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

2. Introduction – Multiple representations and problem solving Physics problems are often solved most easily by using various representations together (mathematics, pictures, graphs, etc.) Physics problems are often solved most easily by using various representations together (mathematics, pictures, graphs, etc.) How can we best teach the use of multiple representations in problem solving? How can we best teach the use of multiple representations in problem solving? Two broad approaches exist: Two broad approaches exist: Explicit : Teaching specific step-by-step problem-solving procedures involving different representations, and emphasize those procedures throughout the course Explicit : Teaching specific step-by-step problem-solving procedures involving different representations, and emphasize those procedures throughout the course Implicit: Demonstrating good problem-solving approaches and including a variety of representations throughout the course, with little explicit instruction on methods Implicit: Demonstrating good problem-solving approaches and including a variety of representations throughout the course, with little explicit instruction on methods

3. Study setup Two large enrollment (~500 student) first-year algebra-based physics courses Two large enrollment (~500 student) first-year algebra-based physics courses Rutgers – Explicit teaching of multiple representation problem solving Rutgers – Explicit teaching of multiple representation problem solving CU – Implicit teaching, through example and accountability CU – Implicit teaching, through example and accountability Question: Will the students show differences in multiple representation use, performance, and attitudes? Question: Will the students show differences in multiple representation use, performance, and attitudes?

4. Data sources Second semester of sequence (after significant class experience). Second semester of sequence (after significant class experience). Data from students who took both semesters Data from students who took both semesters 4 electrostatics questions in recitation, plus one exam/quiz problem 4 electrostatics questions in recitation, plus one exam/quiz problem Problems chosen to benefit from use of pictures and free-body diagrams (FBDs) Problems chosen to benefit from use of pictures and free-body diagrams (FBDs) Short (~20 question) survey on how students use multiple representations in physics. Short (~20 question) survey on how students use multiple representations in physics.

5. Example problems Question 1 A small (100 g) metal ball with +2.0 mC of charge is sitting on a flat frictionless surface. A second identical ball with -2.0 mC of charge is 3.0 cm to the left of the first ball. What is the magnitude and direction of the electric field that we would need to apply to keep the balls 3.0 cm apart? Question 2 A sphere of 0.3 kg is charged to 30 mC. It is tied to the end of a rope and hangs 20 cm directly below a second chargeable sphere. If the rope will break at 4.8 N, what charge needs to be on the second sphere to break the rope? Hint: It may be useful to draw a force diagram. Question 3 A frictionless metal cart is being held halfway between two stationary charged spheres. The cart’s mass is 2.5 kg and its charge is 5.0 mC. The left sphere has a charge of 1 mC and the right sphere has a -2 mC charge. The two spheres are 20 cm apart. At the instant the cart is released, what is the acceleration of the cart? Refer to the included diagrams for help.m = 2.5 kg qcart = 5.0 mC10 cm20 cmqleft sphere = 1.0 mCqrt sphere = -2.0 mCFLsphere on cartFR sphere on cartFsurface on cartFEarth on cart Question 4 A 100 gram ball has a charge of 40 mC. The ball is dropped from a height of 2 m into a vertical electric field. As a result, the ball accelerates towards the floor at a rate of 7 m/s2. Draw a diagram showing all the forces involved in the picture, and calculate the magnitude of the electric field present. m = 2.5 kg q cart = 5.0  C 10 cm 20 cm q left sphere = 1.0  C q rt sphere = -2.0  C F Lsphere on cart F R sphere on cart F surface on cart F Earth on cart

6. Course descriptions Rutgers: PER-based reforms including ISLE (Investigative Science Learning Environment), clickers and the Active Learning Guide Rutgers: PER-based reforms including ISLE (Investigative Science Learning Environment), clickers and the Active Learning Guide Model solutions for homeworks Model solutions for homeworks Multiple-representations recitation/lab tasks Multiple-representations recitation/lab tasks Explicit problem-solving procedures Explicit problem-solving procedures CU: PER-based reforms (clickers, revised labs and recitations, PhET computer simulations) CU: PER-based reforms (clickers, revised labs and recitations, PhET computer simulations) Heavy use of multiple reps. in lecture/exams Heavy use of multiple reps. in lecture/exams Little explicit instruction on problem solving Little explicit instruction on problem solving

7. Success Prob. 1 Prob. 2 Prob. 3 Prob. 4 Rutgers 0.38 (235)* 0.560.32 0.38 (155) CU 0.38 (314) 0.560.43 0.40 (269) Data – Recitation problems *Parentheses indicate sample size N. N is the same for problems 1-3 Comparable performance on all problems but #3 Comparable performance on all problems but #3 Difference is statistically significant, p = 0.008, two- tailed binomial test Difference is statistically significant, p = 0.008, two- tailed binomial test Overall average difference (0.41 vs 0.44) is not significant. Overall average difference (0.41 vs 0.44) is not significant.

8. Data – Recitation problems Fraction of students drawing a picture with their problem solution Fraction of students drawing a picture with their problem solution Prob. 1 Prob. 2 Prob. 3 Prob. 4 Rutgers0.890.890.030.73 CU0.920.910.130.90 P-valueXX0.00010.0001 Rutgers0.590.520.031.71 CU0.800.710.111.69 P-value0.050.0080.0002X Average number of forces identified with each solution. Average number of forces identified with each solution. Note: Forces were required as part of the answer for problem 4.

9. Data – Exam/quiz problem ExamCorrect 1 Force 2 Forces 3 Forces Rutgers 0.56 (283) 0.090.220.51 CU 0.29 (280) 0.230.310.32 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. Student success as a function of number of forces correctly identified. Note that problem statement did not require an FBD.

10. Survey data Three survey questions showed statistically significant positive correlation with student problem performance in both courses: Three survey questions showed statistically significant positive correlation with student problem performance in both courses: I am usually good at learning physics on my own, without any help from others. I am usually good at learning physics on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. How comfortable are you with free body diagrams? How comfortable are you with free body diagrams? Several other questions showed correlations with success in one or the other class, including: Several other questions showed correlations with success in one or the other class, including: I am good at finding and fixing my mathematical mistakes. (Rutgers) I am good at finding and fixing my mathematical mistakes. (Rutgers) I am good at finding and fixing my conceptual mistakes. (CU) I am good at finding and fixing my conceptual mistakes. (CU) When I use multiple representations, I do so because it makes a problem easier to understand. (CU) When I use multiple representations, I do so because it makes a problem easier to understand. (CU) How comfortable are you with graphs? (Rutgers) How comfortable are you with graphs? (Rutgers)

11. Conclusions Students in both courses used multiple representations in their solutions much more often than in previously studied traditional courses 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 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 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)

12. Acknowledgements Thanks to Mike Dubson, Alan van Heuvelen, and Eugenia Etkina. Thanks to Mike Dubson, Alan van Heuvelen, and Eugenia Etkina. Thanks also to the Physics Education Research groups at CU-Boulder and Rutgers. Thanks also to the Physics Education Research groups at CU-Boulder and Rutgers. This work was supported in part by an NSF Graduate Fellowship. This work was supported in part by an NSF Graduate Fellowship.

13. Survey Data - Rutgers I am usually good at learning physics on my own, without any help from others. I am usually good at learning physics on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. I am good at finding and fixing my mathematical mistakes. I am good at finding and fixing my mathematical mistakes. Rate how your ability affects your performance in physics class. Rate how your ability affects your performance in physics class. How comfortable are you with free body diagrams. How comfortable are you with free body diagrams. How comfortable are you with graphs. How comfortable are you with graphs. How often you use written explanations [negative correlation]. How often you use written explanations [negative correlation].

14. Survey Data - CU I am usually good at learning physics on my own, without any help from others. I am usually good at learning physics on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. I am usually good at solving physics problems on my own, without any help from others. I am good at finding and fixing my conceptual mistakes. I am good at finding and fixing my conceptual mistakes. I feel motivated to learn physics. I feel motivated to learn physics. When I use multiple representations, I do so because it makes a problem easier to understand. When I use multiple representations, I do so because it makes a problem easier to understand. When I use multiple representations, I do so because I will be more likely to get the right answer. When I use multiple representations, I do so because I will be more likely to get the right answer. I am good at representing information in multiple ways. I am good at representing information in multiple ways. I am good at figuring out how closely related different representations are (words, equations, pictures, free body diagrams, etc.). I am good at figuring out how closely related different representations are (words, equations, pictures, free body diagrams, etc.). How comfortable are you with free body diagrams. How comfortable are you with free body diagrams. How comfortable are you with equations and numbers. How comfortable are you with equations and numbers.