Comparing Explicit and Implicit Comparing Explicit and Implicit Teaching of Multiple Representation Teaching of Multiple Representation

Use in Physics Problem SolvingUse in Physics Problem Solving

Patrick Kohl, Noah FinkelsteinPatrick Kohl, Noah FinkelsteinUniversity of Colorado, BoulderUniversity of Colorado, Boulder

David RosengrantDavid RosengrantRutgers, the State University of New Rutgers, the State University of New

JerseyJersey

Introduction – Multiple Introduction – Multiple representations and problem representations and problem

solvingsolving Physics problems are often solved most easily by using Physics problems are often solved most easily by using

various representations together (mathematics, pictures, various representations together (mathematics, pictures, graphs, etc.)graphs, etc.)

How can we best teach the use of multiple How can we best teach the use of multiple representations in problem solving?representations in problem solving?

Two broad approaches exist:Two broad approaches exist: ExplicitExplicit:: Teaching specific step-by-step problem-solving Teaching specific step-by-step problem-solving

procedures involving different representations, and emphasize procedures involving different representations, and emphasize those procedures throughout the coursethose procedures throughout the course

Implicit:Implicit: Demonstrating good problem-solving approaches Demonstrating good problem-solving approaches and including a variety of representations throughout the and including a variety of representations throughout the course, with little explicit instruction on methodscourse, with little explicit instruction on methods

Study setupStudy setup

Two large enrollment (~500 student) first-Two large enrollment (~500 student) first-year algebra-based physics coursesyear algebra-based physics courses Rutgers – Explicit teaching of multiple Rutgers – Explicit teaching of multiple

representation problem solvingrepresentation problem solving CU – Implicit teaching, through example and CU – Implicit teaching, through example and

accountabilityaccountability

Question: Will the students show Question: Will the students show differences in multiple representation use, differences in multiple representation use, performance, and attitudes?performance, and attitudes?

Data sourcesData sources

Second semester of sequence (after Second semester of sequence (after significant class experience).significant class experience). Data from students who took both semestersData from students who took both semesters

4 electrostatics questions in recitation, plus 4 electrostatics questions in recitation, plus one exam/quiz problemone exam/quiz problem Problems chosen to benefit from use of pictures Problems chosen to benefit from use of pictures

and free-body diagrams (FBDs)and free-body diagrams (FBDs)

Short (~20 question) survey on how students Short (~20 question) survey on how students use multiple representations in physics.use multiple representations in physics.

Example problemsExample problemsQuestion 1A 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 2A 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 3A 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 kgqcart = 5.0 mC10 cm20 cmqleft sphere = 1.0 mCqrt sphere = -2.0 mCFLsphere on cartFR sphere on cartFsurface on cartFEarth on cart

Question 4A 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 kgqcart = 5.0 C

10 cm

20 cm

qleft sphere = 1.0 C qrt sphere = -2.0 C FLsphere on cart

FR sphere on cart

Fsurface on cart

FEarth on cart

Course descriptionsCourse descriptions

Rutgers: PER-based reforms including ISLE Rutgers: PER-based reforms including ISLE (Investigative Science Learning (Investigative Science Learning Environment), clickers and the Active Environment), clickers and the Active Learning GuideLearning Guide Model solutions for homeworksModel solutions for homeworks Multiple-representations recitation/lab tasksMultiple-representations recitation/lab tasks Explicit problem-solving proceduresExplicit problem-solving procedures

CU: PER-based reforms (clickers, revised labs CU: PER-based reforms (clickers, revised labs and recitations, PhET computer simulations)and recitations, PhET computer simulations) Heavy use of multiple reps. in lecture/examsHeavy use of multiple reps. in lecture/exams Little explicit instruction on problem solvingLittle explicit instruction on problem solving

SuccessSuccess Prob. 1Prob. 1 Prob. 2Prob. 2 Prob. 3Prob. 3 Prob. 4Prob. 4

RutgersRutgers 0.38 (235)*0.38 (235)* 0.560.56 0.320.32 0.38 (155)0.38 (155)

CUCU 0.38 (314)0.38 (314) 0.560.56 0.430.43 0.40 (269)0.40 (269)

Data – Recitation problemsData – 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-Difference is statistically significant, p = 0.008, two-

tailed binomial testtailed binomial test Overall average difference (0.41 vs 0.44) is not Overall average difference (0.41 vs 0.44) is not

significant.significant.

Data – Recitation problemsData – Recitation problems

Fraction of students drawing a picture with their problem solutionFraction of students drawing a picture with their problem solution

Prob. 1Prob. 1 Prob. 2Prob. 2 Prob. 3Prob. 3 Prob. 4Prob. 4

RutgersRutgers 0.890.89 0.890.89 0.030.03 0.73 0.73

CUCU 0.920.92 0.910.91 0.130.13 0.900.90

P-valueP-value XX XX 0.00010.0001 0.00010.0001

RutgersRutgers 0.590.59 0.520.52 0.030.03 1.711.71

CUCU 0.800.80 0.710.71 0.110.11 1.691.69

P-valueP-value 0.050.05 0.0080.008 0.00020.0002 XX

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.Note: Forces were required as part of the answer for problem 4.

Data – Exam/quiz problemData – Exam/quiz problem

ExamExam CorrectCorrect 1 Force1 Force 2 Forces2 Forces 3 Forces3 Forces

RutgersRutgers 0.56 (283)0.56 (283) 0.090.09 0.220.22 0.51 0.51

CUCU 0.29 (280)0.29 (280) 0.230.23 0.310.31 0.32 0.32

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.

Survey dataSurvey data

Three survey questions showed statistically Three survey questions showed statistically significant positive correlation with student significant positive correlation with student problem performance in both courses:problem performance in both courses: I am usually good at learning physics on my own, without any I am usually good at learning physics on my own, without any

help from others.help from others. I am usually good at solving physics problems on my own, I am usually good at solving physics problems on my own,

without any help from others.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 Several other questions showed correlations with success in one or the other class, including:success in one or the other class, including: I am good at finding and fixing my mathematical mistakes. I am good at finding and fixing my mathematical mistakes.

(Rutgers)(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 When I use multiple representations, I do so because it makes

a problem easier to understand. (CU)a problem easier to understand. (CU) How comfortable are you with graphs? (Rutgers)How comfortable are you with graphs? (Rutgers)

ConclusionsConclusions

Students in both courses used multiple Students in both courses used multiple representations in their solutions much more often representations in their solutions much more often than in previously studied traditional coursesthan in previously studied traditional courses

Construction of complete FBD is associated with Construction of complete FBD is associated with success, consistent with previous research.success, consistent with previous research.11

Neither approach studied is clearly ‘better’; both Neither approach studied is clearly ‘better’; both explicit and implicit instruction approaches were explicit and implicit instruction approaches were successfulsuccessful

11 D. Rosengrant, E. Etkina, and A. Van Heuvelen, National Association for Research in D. Rosengrant, E. Etkina, and A. Van Heuvelen, National Association for Research in Science Teaching 2006 Proceedings, San Francisco, CA (2006)Science Teaching 2006 Proceedings, San Francisco, CA (2006)

AcknowledgementsAcknowledgements

Thanks to Mike Dubson, Alan van Thanks to Mike Dubson, Alan van Heuvelen, and Eugenia Etkina.Heuvelen, and Eugenia Etkina.

Thanks also to the Physics Education Thanks also to the Physics Education Research groups at CU-Boulder and Research groups at CU-Boulder and Rutgers.Rutgers.

This work was supported in part by This work was supported in part by an NSF Graduate Fellowship.an NSF Graduate Fellowship.

Survey Data - RutgersSurvey Data - Rutgers

I am usually good at learning physics on my own, without I am usually good at learning physics on my own, without any help from others. any help from others.

I am usually good at solving physics problems on my own, I am usually good at solving physics problems on my own, without any help from others.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 Rate how your ability affects your performance in physics

class. 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 How often you use written explanations [negative

correlation].correlation].

Survey Data - CUSurvey Data - CU I am usually good at learning physics on my own, without any help I am usually good at learning physics on my own, without any help

from others. from others. I am usually good at solving physics problems on my own, without I am usually good at solving physics problems on my own, without

any help from others.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 When I use multiple representations, I do so because it makes a

problem easier to understand.problem easier to understand. When I use multiple representations, I do so because I will be When I use multiple representations, I do so because I will be

more likely to get the right answer.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 I am good at figuring out how closely related different

representations are (words, equations, pictures, free body representations are (words, equations, pictures, free body diagrams, etc.). 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.