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Creativity in Problem Solving
Overview:
While considering the higher-order learning goals of the Mathematical Modeling and Introduction to Calculus course at the United States Military Academy, I began thinking about how we could know if we were successful in making progress towards achieving those goals as a course. I was particularly interested in how well we were doing at developing creative problem solvers.
In an effort to make such evaluation possible, we developed the Mathematical Problem Solving Creativity Rubric. This rubric takes the Association of American Colleges and Universities' definition of creativity and breaks it into five components. Three of these components -- originality, flexibility, and risk -- are considered essential for creative problem solving while the other two -- visualization and elaboration -- are considered potential evidence for creativity but are not essential.
During the Fall 2018 semester, a pilot study was conducted for using the Mathematical Problem Solving Creativity Rubric. The study results were overall positive with students making gains in creativity from pre-test to post-test. While those results were nice to see, it was even nicer to see how consistent the use of the rubric was between the two evaluators. Consequently, we are optimistic about what we are doing in our course to prepare students to be creative problem solvers, and we are encouraged that the Mathematical Problem Solving Creativity Rubric can be used to meaningfully evaluate a course's success or failure to develop creative problem solvers.
Relevant Publications:
- Does Your Course Effectively Promote Creativity? Introducing the Mathematical Problem Solving Creativity Rubric (July 2020)
As believers in the power of blending the creative with the quantitative, we design our courses with an eye towards developing creative problem solvers. However, when it comes time to evaluate our course’s success in developing creative problem solvers we come away with a plethora of qualitative evidence and yet we are left hungry for the quantitative evidence we desire as mathematicians. In this article we describe the development of the Mathematical Problem Solving Creativity Rubric and its pilot use in a freshman-level Mathematical Modeling and Introduction to Calculus course at the United States Military Academy. We not only come away with the necessary quantitative evidence to satiate our hunger for now, but with a rubric that will allow us to do so in future semesters and courses.
- Going Beyond Promoting: Preparing Students to Creatively Solve Future Problems (July 2020)
While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to what they will encounter in the real world.
Future Directions:
- In the Fall 2019 semester the study was replicated with the entire population of students enrolled in Mathematical Modeling and Introduction to Calculus at the United States Military Academy (n approximately 850). A team of 7 evaluators are using the rubric to validate the results of the pilot study.
- Expand the rubric's application to a variety of other matheamtics courses.
- Conduct a similar study to determine the effectiveness of various course elements in developing creative problem-solving skills.
- Explore using the rubric to determine a "creative problem solving baseline" to inform course instruction.