WILL TEACHING MATHEMATICS IN A PHYSICS CLASSROOM IMPROVE STUDENTS' ABILITIES TO DO MATHEMATICS IN A PHYSICS CLASSROOM AND TO LEARN PHYSICS?
Michael Murphy
Committee
Dr. Michael C. Wittmann, Advisor Dr. Tod Shockey Dr. Eric Pandiscio Dr. Donald B. Mountcastle
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Background - Using math in physics Students unable to properly apply mathematics skills in understanding and learning physics
Mountcastle et al. Akatugba and Wallace
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Background - Need for math in physics
Correlation between mathematics abilities and ability to learn physics concepts.
Meltzer
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Cognitive Models Coordination classes - diSessa & Sherin Definition
P-prims and knowledge resources “Readout strategies” to activate networks of resources
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Cognitive Models
Framing - Hammer, Elby, Redish & Scherr Definition
Context dependent activation Tipping point Delay in frame shift
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Research Study Design
Setting
PHY111 laboratory Fall 2004 Experimental groups
Experimental design: Math lessons during 10 physics laboratory meetings
Cue mathematics knowledge in physics setting Access to mathematical thinking skills Examples
. .
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Multiple Assessments
Mathematics
Specially designed diagnostic Rubric used for scoring
Physics
Specially designed diagnostic
Achievement of most students rendered results unhelpful
Physics exams PHY111 & PHY112
Growth of averages between exams
FMCE
Normalized Gain
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Multiple Anaylsis Methods
ANOVA, grouped by
Six lab sections Three experimental groups Six tutorial sections
Mathematics Physics
Two independent sample T-test
Graphing questions (shapes sketched for functions) Linear questions (“y = mx + b”) Exam scores PHY111 Conceptual questions (tutorial-based) Procedural questions (calculation-based) Overall Exam scores PHY112 Overall FMCE Normalized Gain
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Results (ANOVA)
ANOVA f-ratios Multiple groupings Multiple metrics
Math gain graphing
Math gain linear
3.08
Physics gain overall prelim3 v prelim1 1.75
Physics gain overall prelim3 v prelim2 1.32
Physics gain Conceptual prelim3 v prelim2 1.73
6 lab sections
3 experimental groups
2.83
7.06
1.01
3.21
0.43
3.96
0.74
2.63
0.33
2.90
n/a
6 tutorial sections
Indicates significant result Indicates insignificant result
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Results (significant)
T-Test Significant results Math gain graphing Overall Physics gain exam3 v exam 1
3.48
Overall Physics gain exam3 v exam2
7.03
Conceptual Physics gain exam3 v exam2
19.03
Treatment group’s average growth (n=36) Control groups’ average growth (n=48) t-score
Probability that variation is due to chance (p-value)
25.00
8.85
-3.56
-0.22
6.96
3.65
<1%
2.83
<1%
2.11
<5%
2.37
<5%
Effect score
0.80
0.61
0.64
0.52
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Results (insignificant)
T-Test insignificant results Physics gain Procedural Exam2 v Exam1 -9.58
-7.29 -0.42
Physics gain Exam2 v Exam1
Physics gain Conceptual Exam2 v Exam1 -8.12
-5.35 -0.65
Treatment group’s average growth
-3.54
-3.34 -0.06
Control groups’ average growth
t-score Probability that variation is due to chance (p-value)
~100%
>50%
>50%
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Results (PHY112)
T-test second semester results (one-tailed) Treatment group’s average growth (n=26) Control groups’ average growth (n=31) t-score Probability that variation is due to chance (p-value) effect score Physics gain Physics gain prelim3 v prelim2 v prelim1 prelim1
-1.04 -2.48
Physics gain prelim3 v prelim2
1.44
-10.28
-7.52
-2.76
1.62
~ 5%
1.16
< 25%
0.79
<25%
0.43
0.31
0.21
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Results (FMCE)
FMCE gain
Treatment average normalized gain Control average normalized gain t-score
0.38
0.45 -0.89 < 50%
Probability that variation is due to chance
Studies carried out in tutorial sections of the course showed differences in FMCE results, but students from those studies were randomly distributed amongst laboratory sections.
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Summary of the data Treatment vs. Control
• Performance on mathematics diagnostic greater • Greater gains in physics exam data
• Gains higher in the latter part of the semester • Greatest gains on conceptual questions
• FMCE results consistent with exam data
• no difference between groups • material taught early in course
• Delay in gains, but the trend “sticks,” based on PHY112
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Implications
• Math instruction better prepares students to answer questions on a mathematics diagnostic when within a physics classroom. • Delayed effect on conceptual learning gains in physics.
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Consistency with theory
Evidence for frame shift
Improvement in math results Improvement in conceptual questions
Evidence for “tipping point”
Delayed effect in physics improvement
PHY111 shows difference PHY112 suggests a trend
FMCE results suggest tipping later in the semester
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Limitations
Group selection Parallel research Researcher as instructor Limited physics assessments
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