Broadening the horizons of research on discovery-based learning

Today we think of the desired outcomes of mathematics learning as comprising not only students’ mastery of facts and procedures but their emerging from instruction with certain dispositions, their persevering at problem solving, their being inclined to pursue mathematical connections, their being able to produce extended chains of reasoning and communicate them orally and in writing, and their seeing themselves as members of the mathematical community. With these as goals, one’s conception of powerful mathematical instruction changes. And, once one has the understanding that not only students’ content mastery but their beliefs, dispositions, and practices are all shaped by instruction, one’s analytic lenses change as well. The same holds for reading and writing, for social studies, and for every other discipline.

(Schoenfeld, 2016, p. 110)

Abstract

In reviewing the six articles within this Instructional Science special issue, we are reminded of Schoenfeld’s (Educ Res 45(2):105–111, 2016) review of American Educational Research Association president-authored papers for the centennial celebration of AERA. There, he succinctly unveiled the content focus of AERA research in the first half of the twentieth century: “there is content to be mastered; it is the schools’ job to help students master it” (p. 106). Yet, like Schoenfeld says, “A century later, we hear the echoes of this functionality in the calls for ‘21st-century skills,’” (p. 106), and the “skills” of the twentieth and twenty-first century would hardly know each other. Twentieth century skills, as represented in the accounts from past AERA presidents, were product-oriented, like accurate copying and precise handwriting. Twenty-first century skills are focused on creativity, ingenuity, critical thinking, and the like. In our primary research space, mathematics education, problem solving, sense making, and conceptual understanding dominates in the twenty-first century, whereas procedures dominated teaching and learning mathematics in the twentieth century.