• Students worked through two to four representations of each quiz. • In many cases, student solution strategies varied strongly from representation to representation. In other cases, they were more consistent. We present examples of each.

• Student TR solved mathematical, graphical, and pictorial versions of the pendulum quiz displayed above. Strategy summaries (in order of completion):

• Mathematical: The pendulum is 4x as long but is pulled back 4x as far, and so will reach the same final position (incorrect).• Pictorial: The pendulum is pulled back to the same angle and thus won’t travel as far (student recalled a lecture demo where longer pendulums travel slower). TR selected the correct answer.• Graphical: The pendulum is 4x as long and so won’t travel as far; TR selected the correct answer.

• Example: Student JS solved verbal, mathematical, and graphical versions of the pendulum quiz:

• Verbal: Used to arrive at correct answer.• Mathematical: Used combination of above and v(t), x(t) equations to calculate and check correct answer.• Graphical: Used to arrive at correct answer.

The effect of instructional environment on student representational competence

Patrick Kohl and Noah FinkelsteinUniversity of Colorado at Boulder

per.colorado.edu

Student competence with different problem representations has been a subject of recent interest. Studies have included those of student competence with different representations1 and student meta-representational competence2 (what students know about representations).

Research Questions:• How does student performance vary with problem representation?

Is facility with a representation constant across topics?• Are students aware of which representations they handle well (a

meta-representational question)? What impact, if any, does this have on their performance?

• How do different instructional methods affect students’ representational and meta-representational skills?

Introduction

Quiz performance data

End NotesConclusions

Previous work

Student solution strategies

Student assessments of their skills

This work was supported in part by an NSF This work was supported in part by an NSF Graduate Fellowship and by Colorado Graduate Fellowship and by Colorado PhysTEC. Special thanks to the rest of the PhysTEC. Special thanks to the rest of the Physics Education Research group at the Physics Education Research group at the University of Colorado at Boulder. Thanks University of Colorado at Boulder. Thanks also to Drs. Beale, Munsat, and Peterson and also to Drs. Beale, Munsat, and Peterson and Noah Podolefsky for their cooperation and Noah Podolefsky for their cooperation and aid. aid.

Acknowledgements

Current study and materials

Results: Fraction of lectures using a representation

References

Course analysis In-depth interviewsStudent performance data: Quizzes

Statistical significant of choice/control splits (p-values)

Conclusion

• Identical quizzes were given to each of the Traditional and Reform courses. Quizzes were written to match the specific material covered by the Traditional course; thus comparisons of absolute performance are likely invalid.

• We show data from the two 202 courses to allow comparisons of the choice/control splits and performance variations across representation. The 201 data is not shown but is similar to the 202 in terms of relative performances, with higher absolute scores.

Conclusion

• Choice/control splits appear to be influenced by the instructional environment; such splits are essentially absent from the reformed courses and are common in the traditional courses (see highlighted data, for example).

• Hypothesis: Reform-style courses were richer in their use of representations, leading to development of broader student skills. In that case, receiving an assigned rather than a preferred representation would have less impact

• We analyzed traditional 202 and reform 201/202 courses in terms of the representational content of their lectures, exams, homeworks, and recitation/labs

• Homeworks and labs were similar in representational content (though not necessarily in the use of those representations)

• Lectures model representation use for students, exams hold students accountable for representational use: complementary course aspects

Results: Fraction of exams using a representation

• Reform 201/202 courses used more representations and used multiple representations more often.

• This could result in broader student representational skills, which could explain the observed student performance data.

• We interviewed eight students from each of the Reform 201 and 202 classes.

• Students solved a number of the study quizzes, and answered questions regarding the different representations and their formats.

• The in-recitation study quizzes asked students which representational format they preferred to work in. We asked students this same question in the interviews. One out of 16 students contradicted their recitation answer in the interview; the rest did not.

• We examine whether students perform better on the formats they prefer by examining all of the study problems they completed, broken into two groups: problems in representations that they described favorably, and problems in representations described neutrally or unfavorably.

• Six of 15 students perform better on their preferred representations than other; 9 of 15 perform worse. This difference is not significant using a Wilcoxon signed-rank test.

Conclusion

• Students’ quiz strategies often varied strongly with quiz representation, though some students are very consistent across representation.

• Students generally appear to have robust opinions regarding the representations with which they are most competent; these opinions correlate poorly with their actual performances.

1. D. E. Meltzer. “Relation between students’.problem-solving performance and representational mode.” Am. J. Phys., 73:463, 2005.

2. A. A. diSessa and B. L. Sherin. Meta-representation: an introduction. J. of Mathematical Behavior, 19:385, 2000

3. Kohl, P. B. and Finkelstein, N. D. “Representational Format, Student Choice, and Problem Solving in Physics.” Proceedings of the 2004 PERC (in press)

•Student representational skills are influenced by:• Micro-level features (particular features of the problem or representation)3

• Macro-level features (the cumulative effect of instructional environment)•Students have fairly robust opinions of their own representational competence•These opinions are constant across contexts, while their skills are not necessarily•Pervasive use of different/multiple representations in instruction can have a noticeable positive effect on student skills

Repeat of previous study in Physics 201 and 202 taught by a reform-style professor.These three courses taken together allow for comparison across course topic and instructional environment.

Example 201 quizzes are shown. Quiz questions and distractors mapped from one format to the next.

In a previous work,3 we began to investigate these questions. Students in a traditional large-lecture first-year physics course (Physics 202) were given homeworks with problem in four different representations (verbal, mathematical, graphical, pictorial).

Students also received recitation quizzes that came in one of the four representational formats. Students in some recitation sections (choice group) were allowed to choose their format; others (control group) received one at random.

We observed strong and statistically significant differences in performance between the choice and control groups on quizzes. Further, the direction of this effect (whether the choice or control group performed better) varied with representation and topic.

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201 Reform 202 Reform 202 Trad

Verbal

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Pictorial

Multiple

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201 Reform 202 Reform 202 Trad

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Example problem from reform 201 course with mathematical and verbal components

Exams and lecture portions using more than one representation had those portions counted towards each relevant category; totals above 1.0 are possible

201 (Reform) Springs - 0.09 - 0.07

201 Pendulums - - - -

202 (Reform) Diffraction - 0.06 - -

202 Spectroscopy - - - -

Quiz Subject Verbal Math Graphical Pictorial

202 (Trad) Diffraction - - 0.04 0.03

202 Spectroscopy 0.002 0.0001 0.0004 0.001

Pendulum Problem -- Pictorial FormatI pull a pendulum back to the position shown below on the left and let it go. It takes one second to swing into the position shown below and on the right.

Start: After one second:

Now I change the pendulum so that it is four times as long as before, with the same mass. I pull the pendulum back to the same side to the same angle as before and then let it go.

Select the picture that corresponds to the position of the new pendulum after one second. If the pendulum is straight up and down, select the picture that indicates the correct direction of the motion.

A) B) C) D)

Pendulum Problem -- Verbal FormatI set up a pendulum in front of you and pull it back (to your right), and then let it go.

The pendulum takes one second to reach the point opposite from where it started.Now I lengthen the pendulum’s string until it is four times as long as it was, with the

mass unchanged. I pull the pendulum back to the right again (far enough that the string is at the same angle as before), and let it go. Where is it after one second? Circle the correct answer.

A) Straight up and down, and moving left.B) Opposite from its starting position.C) Straight up and down, and moving right.D) Back in its starting position.

Physics 202 - Traditional Verbal Math Graphical Pictorial

Diffraction - Choice 0.35

(N=17)

0.37

(N=57)

0.04

(N=26)

0.82

(N=72)

Diffraction - Control 0.24

(N=17)

0.56

(N=18)

0.25

(N=16)

0.58

(N=19)

Spectroscopy - Choice 0.81

(N=21)

0.90

(N=42)

0.96

(N=28)

0.39

(N=58)

Spectroscopy - Control 0.32

(N=19)

0.13

(N=15)

0.53

(N=17)

0.83

(N=18)

Physics 202 - Reform Verbal Math Graphical Pictorial

Diffraction - Choice 0.15

(N=16)

0.57

(N=34)

0.13

(N=37)

0.21

(N=77)

Diffraction - Control 0.19

(N=46)

0.35

(N=46)

0.14

(N=46)

0.18

(N=44)

Spectroscopy - Choice 0.41

(N=17)

0.32

(N=25)

0.49

(N=37)

0.52

(N=89)

Spectroscopy - Control 0.59

(N=46)

0.39

(N=46)

0.57

(N=42)

0.54

(N=46)

LT

LT