1. Are students good at choosing representational formats for problem solving in physics? P. B. Kohl, N. D. Finkelstein, University of Colorado at Boulder

2. Acknowledgements This work was funded in part by an NSF Graduate Fellowship. This work is part of that of the UC Boulder PER Group

3. Introduction What do we mean by representation?

4. Introduction Numerous studies of and attempts to increase student representational facility –Studies of explicit teaching of multiple- representation approaches –Studies of ‘meta-representational competence’ –Direct comparisons of student performance on different representations

5. Goals To look at student inter-representational competence following Meltzer and others To investigate the effects of student choice on representational performance

6. Methods Studies in two areas: one covering wave optics, one covering atomic physics Approximately 220 students per trial

7. Methods Required HW: 1 topic, 4-formats –Verbal –Mathematical –Graphical –Pictorial In section quiz: 1 question, multiple choice –2/3rds Choose their format –1/3rd Random assignment

8. Methods - Other data Student comments Perceived difficulty (Likert rating)

9. Performance variation with format, ‘isomorphic’ problems HW set on Bohr model

12. Graphical format:77% correct (N = 218) Pictorial format:62% Statistically significant, p = 0.006 (binomial z-test, two-tailed) Answer breakdown indicates preference for ‘energy-level’ distractor

15. Comparisons, choice vs. control groups BohrVerbalMathGraph Choice0.81 (N=21)0.90 (N=42)0.96 (N=28) Control0.32 (N=19) p = 0.002 0.13 (N=15) p < 0.0001 0.53 (N=17) p = 0.0004 Pictorial 0.39 (N=58) 0.83 (N=18) p = 0.0012

16. Performance Data Fraction Correct HW #1 Quiz #1 Choice Quiz #1 Control HW #2 Quiz #2 Choice Quiz #2 Control Verbal0.520.350.240.850.810.32 Math0.600.370.560.850.900.13 Graph0.460.040.250.760.960.53 Pictorial0.540.820.580.620.400.83

17. Conclusion Strong influences on performance –Representational format –Student choice Future work –Expand studies into other topics –Include interviews to probe solution strategies and motivations