Using R to Assess Mathematical Sense-Making in Introductory Physics - - PowerPoint PPT Presentation

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Using R to Assess Mathematical Sense-Making in Introductory Physics - - PowerPoint PPT Presentation

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Using R to Assess Mathematical Sense-Making in Introductory Physics Courses by Brian Danielak, Eric Kuo, Michael M. Hull, and Andrew Elby 2010 UseR! Conference - July 21, 2010 1 I work behind here 2 Students in conventional courses often

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Using R to Assess Mathematical Sense-Making in Introductory Physics Courses

2010 UseR! Conference - July 21, 2010

by Brian Danielak, Eric Kuo, Michael M. Hull, and Andrew Elby

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I work behind here

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Students in conventional courses often treat formulas as algorithms.

Sherin, B. L. (2001). How Students Understand Physics Equations. Cognition and Instruction, 19(4), p. 479

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

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Sense-making is about seeking coherence

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v = v0 + at

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v = v0 + at

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

v = v0 + at v = v0 + at

+ = t1

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

v = v0 + at v = v0 + at

+ + = = t1 t2

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

v = v0 + at v = v0 + at

+ + + = = = t1 t2 t3

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The same mathematical structure models lots of other situations

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+ + + = = = t1 t2 t3

money = P + rt

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+ + + = = = x1 x2 x3

ˆ Y = β0 + β1X1

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So here’s the big Question

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

v = v0 + at v = v0 + at

+ + + = = = t1 t2 t3

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v = v0 + at

if I know the initial velocity... The uniform acceleration... and the time... Then I can calculate the final velocity!

How can we test for thinking like this When we usually test for thinking like this?

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A Tale of 3 Instructors

1 3 2

New Veteran Veteran

Sense-making Traditional Approach

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And one Final Exam

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Multiple Choice Free Response

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And one Final Exam

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Multiple Choice Free Response

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426 Students 3 Classes

2 1 6

Sense-making items

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5 3 4 chosen a priori 7 8

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Class 1 Class 2 Class 3

3 4 2

e-score

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Looking graphically at the data

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Raw Score Distributions by Instructor

rawscore count

5 10 15 20 25 30 35 5 10 15 20 25 30 35 5 10 15 20 25 30 35 2 4 6 8 1 2 3

Sense-making (new) Sense-making (vet) Traditional (vet)

Across all 8 MC items

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Escore Distributions by Instructor

escore count

10 20 30 40 10 20 30 40 10 20 30 40 −1 1 2 3 4 5 6 1 2 3

Sense-making (new) Sense-making (vet) Traditional (vet)

Just the 5 Sense-making Items

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We ran a one-way ANOVA, then MCPs

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Result 1

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Across all 8 Multiple Choice items, Sense-making > traditional approach

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−0.15 −0.10 −0.05 0.00 0.05 0.10 3−2 3−1 2−1

95% family−wise confidence level

Differences in mean levels of instructor Rawratio

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  • TukeyHSD

p-adj Cohen’s d

0.061

  • 0.019
  • 0.080

0.053 0.751 0.007 0.277

  • 0.0839
  • 0.365

Across all 8 MC items

95% Family-wise Confidence Level

1 3 2 1 3 2

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Result 2

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Across the 5 specific sense-making items, Sense-making >> traditional approach

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−0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 3−2 3−1 2−1

95% family−wise confidence level

Differences in mean levels of instructor Eratio

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  • TukeyHSD

p-adj Cohen’s d

0.0450

  • 0.0871
  • 0.132

0.296 0.0130 < 0.001 0.182

  • 0.331
  • 0.510

On Sense-making MCs

95% Family-wise Confidence Level

1 3 2 1 3 2

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Exploring Free-Response Data

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?

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What happens to mechanical energy after the explosion?

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What Happens to the Mechanical Energy

  • f the Two Blocks?

instructor count

20 40 60 80 100 120 140 1 2 3 q09d stays the same increases blank decreases missing value uncodeable

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What Happens to the Mechanical Energy

  • f the Two Blocks?

instructor count

20 40 60 80 100 120 140 1 2 3 q09d stays the same increases blank decreases missing value uncodeable

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What Happens to the Mechanical Energy

  • f the Two Blocks?

instructor count

20 40 60 80 100 120 140 1 2 3 q09d stays the same increases blank decreases missing value uncodeable

43 43 72

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What Happens to the Mechanical Energy

  • f the Two Blocks?

instructor count

20 40 60 80 100 120 140 1 2 3 q09d stays the same increases blank decreases missing value uncodeable

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Mechanical Energy Stays the Same

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43 43 72

Mechanical Energy Stays the Same =

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Sense-making (new) Sense-making (vet) Traditional (vet)

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Mechanical Energy Stays the Same =

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Sense-making (new) Sense-making (vet) Traditional (vet)

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Result 3

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When considering energy, more traditional students asserted something counter-intuitive

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Sense-making (new) Sense-making (vet) Traditional (vet)

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What Happens to the Mechanical Energy

  • f the Two Blocks?

instructor count

20 40 60 80 100 120 140 1 2 3 q09d stays the same increases blank decreases missing value uncodeable

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59 75 33

Mechanical Energy Increases

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59 75 33

Mechanical Energy Increases

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59 75 33

Mechanical Energy Increases

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>

59 75 33

Mechanical Energy Increases

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Sense-making (new) Sense-making (vet) Traditional (vet)

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>

59 75 33

Mechanical Energy Increases

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Sense-making (new) Sense-making (vet) Traditional (vet)

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Result 4

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When considering energy, more sense-making students were consistent with simple intuition.

59 75 33

Sense-making (new) Sense-making (vet) Traditional (vet)

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Ahead,

DRAGONS!

http://www.flickr.com/photos/aztlek/2421800480/in/ set-72157605762980035/

tar be...

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http://www.flickr.com/photos/aztlek/2421800480/in/ set-72157605762980035/

This stuff’s in beta.

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Students Who Quoted ‘‘Conservation of Energy'' as their #§* Explanation for q09d

instructor count

5 10 15 20 25 30 1 2 3 variable 5 5x

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8 11 32

Mechanical Energy Stays the Same...

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Mechanical Energy Stays the Same... Because Energy is Conserved

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Sense-making (new) Sense-making (vet) Traditional (vet)

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Result 5

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When justifying their answer, more traditional students just quoted a rule, ignoring that it was tautological and inaccurate.

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Sense-making (new) Sense-making (vet) Traditional (vet)

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Summary

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Result 3

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When considering energy, more traditional students asserted something counter-intuitive

43 43 72

Sense-making (new) Sense-making (vet) Traditional (vet)

Result 4

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When considering energy, more sense-making students were consistent with simple intuition.

59 75 33

Sense-making (new) Sense-making (vet) Traditional (vet)

Result 5

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When justifying their answer, more traditional students just quoted a rule, ignoring that it was tautological and inaccurate.

8 11 32

Sense-making (new) Sense-making (vet) Traditional (vet) 29 −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 3−2 3−1 2−1 95% family−wise confidence level Differences in mean levels of instructor Eratio
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http://github.com/briandk/user2010public

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Eric Kuo Mike Hull Ayush Gupta Andy Elby

Project Directors Graduate Assistants

Thanks!

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Many Thanks

NSF-DRL grant # 0733613 NSF-EEC grant # 0835880

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Result 3

39

When considering energy, more traditional students asserted something counter-intuitive

43 43 72

Sense-making (new) Sense-making (vet) Traditional (vet)

Result 4

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When considering energy, more sense-making students were consistent with simple intuition.

59 75 33

Sense-making (new) Sense-making (vet) Traditional (vet)

Result 5

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When justifying their answer, more traditional students just quoted a rule, ignoring that it was tautological and inaccurate.

8 11 32

Sense-making (new) Sense-making (vet) Traditional (vet) 29 −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 3−2 3−1 2−1 95% family−wise confidence level Differences in mean levels of instructor Eratio