Diversity, Collaboration, and Learning by Invention

Learning-by-invention is an approach to mathematical instruction where small groups explore possible methods of solution before learning the “right answer” (e.g., Schwartz & Martin, 2004; Kapur & Bielaczyc, 2011). In a series of studies we have been investigating the effects of group composition in terms of math ability on learning by invention. An initial result showed that groups consisting of a mix of both high and low math ability students generated a broader range of solution attempts when asked to invent a formula for standard deviation compared to more homogeneous math ability groups. Moreover, this wider range of solution alternatives predicted better performance on quizzes following a lesson on the topic. Subsequent work is suggesting that who emerges as the leader of the group matters. Ongoing analyses are also exploring which features of the collaborative discourse are critical for students to take advantage of the affordances of learning by invention.