Mathematical Cognition and Learning

My research:

What drives my research is a passionate curiosity to understand how people think about and learn mathematics so as to foster meaningful learning experiences and broad participation in mathematics. My work is fueled by and informed by my own interest in mathematics and my educational orientation – a desire to understand learning processes in a way that can improve both teaching and learning of mathematics for all students.

Brief biographical information:

I am currently an Associate Professor of Mathematics Education in the Department of Mathematics at Western Michigan University.

My original training is in mathematics. Before embarking on my PhD studies in mathematics education, I earned a masters degree in mathematics from UC Berkeley. I wrote my thesis "On fixed points for discrete logarithms" (see attached) under the direction of Carl Pomerance, then of Bell Labs. My advisor at UC Berkeley was Paul Vojta. The research project I wrote about in my thesis began as joint work together with Carl during two summer internships at Bell Labs I participated in as part of my fellowship for graduate studies in mathematics. This work was recently extended and published as a joint paper with Pomerance and Soundararajan in the Proceedings of the Ninth Algorithmic Number Theory Symposium (ANTS IX) as part of the Springer Lecture Notes on Computer Science Series.

During my time as a math PhD student, I thought long and hard about how to use my skills and expertise to make a direct contribution to the lives of those around me. I got in contact with Alan Schoenfeld, a professor of mathematics and mathematics education at UC Berkeley, who became my mentor and future advisor. Together with researchers from UCLA and UW-Madison, Alan was just starting a new NSF-funded Center for Learning and Teaching: DiME (Diversity in Mathematics Education). It sounded like exactly the kind of opportunity I was looking for -- a chance to roll up my sleeves and concentrate on important social issues in the real world while still getting to use my training in mathematics.

My work with DiME introduced me to myriad issues in contemporary public education at multiple levels: structural, community, school, classroom and individual. The conversations I had with my DiME colleagues really stretched me to think about why we teach mathematics and what kinds of things we can do to help all children have access to and engage meaningfully with powerful mathematics. DiME was focused on equity issues as they play out in middle school mathematics classrooms in local school districts. The DiME project involved regular scholarly cross-campus seminars and writing efforts, in addition to our work with local middle school math teachers in their classrooms and in monthly professional development activities.

My research goals have taken shape through my doctoral training, especially through the Diversity in Mathematics Education (DiME), Algebra Teaching Study (ATS), and Research in Cognition and Mathematics Education (RCME) projects at UC Berkeley, as well as through my dissertation research on conceptual change and postdoctoral research on fostering productive disciplinary engagement.

The purposeful interplay between classroom studies and studies of individual cognition is one of the features of my ongoing research program. My dissertation work on conceptual change and strategy change emerged out of a comparative study of eighth grade algebra classrooms I was conducting in conjunction with my work on the Diversity in Mathematics Education Project at UC Berkeley, led by Dr. Alan Schoenfeld. The focus of my classroom study was on transitions to algebraic thinking and opportunities to learn algebra. I collaborated with and studied a single teacher in the context of two different algebra classes that she taught: one regular track and one low track. I explored the link between classroom discourse in the two classes and opportunities to learn the content of a particular strand of the curriculum: solving contextual algebraic tasks. I found that the mathematical discussions in the low-track class were of a qualitatively different nature, having significant implications for students’ future learning, despite the use of the same curricular materials (“A Tale of Two Algebras: Opportunities to Learn Algebra in Low Track Settings,” NCTM, 2010).

In my dissertation (Levin, 2012; Levin, in press), I investigated the fine-grained interrelation between processes of conceptual change and processes of strategy change. The initial impetus for this line of work came from rich tutorial data around students’ approaches to solving contextual algebraic tasks that I had collected in conjunction with the comparative classroom DiME study (described above). In analyzing the data, I was struck by the idea that problem solving could be a window into individuals’ conceptual understanding and as such, be a potentially powerful vehicle for conceptual development. The existing research in psychology framed strategy change in terms of the learning of procedures, neglecting the significant conceptual basis for implementing a procedure and the role of conceptual development in strategy change. In this work, I extended a theory of conceptual change, coordination class theory (diSessa & Sherin, 1998), which resulted in shifting the discourse around what it means to understand both concepts and strategies away from the traditional separation of these kinds of knowing (“conceptual knowledge” versus “procedural knowledge”), toward a more integrated perspective with both procedural and conceptual entailments. You can read about this data and strategy systems in my recent Cognition and Instruction article on the subject.

As an extension of my work on conceptual change and strategy change, I have moved from studying learning and conceptual change in clinical settings to considering how such perspectives can be brought to bear on more naturalistic data in the classroom and professional settings. Levin & diSessa, 2016 gives a coordination class theory reformulation and extension of Stevens and Hall’s notion of disciplined perception (Stevens & Hall, 1998). Our reformulated disciplined perception perspective dovetails nicely with both my agenda to explore learning and conceptual change processes across an increasingly wide range of contexts, and also with my agenda to try to integrate the results of analyses of learning done from multiple theoretical and methodological perspectives (See my co-edited volume, Knowledge and Interaction: A Synthetic Agenda for the Learning Sciences on the agenda of integrating methodological perspectives on learning, diSessa, Levin, & Brown, 2016).

During my postdoctoral work, I broadened my perspective on learning through collaborative work I have been engaged in with the physics education research group at the University of Bologna, led by Dr. Olivia Levrini (where I was a visiting scholar in the fall semester, 2012). We initiated a collaborative project concerned with the analysis of classroom discourse that fosters productive disciplinary engagement (Engle & Conant, 2002) and what we have termed appropriation (Levrini et al, 2015), building up Bakhtin and Rogoff, in order to capture the process by which students make the content they are learning (in this case, thermodynamics) their own. The operational discourse markers for this broader kind of learning (appropriation) are linked to students’ affect and identity, as well as to their conceptual understanding. A practical impetus for this work is the drive to increase access to STEM fields through designing curriculum materials and classroom interactions that engender a deeply personal relationship to and understanding of the specifics of disciplinary content. Our piece in the Journal of the Learning Sciences operationalizes the construct of appropriation for science learning. We have written about the nexus of identity and conceptual change Amin & Levrini's Converging Perspectives on Conceptual Change: Mapping an Emerging Paradigm. Together with Olivia Levrini and Jim Greeno, I was also the section editor for the section on Identity and Conceptual Change.

Personal:

During graduate school, I spent two years in Pisa, Italy with my husband Aaron, a postdoctoral fellow at the "Ennio De Giorgi" mathematics research center. We moved back to the states summer 2009. In 2009-10, I was based in Berkeley and Aaron spent a year as a member of the Institute for Advanced Study in Princeton, NJ. I finished my PhD at Berkeley in December, 2011 and began a postdoctoral research position in the Program in Mathematics Education (PRIME) at Michigan State University. In August, 2015, I began my current position as an assistant professor of mathematics education in the Department of Mathematics at Western Michigan University.

I am a serious violinist who enjoys participating in chamber music workshops and festivals and preparing community recitals and concerts. During my time in Berkeley, I was the concertmaster of the Prometheus Symphony Orchestra and also performed with the Kensington Symphony and the Berkeley Community Chorus and Orchestra. When I graduated from Berkeley, I gave a recital to raise funds for pancreatic research in the name of one of my graduate school mentors. Randi Engle (Raise the Cure for Randi).