Weaving creativity into mathematics
Sometimes creating a mathematics problem can be just as exciting as coming up with the solution. That’s what sophomore and junior high school students enrolled in a pre-calculus course learned recently as the result of research conducted by Jerald Thomas, Associate Professor of Education, and Illinois Mathematics and Science Academy faculty member Vince Matsko (currently with the Princeton International School of Mathematics and Science).
“Dr. Matsko and I were interested in whether allowing students to write and answer their own mathematics problems would lead to deeper conceptual understanding, engagement and motivation,” said Thomas. “He is always exploring ways that he can challenge and assess students at appropriate levels. Although we were looking at a small sample of gifted students, the results of our exploratory study suggest that Matsko’s approach engages students and leads them to think about their own thinking.”
In his presentation to AU faculty, Thomas explained that expert problem solvers are original, creative thinkers who are able to devise novel approaches to solving ill-structured or ambiguously posed problems. Yet, mathematics students at the high school level are usually asked to solve by known techniques, and as a result do not develop the skills necessary to attack real-world problems.
Thomas and Matsko had students create and solve their own problems as assignments in mathematics classes to give them an experience of interacting with mathematics problems beyond the routine and mechanical. Their results suggest that such experiences could also be valuable in other disciplines.
“One obvious area that students often engage in such an exercise is in history, specifically counterfactual history,” said Thomas. “For example, what would have happened if Lincoln had not been assassinated? I think one big message from our study is that we have to give students permission to ask questions, important questions, which is something that many teachers and most students are not accustomed to doing.
“From my perspective, one of the most interesting findings was that students derived their problems from very interesting sources. One student was a dancer and wrote a geometry problem that related to her dance experience. Another student had an interest in aviation and created a problem based on the shapes in aircraft.”
The students appreciated the benefits of problem creation as well. One research participant said, “It has taught me to think differently and be more open minded about the place of mathematics in everyday life.”