Heuristics Employed by Problem Solvers Engaged in a Robotics-based Task

Patricia Vela

Despite efforts to improve students’ mathematical problem solving, the majority of students still face great difficulty with problems that require analysis or creative mathematical thinking –nonroutine problem solving. Because Polya’s heuristics have often proved fruitful in solving nonroutine problems, the purpose of this dissertation is to explore the potential of a robotics-based task to stimulate problem-solvers to use Polya’s heuristics. Structured, task-based interviews will be used to examine the observable heuristics elicited by a robotics-based task from twelve participants: six undergraduate students and six high school students. Structured, task-based interviews, audio and video recorded, will be coded using a modified version of Kilpatrick’s problem-solving coding system which uses Polya’s work as the theoretical foundation. Data will be collected during an initial interview conducted prior to the robotics-based task to provide some baseline information about the participants’ mathematics background and affect towards robotics. A final interview will be conducted after the robotics-based task to capture the participants’ awareness of the heuristic behaviors they implemented, and to gather feedback regarding the robotics-based task. A checklist matrix will be used to analyze data from the initial and final interviews. This research is valuable to the education community because students’ mathematics conceptualizations are influenced by the instructional tasks given to them in mathematics classrooms. A greater awareness of how instructional tasks stimulate students’ thinking processes can help mathematics educators communicate mathematics better to students, improving students’ nonroutine problem-solving skills and their relationship with mathematics.

About Patricia Vela

Patricia Vela is a Mathematics Education Ph.D. student at Emory University. She is interested in understanding how technological artifacts, such as robots, can serve as thinking tools to make mathematics more accessible and enjoyable to students. Her research is motivated by her experiences as an undergraduate mathematics student and her nine years teaching high school mathematics. As an undergraduate student at UC Berkeley, Patricia realized that her professors and peers were using problem solving strategies to stimulate their mathematical thinking. Later, she learned that they were using some of Polya’s heuristics and became enthusiastic about the potential of Polya’s work to make mathematics more accessible to students. As a high school teacher, she noticed her students’ unbreakable motivation to figure out robotics challenges. Through her work, she hopes to find robotics-based task that strengthen students’ mathematical knowledge and their enjoyment for mathematics.