced with clear contradictions or questionable conclusions, they did not always seek out resolutions for these uncertainties. One possible explanation for why students did not seek out resolutions for these uncertainties is because they did not believe they possessed the mathematical authority to do so.