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- 1. Colleen M. Ganley & Sara A. Hart Psychology FCRR, FCR-STEM Florida State University hart@psy.fsu.edu @saraannhart ganley@psy.fsu.edu @colleenganley
- 2. Background
- 3. • Student attitudes are related to higher mathematics achievement • Expectations of success, comparisons of ability, academic-self concept, confidence of own ability, etc (Reyes & Stanic, 1988; Randhawa et al, 1993, House, 1993, House, 1995) • Cognitive factors are also related to higher mathematics achievement • Numerosity, spatial abilities, memory, etc (Halberda et al., 2008; Siegler & Opfer, 2003; Casey et al., 1995) • But these aren’t surprising, even for predicting success in Calculus (and Calculus II) Understanding which students are successful
- 4. • Online learning is becoming more available and popular • These courses provide more data related to the “user” • Every action of the student within the course is tracked • Can these data be used to understand success in the course? • Future goal of intervening with students at risk for failure early in the course Understanding which students are successful in a hybrid Calc course
- 5. • What are the most important individual differences predictors of success in a hybrid user-driven Calculus II course? • We will examine both clickstream data and information about students’ attitudes and cognitive performance Research Question
- 6. • Spring 2014 Calculus II course at FSU • Hybrid course with a flipped classroom • Students used the online course platform (WEPS https://myweps.com/moodle/) to watch videos of the course content and solved problems in class with professor • All teaching content was available to students at all times (graded items time available only) Methods
- 7. • Participants • 84 participants (43% female, 84% White) • Took ~45min battery of demographics, student attitudes and cognitive measures (mostly online in qualtrics) • Outcome variable • Final grade (0-100) in Calculus II course Methods
- 8. • Math Confidence (adapted from confidence subscale of Fennema & Sherman, 1976) • Generally I have felt secure about attempting mathematics • I am sure I could do advanced work in mathematics • I can get good grades in mathematics • Math has been my worst subject Attitudinal Measures
- 9. • Math Anxiety (MARS-R; Plake & Parker, 1982) • Please indicate the amount of anxiety you feel in each of the following situations. • Buying a math textbook. • Looking through the pages on a math text. • Having to use tables of formulae. Attitudinal Measures
- 10. • Panamath “Dots Task” (Halberda et al., 2008) • Approximate Number System • Are there more yellow or blue dots? Cognitive Measures
- 11. • Mental Rotation Test (Vandenberg & Kuse, 1978) Cognitive Measures
- 12. • So much available information • How to get it into something useable in more “traditional” statistical models? • We just want a number!!! • Tried to use variables that we thought we had reasonable interpretations of (but honestly still unsure) Online Course Measures
- 13. • Online workshops (graded homeworks) • Mean time to submission across 13 workshops • From 0-100, with 100 being submitted exactly at time due (from when workshop was available) • Mean time to submission of graded workshop assignments of other students • From 0-100, with 100 being submitted exactly at time due (from deadline of workshop) Online Course Measures
- 14. • Online quizzes • Unlimited attempts at quizzes (7 total) • Sum of total number of attempts Online Course Measures
- 15. Results - -
- 16. • Research question: of our key variables of interest, what are the most useful for predicting final grade? • Dominance analysis allows for this specific test (Budescu, 1993; Azen & Budescu, 2003) • All key variables were added to the model, and pitted against each other for relative importance • https://pantherfile.uwm.edu/azen/www/damacro.h tml • 1000 bootstrapped samples Dominance Analysis (DA)
- 17. • Complete dominance • (math confidence = quiz attempts = assessment time) > (math anxiety = mental rotation = ANS = workshop time) • Reproducibility quite low (<10%) • General dominance • (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation) • Reproducibility is high across parentheses DA results
- 18. • (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation) DA results 0.1 0.09 0.06 0.02 0.02 0.010.005 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Final Grade Mental Rotation Workshop Time ANS Math Anxiety Math Confidence Quiz Attempts Assessment Time
- 19. Latent Profile Analysis • Please keep in mind the following are very underpowered • Intention was to have more data for full model • Simulation studies suggest we need at least n=200 at first, and to feel comfortable making reliable predictions with our model likely closer to n = 500 (Nylund, Asparouhov & Muthen, 2007)
- 20. Mental Rotation ADHD_In att Math Anxiety Math Confidenc e Math Interest Math Motivation Math Importanc e ANS Class 1 n = 77 0.064 0.065 -0.15 0.379 0.425 0.435 0.413 -0.213 Class 2 n = 17 -0.265 -0.32 0.542 -0.975 -1.225 -1.216 -0.945 -0.292 Class 3 n = 4 0.124 0.351 0.031 -1.754 -1.411 -1.603 -2.412 3.828 -3 -2 -1 0 1 2 3 4 5 Score
- 21. Final Grade Exam 1 Exam 2 Exam 3 Diagnostic Test class 1 0.09 0.15 0.07 0.09 0.12 class 2 0.02 -0.32 0.1 -0.05 -0.13 class 3 -1.59 -1.05 -1.56 -1.29 -1.06 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Score
- 22. • Student attitudes relatively important • Replication of previous literature showing math confidence important positive predictor of math/Calculus success (e.g., House, 1995) • Possibly role for measuring math anxiety too • May be due to this being Calc II • What happened to the cognitive predictors? Discussion
- 23. • Online data also important relative predictors • Assessment total negative predictor • “procrastination” variable • OR, students who struggle in Calculus found this very hard • Number of times retake quiz positive predictor • “perfection” variable Discussion
- 24. • We learn more when we look at BOTH: • student’s interactions with online platform to prediction of student success AND • known “psychological” student characteristics • But SO MUCH data, and most of it requires huge assumptions • Hard to know what we are measuring with the online variables! Conclusion
- 25. • What other information can we get from clickstream data that might be useful? • How to get it into a useable form? • Can we predict how students will use the online system from their characteristics? • Can we then use this information to develop a recommendation system? Future Directions
- 26. • NSF grants 1450501 & E2030291 • Dr. Olga Caprotti & Yahya Almalki hart@psy.fsu.edu @saraannhart Acknowledgements ganley@psy.fsu.edu @colleenganley

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