Using strands of tasks to promote growth of students’ mathematical understanding
John Francisco and Gunnar Gjone
This article reports on the mathematical activity of a group of five high school students (15–16 year olds) who worked together on a series of challenging task in combinatorics and probability. The students were participants in an after-school, classroom-based, longitudinal research on students’ development of mathematical ideas and different forms of reasoning in several mathematical content strands. The purpose of the article is to contribute insights into how to promote growth of students’ mathematical understanding through problem-solving activities. In particular, the article shows that problem-solving activities involving strands of challenging tasks have the potential to promote growth of students’ mathematical understanding by providing opportunities for students to engage in reasoning by isomorphism. This is a type of reasoning whereby students rely on structural similarities, i.e., isomorphism among mathematical tasks to solve or deepen their understanding of the tasks. Implications for classroom teaching, and environmental conditions that promote reasoning by isomorphism are also discussed.
John Francisco is assistant professor in mathematics education in the School of Education at the University of Massachusetts at Amherst, USA. His research interests include students’ development of mathematical ideas and reasoning, personal epistemological beliefs and teacher learning.
Gunnar Gjone is professor of mathematics education at the University of Oslo, Norway, and guest professor at Karlstad University Sweden. His research interests are mathematics teaching and learning in lower and upper secondary school, as well as teacher training. He has special interest in the use of ICT in students’ learning of mathematical concepts.