Individual Differences Related to College Students’ Course

Performance in Calculus II

Colleen M. Ganley & Sara A. HartPsychology

FCRR, FCR-STEMFlorida State University

hart@psy.fsu.edu@saraannhart

ganley@psy.fsu.edu@colleenganley

Background

• 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?• We will examine both clickstream data and

information about students’ attitudes and cognitive performance

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 (mostly online in qualtrics)

• Outcome variable• Final grade (0-100) in Calculus II course

Methods

• 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

• 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

• Panamath “Dots Task” (Halberda et al., 2008)• Approximate Number System • Are there more yellow or blue dots?

Cognitive Measures

• Mental Rotation Test (Vandenberg & Kuse, 1978)

Cognitive Measures

• 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

• 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

• Online quizzes• Unlimited attempts at quizzes (7 total)• Sum of total number of attempts

Online Course Measures

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

0.060.020.020.010.005

Mental RotationWorkshop TimeANSMath Anxiety Math ConfidenceQuiz AttemptsAssessment Time

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)

Mental

Rotat

ion

ADHD_In

att

Math Anxi

ety

Math Confi

dence

Math In

terest

Math Moti

vatio

n

Math Im

portan

ce ANS

-3

-2

-1

0

1

2

3

4

5

Scor

e

Final Grade Exam 1 Exam 2 Exam 3 Diagnostic Test

-2

-1.5

-1

-0.5

0

0.5

Scor

e

• 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

• 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

• 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

• 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

• NSF grants 1450501 & E2030291• Dr. Olga Caprotti & Yahya Almalki

hart@psy.fsu.edu@saraannhart

Acknowledgements

ganley@psy.fsu.edu@colleenganley