Research

Algebra students’ learning in secondary mathematics schools is a priority topic in education policy, practice, and research. A major impetus driving my research activities is to address bridge theoretical and practical issues related to how secondary students learn mathematics. I focus on students’ learning of algebra and functions with technology-rich multiple representations (Cartesian graphs, function tables, expressions and equations, dynamic and concrete diagrams).

Meaningful Mathematics Learning Research Group

The goal of the meaningful math learning research group is to understand and support students’ reasoning with multiple representations of big mathematical ideas including equivalence, equation solving, and functions (Table 1). We investigate constructs of representational fluency, quantitative reasoning, equivalence thinking, and functional thinking. We ask:

  • How are students’ reasoning with representations and quantitative reasoning linked?
  • What are instructional supports for students’ reasoning with representations of quantitative relationships?
Meaning making is a creative act. (Summary by Nicole L. Fonger, v2019)

A driving goal of our work is to link research and practice in school algebra through communication, partnership, and design-based implementation research.

Figure 1. Communication and partnership are key mechanisms to blur research-practice boundaries. (Sketchnote by Nicole Fonger, v 2020)

Our research is situated in and responsive to the contexts of urban public schools with a focus on issues and ideas that are relevant to secondary school students, teachers, and teacher leaders (Figure 2).  Key questions include

  • What does it mean to blur the boundaries between research and practice when our goal is to promote equitable learning opportunities for all learners of mathematics?
  • How if at all were research-practice connections strengthened in the context of a teacher-researcher collaboration in an era of high-stakes accountability?
Figure 2. This figure depicts some of the places and people (stakeholders) involved in supporting students’ learning in algebra classrooms. At left, the scope of the lens is depicted broadly through state and district policy and initiatives. The center depicts a school view including principals, teachers, support staff, and students. I situate my work in partnership with these places and people and center the use of learning trajectories and learning progressions as tools to guide interventions in classroom practice. (Sketchnote by Nicole L. Fonger, v. 2019)

Examples of Recent Research

Here is a video capturing some results across three ongoing research projects in an effort to link research and practice. See also Papers I’ve written, Visuals of my Research, and a description of my Research Program. Some my work published work is posted online: Research GateGoogleScholar. If interested, here are Select Presentations

Fonger – Research Brief

I have also worked with Dr. Amy Ellis on the SPARQ project supporting my interest in learning trajectories for students’ understanding of functions.

One thought on “Research

  1. Your video is very informative and easy to follow. I actually learned an interesting way to visually illustrate the distinction between variation, co-variation, and correspondence. Nice work.

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