Across all of my research I seek to better understand both students' meaningful learning of mathematics, and the nature of supports for that learning
Dr. Fonger researches how students learn mathematics, with a focus on students’ learning of algebra and algebraic thinking across K-12 schooling. In future work, Nicole plans to extend her focus on student cognition, curriculum, and instructional supports to include affective dimensions of learning and well-being. Dr. Fonger has published her work on learning trajectories and learning progressions, which model students’ learning of mathematics over time in relation to curricular and instructional supports for learning. Nicole has also published research reports on her characterizations of students’ representational fluency, a construct to model students’ use of symbols, tables, and graphs in doing and communicating about mathematics with multiple representations. Some of this work is published in proceedings for the North American Chapter of International Group for the Psychology of Mathematics Education (PME-NA). Finally, Professor Fonger publishes research findings that focus on linking research and practice, to bridge the work of mathematics educators in higher education and in school settings, with a focus on secondary math teachers.
Top-level research questions:
Current strands of my research and practice work in mathematics education include:
Please contact me directly if you are interested in collaborating with me. I would love to hear from undergraduate and graduate students, faculty, staff and postdocs, teachers, teacher leaders, and community members. Additional information about these projects is available below, and on my website under Research.
Project: Reality Math Circle Partnership with Syracuse City School District
This project has three Foci:
Project: Learning Trajectories and Learning Progressions in Algebra and Algebraic Thinking
Focus: A learning trajectory integrates conceptual learning goals, mathematical instructional supports and tasks, and characterizations of students’ conceptions vis-a-vis their discursive activity. How does students’ conceptual understanding grow in relation to instructional supports? What is unique about a learning trajectory approach in modeling learning and supports for learning?
Project: Heart-Centered Pedagogy and Mindfulness
Focus: How are cognition, emotion, social relations, and sensation experienced in math learning? How do these dimensions of experience amplify meaningful math learning — especially at the intersection of mathematics and mindfulness? What does it mean to teach mathematics with kindness in mind? How might teaching growth mindset support algebra students' development of productive disposition toward mathematics?
Project: Linking Research and Practice
Focus: How are community, collaboration, and communication central to linking research and practice in mathematics education? What are productive images and metaphors for linking research and practice (that help us move beyond a deficiency or ‘gap’ focused storyline). My goal is to create additional video-based content of research to support broader and clearer dissemination of research.
Project: Representational Fluency and Meaning-Making
Focus: Representational fluency involves creating, interpreting, and connecting multiple representations in doing and communicating about mathematics. I believe engaging in these processes is one way to support to meaning-making about mathematical ideas.
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