Curtis Bennett: Thinking Like a Mathematician

Course Context

SoTL Question

Activity Description >>

SoTL Process

Conclusion

Semester-Long Project Description in Curtis Bennett's words:

"The first day of the course, I hand out a list of 17 potential project questions (these come from a variety of sources - many of them from my colleagues) and ask the students to return a list of their top 5 choices from the list, together with students that they would like to work with.

I then assign groups of three students to a question. Each group, however, does a different question. I try to pair up students that want to work together, although I make no promises about doing so. As part of the syllabus, they are handed out a rubric for the grading of the paper as well as instructions for the paper. One included assumption on the projects is that the question that is asked is only the starting point for the project.

The projects play a major role in the class, as is shown by their 30% of the grade requirement. They work to satisfy four of the five process objectives of the class."

Project Objectives
      • For students to successfully experience mathematical research on their own.

      • For students to learn the value of asking richer mathematical questions. "I want them to see how the richer mathematical questions can provide them with greater understanding on working on the projects."

      • For students to gain a deeper understanding of themes of mathematics, and how various subjects in mathematics can relate to a common theme.

      • For the students to experience solving a mathematical problem similar to how mathematicians might do so. "The main goal for me is that the students learn to attack problems on their own." Thus it is particularly important that they do not look answers up in outside sources.

      • For students to be able to look at advanced mathematics topics (Numbers as lengths: constructible numbers. Numbers as sums, products, quotients, and differences of radicals: Solving quadratic and cubic equations.
        Algebraic versus transcendental numbers. Dedekind Cuts and the real number line)and see how they are reflected in the high school curriculum and how these advanced topics might inform their teaching of high school mathematics.

      • "I hope that in doing the project and thinking about how it applies to the high school curriculum, they will also gain some experience in trying to transform content knowledge (the answer to their project) to pedagogical content knowledge (how it might apply to the curriculum)."