Using Design Research: Developing instructional materials for teaching rate of change with iPads

1. Using Design Research: Developing instructional materials for teaching rate of change with iPads Curtis Kendrick – Charlotte, NC William Hall – Raleigh NC

2. Interests/Motivation • Rate of change • Lesh, Post, & Behr (1998) argued that proportional reasoning is both the capstone of the middle school mathematics program and the cornerstone of all that is to follow. • Proportional or linear reasoning is a major tool for human beings in many cultures to interpret real world phenomena (Post, Behr, & Lesh, 1988; Spinillo & Bryant, 1999). • Proportional reasoning is a term that denotes reasoning in a system of two variables between which there exists a linear functional relationship—leads to conclusions about a situation or phenomenon that can be characterized by a constant ratio (Karplus, Pulos, & Stage, 1983).

3. Interest/Motivation • Technology • Technological literacy is vital to success in modern society • Large intersection between mathematical and technological literacy • Activity development utilizing technology needs to be researched rigorously • Many U.S. schools are adopting iPads as their chosen technology and are committing to electronic textbooks

4. Why Design Research? • Interested in designing activities utilizing modern technology • Want to develop theory explaining how students interact with touch technology, specifically while they learn about rate of change • Not only interested in if the instructional sequence is effective, but why it works

5. Phase One: Design Phase • Local instruction theory • Research • Historical development of rate of change • Domain specific cognitive development (i.e. what we know about how students think about rate of change) • Instructional materials for rate of change that have been researched in the past • Student learning with technology, specifically the iPad • Specific affordances of the iPad

6. Phase One: Design Phase • Local instruction theory (cont.) • Establish learning goals • Help students learn about additive & multiplicative rates of change • Engage students using touch technology with the iPad • Use specific affordances of iPad to teach rate of change • Hypothetical Learning Trajectory • Combining the research and learning goals to hypothesize a sequence of activities to help students learn about additive and multiplicative rates of change using the iPad

7. Phase One: Design Phase • Technological affordances and rate of change • Using the accelerometer in the iPad for data collection • Introducing the concept of rate of change using movement; embodiment of motion and change • Students can see different representations of rate of change simultaneously (e.g. graph & motion) • Touch Technology • Have students interact with representations in a way not permitted by other technologies • iPad as a research tool • Have students use web to research functional relationships (e.g. linear vs. exponential growth in the real-world)

8. Phase Two: Design Experiment • Implement the instructional sequence • Pilot investigation • Collect data on student learning • Video data of students working with the material • Video data of class discussion • Look at discourse (i.e. ideas “taken-as-shared”) • Collecting student artifacts not caught on iPad • Interviews with students about rate of change • Pre, mid, & post? • Interviews with students about technology • Pre, mid, & post? • Field notes by researchers/teachers, including reflections on the lessons

9. Phase Three: Retrospective Analysis • Analysis • Debriefing with research team to discuss lessons and field notes • Coding all video data (interviews & class work) • Grounded theory approach to analysis • Revisit learning goals in light of reflections and field notes • Revisit the theory of how students learn rate of change and how they interact with the technology • Use lessons from analysis to revise our hypothetical learning trajectory, including both our theory and specific instructional sequence.

10. Next Steps… • Get ready for larger implementation and begin the cycle again!