One way to link research and practice is to interpret theory with the aim of improving practice.
In one study I conducted I developed a framework or lens for seeing how students create, interpret, and connect one or more representations for doing and communicating about mathematics as they solved problems.
A first implication of this work is to get students to ENGAGE with one or more representations by ASKING…
—what do you see?—explain it
–Show me, so we can both see—create it on your paper or technology
–Tell me, how are these related?—elaborate the connection
A second implication of this research is to value emerging representational fluency. As students are learning new ideas, students might create incomplete representations, or might interpret their meaning in a way that doesn’t match the disciplinary conventions and norms.
–From a growth-mindset perspective, emerging fluencies are opportunities to grow and develop sense-making
–I am reminded of a quote from Brené Brown – that as long as we are creating, we are cultivating meaning—
Finally, to grow meaningful representational fluency, it helps to ground instructional design on supporting core mathematical concepts. For example, the data for this research was focused on mathematical equivalence of expressions and equations to support equation solving with multiple representations. Functions are a rich area to support meaningful understanding of correspondence and rate of change in linked quantities.
I invite you to engage with this work, and to reach out. I’d love to know… what are you noticing? What are you wondering? You can reach me, Nicole L. Fonger, at NMLFONGER on twitter and Instagram.