Designing for Consequential Engagement: The Role of ‘Push Back’ on Student Thinking

Melissa Sommerfeld Gresalfi

Researchers have suggested that encouraging students to pursue mathematics in school and beyond should involve more than arguing about the best strategies for increasing achievement, and instead requires attending to the nature of students’ engagement with mathematics. Beyond ensuring that students are able to answer mathematics questions accurately, there is a concern with the dispositions that students form in relation to a domain; the ways that students approach, engage, and feel about the subject matter. The study will examine how creating opportunities for students to engage consequentially with mathematics supports the dispositions they develop towards the domain. Engaging consequentially with information involves interrogating the usefulness, impact, or significance of particular tools on outcomes. One way to create opportunities for students to engage consequentially is to embed mathematics problems in authentic contexts. Beyond simply providing “relevance” for disciplinary work, contexts can serve as a resource for learning and reflection by pushing back on students’ disciplinary reasoning. Thus, consequential reflection can support students’ deep mathematical engagement because being asked to consider how and why a particular strategy or procedure impacted a solution actually shapes one’s understanding of the strategy or procedure itself.The hypothesis tested in this study is that creating opportunities for students to engage consequentially with content will lead to productive dispositions towards mathematics by supporting practices of meaningful disciplinary engagement and the development of a notion of oneself as someone whose actions can have impact. I will investigate the role of consequentiality by comparing three units situated in two project-based mathematics curricula, and will document how aspects of curricular designs impact student engagement with mathematical ideas and the development of more enduring dispositions. This study will contribute to educational research by supporting a deeper understanding of which aspects of instructional methods are most effective for what purpose, under which circumstances, and for whom.

About Melissa Sommerfeld Gresalfi

Melissa Gresalfi is an Assistant Professor in the Learning Sciences at Indiana University and the Associate Director of the Center for Research on Learning and Technology. Gresalfi has served as PI or co-PI on numerous grants funded through the National Science Foundation, the MacArthur Foundation, and the Institute of Education Sciences. These projects share a commitment to understanding how classroom structures and curricular designs create (or limit) opportunities for students to engage meaningfully with information. Her research investigates two interconnected issues: how aspects of instructional practice shape the opportunities to learn that are offered and realized by students; and how instructional designs lead to the development of new understandings and dispositions to learn more broadly (Cobb, Gresalfi, & Hodge, 2009; Gresalfi, 2008, in press; Gresalfi, Barab, Siyahhan, & Christensen, 2009; Gresalfi & Cobb, 2006). In studying dispositions, Gresalfi’s research has focused on outcomes beyond mastery of particular content. Building on research that has argued that what students learn cannot be separated from how they learn it, Gresalfi examines the mechanisms that underlie the ways that dispositions are enacted in moments of interaction, and how aspects of classroom practice impact this enactment (Cobb et al., 2009; Gresalfi, 2008, in press; Gresalfi & Lehrer, April, 2008; Gresalfi, Martin, Hand, & Greeno, 2009). In so doing, her work demonstrates that social, affective, and motivational factors are not simply influences on learning, but are, instead, central to and inseparable from the learning process.