How To Teach Math In Physics

Transcription

1 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 1

2 Background - Using math in physics Students unable to properly apply mathematics skills in understanding and learning physics Mountcastle et al. Akatugba and Wallace 2

3 Background - Need for math in physics Correlation between mathematics abilities and ability to learn physics concepts. Meltzer 3

4 Cognitive Models - Coordination classes - disessa & Sherin Definition P-prims and knowledge resources Readout strategies to activate networks of resources 4

5 Cognitive Models Framing - Hammer, Elby, Redish & Scherr Definition Context dependent activation Tipping point Delay in frame shift 5

6 Setting Research Study Design 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 6

7 Mathematics Multiple Assessments 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 7

8 Multiple Anaylsis Methods ANOVA, grouped by Six lab sections Three experimental groups Six tutorial sections Two independent sample T-test Mathematics Graphing questions (shapes sketched for functions) Linear questions ( y = mx + b ) Physics Exam scores PHY111 Conceptual questions (tutorial-based) Procedural questions (calculation-based) Overall Exam scores PHY112 Overall FMCE Normalized Gain 8

9 ANOVA f-ratios Multiple groupings Multiple metrics Results (ANOVA) Math gain graphing Math gain linear Physics gain overall prelim3 v prelim1 overall prelim3 v prelim2 Conceptual prelim3 v prelim2 6 lab sections experimental groups tutorial sections n/a Indicates significant result Indicates insignificant result 9

10 Results (significant) T-Test Significant results Treatment group s average growth (n=36) Control groups average growth (n=48) Math gain graphing Overall exam3 v exam 1 Overall exam3 v exam2 Conceptual exam3 v exam t-score Probability that variation is due to chance (p-value) <1% <1% <5% <5% Effect score

11 Results (insignificant) T-Test insignificant results Treatment group s average growth Control groups average growth Exam2 v Exam1 Procedural Exam2 v Exam1 Conceptual Exam2 v Exam t-score Probability that variation is due to chance (p-value) ~100% >50% >50% 11

12 T-test second semester results (one-tailed) Treatment group s average growth (n=26) Control groups average growth (n=31) Results (PHY112) prelim3 v prelim1 prelim2 v prelim1 prelim3 v prelim t-score Probability that variation is due to chance (p-value) ~ 5% < 25% <25% effect score

13 Results (FMCE) FMCE gain Treatment average normalized gain 0.38 Control average normalized gain 0.45 t-score Probability that variation is due to chance < 50% 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. 13

14 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 14

15 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. 15

16 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 16

17 Limitations Group selection Parallel research Researcher as instructor Limited physics assessments 17