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Melissa S. Gresalfi

Dean of the Ingram Commons
Professor of Mathematics Education and Learning Sciences and Learning Environment Design, Department of Teaching and Learning

Research Interests

Professor Gresalfi’s research asks a central question: How do people’s experiences in the world influence who they become: how they act, what they think about themselves, and how others come to see them?  This question—how identities develop and change—is guided by a Situative perspective on learning, which drives her research into different kinds of contexts that form our experiences in the world.

Her research has predominantly focused on students’ experiences in mathematics—in school and out of school—and how and why those experiences so often lead students to conclude that they are not capable of or interested in continuing with mathematics. This research has considered how moments of interaction in classrooms create opportunities for students to think about mathematics in particular ways, and to be seen as more or less competent in relation to the discipline. Her research has also connected these moments to broader narratives around gender, race, and what “counts” as mathematics. This work challenges the idea that achievement, excellence, motivation, or competence are individual accomplishments, but are instead a “joint accomplishment” between the learner, other people, tasks, norms, opportunities, stereotypes, and expectations.

 Her work has focused specifically on how the nature of the context in which one is learning influences students’ experience. Over her career Professor Gresalfi’s funded projects have examined student collaboration, classroom norms, curricular structures such as Project-Based Learning, task development, video games, textile craft, play, and computer programming. This work shares the goal of trying to transform the spaces where people learn—in school and out of school, formal and informal—such that students have opportunities to engage with mathematics that involves sense-making, decision-making, and problem solving.  These projects share a commitment to fostering experiences that create opportunities for students to see themselves as competent, capable, and valued members of the learning community.

Current Projects

Supporting Playful Learning in Elementary Mathematics Classrooms

This project, a collaboration with Professors Anita Wager and Amy Parks (MSU), investigates play in early elementary math education through a four-year longitudinal study that documents teacher learning and connects teacher practice with in-depth qualitative analyses of children over multiple years. Teachers will experience professional development where they will engage in play as learners and learn how to design tasks that incorporate play. Subsequently, the teachers will implement strategies in their classrooms. The longitudinal design will support analyses of teachers over time (kindergarten teachers will participate for three consecutive years), and in relation to grade level. This project will also explore children’s experiences over time and in relation to teachers’ experience. In so doing, this project will develop three in-depth accounts using qualitative methods: 1) How kindergarten teachers learn to integrate play into their instruction and how their teaching changes over time; 2) How the task of integrating play changes with respect to different grades and different content; and 3) How the relationship that children develop with mathematics might be transformed by experiencing playful mathematics learning over their early elementary careers. In this exploratory analysis, the researchers will employ qualitative methods, including video, video club, and in-class observations and teacher interviews and analytic methods including emergent coding, and coding schemes from research on high-quality mathematics teaching. The data collected through this project will offer insight into children’s trajectories of participation across the first three years of elementary school and shed light on how children’s relationship with the discipline of mathematics could be transformed. Funded by the National Science Foundation, DRL-2101356

Project CAMPS: Computing and Math in Play Spaces

This project, a collaboration with Professor Corey Brady, designs and studies new learning environments integrating mathematical and computational thinking. While integrating content has been suggested as a strategy for students' learning, there has been limited investigation about how mathematics and computational thinking should be connected in learning experiences. Using design-based research as a methodology to support iterative design and research, the project will explore two core tensions that are relevant to the integration of mathematics and computational thinking. Each tension deals with how to balance competing goals, and investigates the influence of foregrounding one goal over another. Specifically, the project will design, test, and begin to apply in schools a set of modules that contrast: 1) foregrounding mathematics vs. computational thinking; and 2) foregrounding agency vs. structure. The research questions to be investigated include: (1) What are the advantages of modules that teach mathematics through computational thinking (foregrounding mathematics) vs. those that teach computational thinking through mathematics (foregrounding computational thinking)? (2) What are the advantages of modules that teach computational thinking through open exploration (agency) vs. game play (structure)? (3) What kinds of instructional supports do math teachers need or request as they are teaching students at the intersection of computational thinking and mathematics? Funded by the National Science Foundation, DRL-1742257.

Recently Completed Projects

Re-crafting Mathematics Education

The Recrafting Mathematics Education project seeks to better understand how mathematics is currently embedded in women's crafting practices and, more specifically, to build on those crafting practices to develop activities that allow students to see and experience mathematics in its application. This approach to teaching mathematics is tightly linked with the embodied cognition approach, which posits that the experiences of the body both are influenced by and also influence the functioning of the mind. Said differently, understanding mathematics by engaging the body offers opportunities to understand mathematics differently than when merely engaging with symbol systems (Lakoff & Nunez, 1997; 2000). Specifically, we focus on the ways in which women participate successfully in advanced mathematics throughout their lifetimes by considering women’s crafting activity, and then build on those instances of success to consider how to incorporate these practices into the institutional contexts from which women often turn away. This involves deeply understanding not just the context of the craft, but also the culture of crafting that continues to attract and maintain women’s participation. Our research questions target both the mathematical practices inherent in particular crafting traditions, as well as the individual mathematical reasoning of expert crafters as they engage in sustained practice. Funded by the National Science Foundation, DRL-1420488

Playful Mathematics Learning

This project, a collaboration with Professor Ilana Horn, explores spaces of possibility for what mathematical engagement might look like if we reimagine the enterprise by focusing on learning environments that support mathematical practices, and, in turn, children’s deeper learning of mathematical content.  In this project, we look to informal mathematical play for inspiration, as we know that school mathematics is typically narrow and constrained, failing to engage students in the thinking, reasoning, and problem solving that is the currency of out-of-school and professional mathematical practice.   When math is taught differently however, more students identify with the discipline. This project presents a unique opportunity to study children engaged with mathematics in an informal setting, the Minnesota State Fair, facilitated by mathematically knowledgeable volunteers. The Math On-a-Stick mathematical playground provides a place for children to engage with mathematics by exploring patters, asking quantitative questions, and investigating shape and space to mathematize their play. The project will investigate three research questions: (1) How does the design of various parts of the exhibit differently support rich mathematical interactions between children and mathematicians? (2) How do children engage different parts of the exhibit? How do differences in engagement relate to (a) exhibit design and (b) prior mathematical experience? (3) How do exhibit volunteers, mathematicians, and caregivers interact to support (or undermine) students' mathematical play? The project will use participant observation and videography to capture visitors' activities through the exhibit, analyzing them as qualitative case studies. Funded by the National Science Foundation, DRL-1643313

The Role of Feedback in Digital Games

The goal of this project, a collaboration with Professor Sasha Barab at Arizona State University, is to design and investigate the potential of videogame technologies for supporting formative and summative feedback for students and teachers. This project will examine the role of different forms of feedback on students’ learning and engagement with mathematics. Specifically, we will work in the context of two different immersive experiences (video games) designed as part of the Atlantis Remixed platform. We will design and study six different versions of these games in order to better understand how different forms of feedback (feedback that is directly tied to the narrative, directly tied to content, or a blend of both) as well as the timing of when feedback is given (its frequency and relation to major assessment moments) are related to how students actually work with the mathematical content (engagement) and what they eventually come to understand (learning). Funded by the National Science Foundation. DRL-1252380