Capitol Tech U Doctoral Presentation - April 2024.pptx
Markov Chains Enhance Personalized Learning Paths 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
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
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
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)
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
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