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Predicting Student Performance in Solving Parameterized Exercises

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In this paper, we compare pioneer methods of educational
data mining field with recommender systems techniques for predicting
student performance. Additionally, we study the importance of including
students’ attempt time sequences of parameterized exercises.
The approaches we use are Bayesian Knowledge Tracing (BKT), Performance
Factor Analysis (PFA), Bayesian Probabilistic Tensor Factorization
(BPTF), and Bayesian Probabilistic Matrix Factorization (BPMF).
The last two approaches are from the recommender system’s field.We approach
the problem using question-level Knowledge Components (KCs)
and test the methods using cross-validation. In this work, we focus on
predicting students’ performance in parameterized exercises. Our experiments
shows that advanced recommender system techniques are as accurate
as the pioneer methods in predicting student performance. Also, our
studies show the importance of considering time sequence of students’
attempts to achieve the desirable accuracy.

Published in: Data & Analytics
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Predicting Student Performance in Solving Parameterized Exercises

  1. 1. Predicting Student Performance in Solving Parameterized Exercises 2Shaghayegh Sahebi (Sherry) • One question template with multiple parameter sets – One template generates many questions – Each question be repeated multiple times by the same student – Makes cheating difficult – The student can learn by practicing over time
  2. 2. Predicting Student Performance in Solving Parameterized Exercises 3Shaghayegh Sahebi (Sherry)
  3. 3. Predicting Student Performance in Solving Parameterized Exercises 4Shaghayegh Sahebi (Sherry) • Unproductive repetitions – Students who are not good in managing their learning [Hsiao et. al, 2009] • How to avoid this? – Personalized e-learning system – Predict the success of students’ future attempts the same way as recommender systems – Predicting students’ performance (PSP)
  4. 4. Predicting Student Performance in Solving Parameterized Exercises 5Shaghayegh Sahebi (Sherry) • In static questions, the student solves a problem once – No attempt sequence on each question – Time-ignorant methods work well • Collaborative filtering approaches • Assumption in parameterized questions: the student can learn by practicing over time – Attempt sequence for each student on each question
  5. 5. Predicting Student Performance in Solving Parameterized Exercises 6Shaghayegh Sahebi (Sherry) • To study the – recommender systems approaches – effect of attempt sequence in PSP for parameterized questions • Approaches: – Bayesian Knowledge Tracing (BKT) – Performance Factor Analysis (PFA) – Bayesian Probabilistic Matrix Factorization (BPMF) – Bayesian Probabilistic Tensor Factorization (BPTF) – Max baseline
  6. 6. Predicting Student Performance in Solving Parameterized Exercises 7Shaghayegh Sahebi (Sherry) • Markov Model with two states • Models attempt sequence explicitly K K K Q Q Q Initial knowledge Learning P(T) P(G), P(S)
  7. 7. Predicting Student Performance in Solving Parameterized Exercises 8Shaghayegh Sahebi (Sherry) • Regression model • No attempt sequencing but implicitly models attempt history m(i, j Î KCs ,k Î items,s,f) = bk + (gj si,j + rj fi,j ) jÎKCs å
  8. 8. Predicting Student Performance in Solving Parameterized Exercises 9Shaghayegh Sahebi (Sherry) • From collaborative filtering • No attempt sequence modeling • We use Bayesian Probabilistic Matrix Factorization (BPMF) [Xiong et al., 2010] • Other models were used for static questions [Thai-Nghe et al., 2011] 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 Students Questions/ topics 0.9 0 1.5 0.4 0 1.4 0 0.9 Students KCs 0.8 0.5 0 0.3 0 0 0.5 0.8 KCs Questions/ topics
  9. 9. Predicting Student Performance in Solving Parameterized Exercises 10Shaghayegh Sahebi (Sherry) • Adds attempt sequence modeling to BPMF • We use Bayesian Probabilistic Tensor Factorization (BPTF) • Other models used for static questions Students Questions/ topics …
  10. 10. Predicting Student Performance in Solving Parameterized Exercises 11Shaghayegh Sahebi (Sherry) • Predicting success (majority class) for every attempt
  11. 11. Predicting Student Performance in Solving Parameterized Exercises 12Shaghayegh Sahebi (Sherry) • From QuizJET system • Java Programming Questions • Six semesters • 166 Students • 103 questions • 69.04% success records (majority class)
  12. 12. Predicting Student Performance in Solving Parameterized Exercises 13Shaghayegh Sahebi (Sherry) • Time-aware methods: – BKT: explicitly – PFA: counting previous success/failure – BPTF: student’s performance changes smoothly over time • Time-ignorant methods: – Matrix factorization (BPMF) – Max baseline • Collaborative filtering approaches: – Tensor factorization (BPTF) – Matrix factorization (BPMF) • Knowledge component: question • 5-Fold user-stratified cross validation – 80% of users in train data, rest in test data
  13. 13. Predicting Student Performance in Solving Parameterized Exercises 14Shaghayegh Sahebi (Sherry)
  14. 14. Predicting Student Performance in Solving Parameterized Exercises 15Shaghayegh Sahebi (Sherry) 64 66 68 70 72 74 76 78 Accuracy
  15. 15. Predicting Student Performance in Solving Parameterized Exercises 16Shaghayegh Sahebi (Sherry) 900 950 1000 1050 1100 1150 1200 BKT PFA BPTF False Positive
  16. 16. Predicting Student Performance in Solving Parameterized Exercises 17Shaghayegh Sahebi (Sherry) 0 50 100 150 200 250 300 350 400 450 BKT PFA BPTF False Negative
  17. 17. Predicting Student Performance in Solving Parameterized Exercises 18Shaghayegh Sahebi (Sherry) 0 20 40 60 80 100 120 140 BKT PFA BPTF BPMF Minority Recall Majority Precision
  18. 18. Predicting Student Performance in Solving Parameterized Exercises 19Shaghayegh Sahebi (Sherry) 0 20 40 60 80 100 120 140 160 180 BKT PFA BPTF BPMF Majority Recall Minority Precision
  19. 19. Predicting Student Performance in Solving Parameterized Exercises 20Shaghayegh Sahebi (Sherry) • Attempt sequence is important in PSP for parameterized questions • Recommender systems approaches are as good as the pioneers PSP methods – if they consider attempt sequence – Do not need to know the exact Knowledge Components – Encourages more research on applying more recommendation techniques in PSP
  20. 20. Predicting Student Performance in Solving Parameterized Exercises 21Shaghayegh Sahebi (Sherry) • Other collaborative filtering approaches • Ensemble of approaches • Effect of knowledge structure (our AIEDCS paper) • Personalize students’ experience according to our results
  21. 21. Predicting Student Performance in Solving Parameterized Exercises 22Shaghayegh Sahebi (Sherry) Thank You!
  22. 22. Predicting Student Performance in Solving Parameterized Exercises 23Shaghayegh Sahebi (Sherry) • EM algorithm for BKT and set the initial parameters as follows: p(L0) = 0:5 , p(G) = 0:2 , p(S) = 0:1 , p(T) = 0:3 . For running PFA, we use • the implementation of logistic regression in WEKA [3]. • For BPTF and BPMF: Matlab code prepared by Xiong et. al. We experimented with different latent space dimensions for BPTF and BPMF (5, 10, 20 and 30) and chose the best one, which has the latent space dimension of 10
  23. 23. Predicting Student Performance in Solving Parameterized Exercises 24Shaghayegh Sahebi (Sherry) • Predicting the student’s capability to solve a problem or perform an educational task, mostly based on her performance in the past • Predicting success/failure in solving a question • Questions can be related to topics (Here, each topic can have multiple questions and each question is related to one topic)
  24. 24. Predicting Student Performance in Solving Parameterized Exercises 25Shaghayegh Sahebi (Sherry) No significant accuracy difference between all methods except BPMF and Max Baseline (P<0.05)
  25. 25. Predicting Student Performance in Solving Parameterized Exercises 26Shaghayegh Sahebi (Sherry)
  26. 26. Predicting Student Performance in Solving Parameterized Exercises 27Shaghayegh Sahebi (Sherry) PFA tends to predict more failures for the students.
  27. 27. Predicting Student Performance in Solving Parameterized Exercises 28Shaghayegh Sahebi (Sherry) If BKT predicts a failure for a student, this prediction is more likely to be true compared to the other methods
  28. 28. Predicting Student Performance in Solving Parameterized Exercises 29Shaghayegh Sahebi (Sherry) if PFA predicts a success for a student, this prediction is more likely to be true compared to the other methods
  29. 29. Predicting Student Performance in Solving Parameterized Exercises 30Shaghayegh Sahebi (Sherry)
  30. 30. Predicting Student Performance in Solving Parameterized Exercises 31Shaghayegh Sahebi (Sherry) • Maj. Prec: TP/(TP+FP) • Min Prec: TN/(TN+FN) • Maj. Recall: TP/(TP+FN) • Min Recall: TN/(TN+FP) • Accuracy: (TP+TN)/all

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