NOM NOM NOM: Chewing on the Nature of Mathematics

There has been a call for students of mathematics to understand the construct of the nature of mathematics (NOM). In order for students to understand and become familiar with NOM and their own views regarding NOM, students need opportunities to grapple with different foundational aspects of NOM. We utilized an exploratory mixed methods design with embedded cases to begin to understand undergraduate students’ conceptions regarding NOM. Students responded to statements about the nature of mathematics, such as “There is usually only one correct way to solve a mathematics problem.” Quantitative analysis of students’ overall scores on the survey suggests undergraduate students espoused slightly more sophisticated views of NOM than not. An examination of students’ scores by STEM versus non-STEM majors revealed that STEM majors did in fact have a higher score than non-STEM majors. Analysis of the qualitative responses revealed that when students were asked to specifically reflect on ideas of NOM, the majority said they agreed, explaining “Yes. Even though it is a very broad definition it does define everything in the scope of mathematics.” No one student stated that they fully disagreed, but instead commented on specific aspects. For example, “I agree with everything except beautiful. I think you have to be passionate about math to see it as beautiful.” Our results support the idea that reflection is key in gaining more sophisticated views for all undergraduates, which has implications for the incorporation of NOM in future mathematics classrooms.

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