Reflections on mathematics education research questions in elementary number theory, 2002 (original) (raw)

Learning and Teaching Number Theory: Research in Cognition and Instruction, ). S. R. Campbell and R. Zazkis (Eds.), (pp. 213-230), Monograph Series of the Journal of Mathematical Behavior Vol. 2, Westport, CT, Ablex Publishing, 2002.

This is the summary chapter of the monograph. It begins: This monograph intentionally raises more questions than it answers. Indeed the editors' aims included convincing readers that many interesting questions in the teaching and learning of number theory await their attention, and that there are engaging number theory tasks with which to investigate students' mathematical sense making. Number theory appears to be a rather neglected area in the mathematics education research literature. Whether one looks at the NCTM Handbook of Research on Mathematics Teaching and Learning (Grouws, 1992) or the NCTM Yearbook, Developing Mathematical Reasoning in Grades K-12 (Stiff, 1999), one finds almost nothing on students' engagement with number theory topics. By number theory we mean, as do the monograph editors, results concerning the structure of the integers that are not primarily computational, for example, questions about factorization or the distribution of primes. Whatever the reasons for this research lacuna, this monograph, devoted entirely to various number theory investigations and reports, should help fill this void and heighten the community's awareness of the potential for fruitful investigations. These might concern individual students' cognitions on a variety of topics from divisibility and prime factorization to number theoretic generic proofs and mathematical induction, or they might be more socio-cultural studies.