Associate Professor of Mathematics Education and Learning Sciences and Learning Environment Design, Department of Teaching and Learning
Professor Gresalfi’s research considers cognition and social context by examining student learning as a function of participation in activity settings. Following a situative perspective on learning, she has investigated the development of dispositions towards learning in mathematics classrooms by examining how opportunities to learn are constructed, and how, when and why different students take up those opportunities. Using this lens, Gresalfi has explored the extent to which classroom practices are equitable and examined categories such as race, gender and previous mathematical experience as they arise in interaction.
Gresalfi’s work on the design of learning environments has focused on transforming learning spaces to focus student activity on mathematical engagement that involves sense-making, decision-making and problem solving. Her projects focus on the role of play and experimentation on supporting learning through videogame design, informal learning, textile design and computational thinking.
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, 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 patterns, asking quantitative questions and investigating shape and space to mathematize 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.
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 into 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 against computational thinking; and 2) foregrounding agency against structure. The research questions to be investigated include: (1) What are the advantages of modules that teach mathematics through computational thinking (foregrounding mathematics) versus 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) versus 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?
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 in students’ learning and engagement with mathematics. Specifically, we will work within 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 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). This project is funded by the National Science Foundation.
Re-crafting Mathematics Education
This project, a collaboration with Professor Kylie Peppler at Indiana University, 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.
Grinding New Lenses
The goal of this project is to empower students to view the world as a complex system. Viewing everyday situations from a systems-based perspective is an important aspect of literacy for students and teachers living in an increasingly digital society. The promise of understanding how systems work is that it creates a new and more effective lens for seeing, engaging and changing the world (Jacobson & Wilensky, 2006). In a digital era, systems thinking takes on a new and increasing importance. This is because complex systems are important to our understanding and design of web-based communities, gaming environments, social networks, virtual economies and most of our everyday online activities. To better understand how to support students in developing a lens toward seeing and interpreting the world in terms of the systems that organize it, we will create a modular curriculum framework for supporting the development of systems thinking. The goal of these designs is to help students understand how systems work and look across contexts in order to recognize systems in multiple instantiations. Each module was built to leverage an existing technology that supports students’ engagement with design — GameStar Mechanic; Scratch, and the LilyPad Arduino. These modules are currently being published by MIT Press. This project is funded by the MacArthur Foundation. Read more about the books on the MIT Press website.