Chandra Orrill (PI)
James Burke (Postdoc)
Rachael Brown (Penn State Abington)
Marty Epstein, Akira Harper, Hamza Malik,
Gili Nagar, John Millett, Jinsook Park, Senai Sahle
National Science Foundation
Proportions Playground Toys
This project is exploring how we might be able to promote mathematical reasoning about proportional situations in dynamic environments. We are interested in promoting 6th and 7th grade teachers’ proportional reasoning through a six-hour professional development experience focused on using the dynamic “toys” as the basis for rich conversations about mathematics.
We have four main research questions for this work:
- How do teachers interact with the Proportions Playground toys to reason about proportional situations,
- What knowledge resources do teachers invoke to solve tasks using the toys in the Proportions Playground?
- What evidence is there of participants making connections between and among knowledge resources as they work with the Proportions Playground tasks?
- What evidence is gained about the potential value of the Proportions Playground for supporting teachers in reasoning about proportional situations?
Theory of Learning
Dynamic tasks engage teachers in reasoning about proportional relationships rather than focusing on calculating answers.
Dynamic tasks provide a basis for rich discussion in PD settings.
Conversations, combined with rich tasks, support the development of connections between knowledge resources.
Engaging with multiple representations promotes reasoning in a variety of ways and that is a feature of having a robust understanding.
Engaging with student thinking (e.g., through sample work) provides opportunities to push teacher understanding deeper because it encourages teachers to think in ways that are novel to them and that rely on multiple knowledge resources.
Focusing on playing with mathematical ideas allows engagement in reasoning and argumentation rather than learning to find shortcuts.
Why Do We Do This Work?
In previous work, we noticed that teachers interact differently with dynamic environments than with paper-and-pencil ones. So, we thought it would be interesting to understand how teachers can interact with dynamic toys and what impact that might have on how they participate in professional development. We use the playground and toys metaphors to reinforce that math should be fun and we should all spend more time trying out ideas to see how they work.