Markov Chain and Classification of Difficulty Levels Enhances the Learning Path in One Digit Multiplication
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This document discusses using Markov chain analysis and difficulty level classification to improve personalized learning paths for one digit multiplication. Key points: - Researchers analyzed over 500,000 multiplication calculations from primary school students to cluster questions by difficulty and identify patterns in student answers. - Markov chain models were used to analyze transition probabilities between answer types (right, wrong) both at the individual question level and overall. - Questions were classified into 6 optimal difficulty clusters, and patterns were found regarding which operands make questions easier or harder. - The analysis informs an adaptive algorithm to select the next question based on the student's previous response and difficulty level of the prior question. This provides personalized recommendations to improve learning paths.
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Markov Chain and Classification of Difficulty Levels Enhances the Learning Path in One Digit Multiplication
- 1. Markov Chain and Classification of Difficulty Levels Enhances the Learning Path in One Digit Multiplication Behnam Taraghi, Anna Saranti, Martin Ebner, Martin Schön
- 3. What it is about ?
- 4. ! Learning Analytics is the use of intelligent data, learner-produced data, and analysis models to discover information and social connections, and to predict and advise on learning. Learning Analytics Georg Siemens (2010) http://www.elearnspace.org/blog/2010/08/25/what-are-learning-analytics/
- 5. ! Learning Analytics is about collecting traces that learners leave behind and using those traces to improve learning. Learning Analytics Erik Duval (2012) http://www.slideshare.net/erik.duval/learning-analytics-13050389
- 10. Schön, M., Ebner, M., Kothmeier, G. (2012) It's Just About Learning the Multiplication Table, In Proceedings of the 2nd International Conference on Learning Analytics and Knowledge (LAK '12), Simon Buckingham Shum, Dragan Gasevic, and Rebecca Ferguson (Eds.). ACM, New York, NY, USA, 73-81 Algorithm
- 11. What is done as next step ?
- 12. ! ! - ... collect data: more than 500,000 calculations ! - ... pupils from different primary schools ! -... analyze preprocessed data ! - ... cluster arithmetic questions according to their difficulty ! - ... identify influential structures in each user’s answers ! - ... offer personalized recommendation for each pupil One Digit Multiplication
- 13. Answer Type Preceding Answer Current Answer R - R W - W RR R R RW R W WR W R WW W W Answer Types
- 14. ! Question Difficulty: R & W
- 15. Question Difficulty: RW, WR & WW !
- 16. Question Difficulty: RW, WR & WW ! !
- 17. Question Difficulty Clusters (8 - 22 - 60) !
- 18. ! ! - states: answer types to each question ! - transition links: probability to the answer type of the subsequent same posed question in the sequence ! - for each 90 questions the MC model is applied individually ! ! Markov Chain Analysis (per Question)
- 19. Markov Chain Analysis (per Question)
- 20. ! ! - states: answer types to each question ! - transition links: probability to the answer type of the subsequent posed question in the sequence Markov Chain Analysis (over all Questions)
- 21. Markov Chain Analysis (over all Questions) k = 1 k = 3k = 2 k = 5Answer types k = 4 RW WR 46.0 25.30 70.69 61.02 76.88 84.77 77.20 86.92 78.79 92.52 not observable in the set of easy questions
- 22. Markov Chain Analysis (over all Questions) Answer types k = 2k = 1 k = 3 k = 4 k = 5 R W 69.66 30.44 RR 12.8 87.2 RW 53.29 46.71 WR 7.11 92.89 WW 10.15 89.85 Others 31.01 68.99 71.52 28.48 23.03 76.97 77.59 22.41 9.37 90.63 16.14 83.86 55.29 44.71 72.26 27.74 42.28 57.72 89.02 10.98 7.69 92.31 29.30 70.70 66.51 33.49 72.66 27.34 51.38 48.62 92.48 7.52 0 100 39.13 60.87 74.98 25.02 72.92 27.08 50.00 50.00 93.57 6.43 0 100 41.67 58.33 80.63 19.37
- 23. Which question to pose as next ?
- 24. - Question q from cluster c is answered correctly - take Q = q+1 out of cluster C = c or c+1 ! - Question q from cluster c is answered incorrectly - take Q = q+1 out of cluster C = c or c-1 ! ! - adapt the algorithm used to pose a question according to identified difficulty levels - choose question Q from cluster C that owns the highest proportion rate referring to answer type WR or RR
- 25. ! ! - 1x1 multiplications were classified into 6 optimal difficulty clusters ! - most difficult questions: 6*8, 7*8, 8*6, 8*7, 8*4, 8*8, 6*7, 4*8 ! - the multiplications where 1, 2, 5, 10 occur as operands can be classified as easy to learn ! - 3, 4, 6, 9, and especially 7, 8 operands build multiplications that can be classified as difficult ! - adapt the algorithm used to pose a question according to identified difficulty levels ! - use the detected patterns to let teachers intervene if required. Conclusions
- 26. Graz University of Technology SOCIAL LEARNING Computer and Information Services Graz University of Technology Behnam Taraghi Slides available at: http://elearningblog.tugraz.at behi_at