PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
What should undergraduate mathematics majors understand about the nature of mathematical knowledge?
Page: 1080
A primary function of mathematics education is that students understand the subject matter ofmathematics. That is, students are supported in understanding mathematical concepts andattaining mathematical knowledge. But there is another function of mathematics education, oftenunaddressed in research, which deserves more attention. In addition to learning content, studentsmust be supported in developing informed views about the human processes by whichmathematical knowledge is produced and the unique characteristics of that knowledge. Throughan exploration of humanistic philosophy of mathematics, the purpose of this paper is to identifycharacteristics of the nature of mathematical knowledge that may be important for undergraduatemathematics majors to know and understand. Four characteristics are discussed: mathematicalknowledge is subject to revision; mathematical knowledge is socially validated; proofs are bearersof mathematical knowledge; and informal mathematical work is the foundation of formalknowledge.Key words: