I am dedicated to the advancement of our knowledge of the learning of mathematics. My research program centers on advancing theories of learning and curriculum design for the learning and teaching of algebra. My research program is concerned with advancing our knowledge of the learning of mathematics through characterizing and supporting secondary students’ learning of core algebraic concepts and practices. My research program is guided by the following fundamental questions: What are effective curricular and instructional supports for supporting change in students’ representational fluency with computer algebra systems? How are students’ learning of core algebraic concepts and representational fluency in solving problems related? These questions have theoretical and practical import for advancing the field of mathematics education in international settings, especially in the domains curriculum studies, theories of learning, and mathematics technology.
Theoretical Stance and Methods
I take the stance that both means of support and means of assessing and characterizing student learning are central in advancing local instructional theory, theories of learning, and best practices in mathematics curriculum and instruction. I investigate supports for learning and teaching with technology through design experiments focused on cycles of design, experimentation, and analysis. I conduct clinical and task-based interviews with individual or pairs of students to understand students’ conceptions and representational fluency in doing and communicating about mathematics. I primarily conduct qualitative data analysis including constant comparative analysis and axial coding in the tradition of grounded theory.
Current Research Projects
My engagement in collaborative research endeavors has supported my individual research agenda on students’ learning and thinking practices in the context of school algebra. Most notably, in my current position at the University of Wisconsin-Madison, I collaborate on several externally funded projects focused on the advancement of knowledge on student learning over time. For example, on Project LEAP (Learning through an Early Algebra Progression) I advance a theoretical framework and methodological approach to articulating learning progressions. In Fonger, Stephens, Knuth, and Blanton (under review), we articulate the four-components of a learning progression—curriculum, instruction, assessment, and levels of sophistication in student thinking—and how this approach integrates research across science and mathematics education in K-12 schools and tertiary levels. As another example, on Project SPARQ (Supporting Students’ Proof Practices through Quantitative Reasoning in Algebra) I investigate secondary students’ conceptions of functions in relation to their meanings of symbolic rules (Fonger, Ellis, Dogan, accepted). In this project I take a learning trajectory approach to understanding the relationships among instructional learning goals and tasks, and students’ processes of learning. These two ongoing research projects showcase my professional commitment to the advancement of theory on learning, how curriculum and instruction influence learning, and an in-depth examination of students’ conceptions of equations and functions and practice of representing.
Intellectual Merit and Broader Impact
My research contributes to literature in mathematics education on how students’ conceptions of mathematics and representational fluency in solving problems interact in rich instructional settings. Results of my research contribute to our understanding of features of curriculum and instructional design that are supportive of students’ learning and representational fluency in algebra. Broadly, my research (a) generates knowledge on improved student learning processes and outcomes in school algebra, a gatekeeper to higher-level mathematics and other STEM domains, and (b) improves mathematics education and educator development by a research and dissemination plan that targets benefits for teachers, university instructors, and curriculum developers. My research agenda is rooted in an goal to link research and practice to support meaningful learning of mathematics for all students.