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Individual Differences Related to College Students’ Course
Performance in Calculus II
Sara A. HartColleen M. Ganley
In Memoriam: Mika SeppälaPsychology, FCRR, FCR-STEM, Mathematics
Florida State University
[email protected]@saraannhart
• 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
• 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
• What are the most important individual differences predictors of success in a hybrid user-driven Calculus II course?• Does clickstream data add more information
beyond student characteristics?
Research Question
• 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
• Participants• 84 participants (43% female, 84% White)• Took ~45min battery of demographics, student
attitudes and cognitive measures
• Outcome variable• Final grade (0-100) in Calculus II course
Methods
• Key Predictor Measures • Math confidence (adapted from confidence subscale of
Fennema & Sherman, 1976)
• Math anxiety (MARS-R; Plake & Parker, 1982)
• Spatial skills (Mental Rotation Test; Vandenberg & Kuse, 1978)
• Non-symbolic number approximation (Panamath; Halberda & Feigenson, 2008)
Methods
• Key Predictor Measures• 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 quizzes• Unlimited attempts at quizzes (7 total)
• Sum of total number of attempts
Methods
Results
-
-
Results
-
-
• 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.html• 1000 bootstrapped samples
Dominance Analysis (DA)
• 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
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• (assessment time > quiz attempts > math confidence > math anxiety) > (ANS > workshop time > mental rotation)
DA results
Final Grade0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.1
0.09
0.06
0.020.020.010.005
Mental Rotation
Workshop Time
ANS
Math Anxiety
Math Confidence
Quiz Attempts
Assessment Time
• 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?
• 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
• There is value-added for including student’s interactions with online platform to prediction of student success• In addition to (and above!) known
“psychological” student characteristics • But SO MUCH data, and most of it requires huge
assumptions
Conclusion
• NSF grants 1450501 & E2030291• Dr. Olga Caprotti & Yahya Almalki
[email protected]@saraannhart
Acknowledgements
