Comparing Explicit and Implicit Teaching of Multiple Representation Use in Physics Problem Solving

1. Comparing Explicit and Implicit Teaching of Multiple Representation Use in Physics Problem Solving David Rosengrant, Rutgers, The State University of New Jersey Patrick Kohl and N. Finkelstein, University of Colorado at Boulder

2. Talk Outline • Introduction – Solving problems with multiple representations • Methods; Course descriptions • Data – Student use of and success with multiple representations • Data – Student reflection on multiple representation use • Conclusions

3. Introduction • What do we mean by multiple representations? • How can we help students to learn to use multiple representations? • Explicitly • Implicitly

4. The Experiment • Two large enrollment first-year algebra-based physics courses. • Rutgers – Explicit use and instruction of multiple representations during concept construction and problem solving • CU – Implicit approach: Professor uses a variety of representations when solving problems in lecture; exams require multiple representation use; little explicit instruction • BOTH courses are PER based • Questions: • Will the students use multiple representations differently? • Will they differ in problem solving performance?

5. Sources of Data • 4 electrostatics problems in recitation, plus one exam/quiz problem • 4 problems are different layout • Students received credit for attempting recitation problems

6. Course description: Rutgers • Substantial PER-based reforms (ISLE curriculum, clickers, revised labs and recitations, ActivPhysics computer simulations) • Heavy and systematic use of multiple representations in lectures and in recitations • Specialized course packet emphasizing multiple representations • Explicit instruction on multiple representation techniques

7. Steps in Problem Solving Process • Picture and Translate: • Sketch the situation described in the problem; include all known information. • Choose a system object and make a list of objects that interact with the system. • Simplify: • Consider the system as a particle. • Decide if you can ignore any interactions of the environment with the system object. • Represent Physically: • Draw a free-body diagram for the system. Label the forces with two subscripts. Make sure the diagram is consistent with the acceleration of the system object (if known). Include perpendicular x and y coordinate axes. • Represent Mathematically: • Apply Newton’s second law in component form to the situation you represented in the free-body diagram. • Add kinematics equations if necessary. • Solve and Evaluate: • Solve the equations for an unknown quantity and evaluate the results to see if they are reasonable (the magnitude of the answer, its units, how the solution changes in limiting cases, and so forth).

8. Free body diagrams (FBD) You are riding to the top floor of your residence hall. As the elevator approaches your floor, it slows to a stop. Construct an FBD for the cable car [with you inside] as the object of interest as the car slows down to a stop. Cable Earth

9. Course description: CU • Substantial PER-based reforms (clickers, revised labs and recitations, PhET computer simulations) • Heavy use of multiple representations in lecture and on exams • Little explicit instruction on multiple representation techniques

10. Data – Performance, 4 questions • Problem 3 performance difference is significant at p = 0.008 level; average difference is not significant

11. Data – Representation use, 4 problems

12. Data – Representation use, exam/quiz problem • More than 95% drew a picture at both universities. • Fraction answering problem correct, and identifying 1, 2, or 3 forces correctly in solution. Note: Rutgers exam is multiple choice and CU quiz is free response. • Rutgers students construct complete FBD significantly (p = 0.0001) more often.

13. Data – Success vs. representation use, exam/quiz problem • Note: Rutgers test was multiple choice; CU quiz was free-response

14. Limitations of Study • Language favors CU in some cases, Rutgers in others • Problem 2: asked for Force Diagram, Rutgers students are familiar with FBD not Force Diagram • Exam problem versus quiz problem • Graded problem is in different format [multiple choice vs. free response]

15. Conclusions • Students in both courses used multiple representations in their solutions much more often than in previously studied traditional courses • Construction of complete FBD is associated with success, consistent with previous research.1 • Neither approach studied is clearly ‘better’; both explicit and implicit instruction approaches were successful 1 D. Rosengrant, E. Etkina, and A. Van Heuvelen, National Association for Research in Science Teaching 2006 Proceedings, San Francisco, CA (2006)

16. Further Studies • More trials • How does the format of the problem influence the construction of multiple representations? • Preliminary study PERC poster Wed. night • Future joint studies

17. Acknowledgements • Thanks to Alan van Heuvelen, Mike Dubson, and Eugenia Etkina. • Special thanks to the Physics Education Research groups at Rutgers and CU-Boulder • This work was supported in part by an NSF graduate fellowship.