Learning in collaborative settings: students building on each other's ideas to promote their mathematical understanding

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas in problem-solving settings. The students solved the problem and produced a valid justification of their solution. This study shows that collaborative activity can help promote students' mathematical understanding by providing opportunities for students to critically reexamine how they make claims from facts and also enable them to build on one another's ideas to construct more sophisticated ways of reasoning. Implications for classroom teaching and ideas for future research are also discussed. The study helps address a documented need for a better understanding of how mathematical learning evolves in social settings.