markov chain and classification of difficulty levels enhances the learning path in one digit...
DESCRIPTION
Presentation at HCII 2014 conference, Crete, GreeceTRANSCRIPT
Markov Chain and Classification of Difficulty Levels Enhances
the Learning Path in One Digit Multiplication
Behnam Taraghi, Anna Saranti, Martin Ebner, Martin Schön
What it is about ?
!
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/
!
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
http://www.flickr.com/photos/neeravbhatt/6995946039
http://mathe.tugraz.at
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
What is done as next step ?
!!
- ... 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
Answer Type Preceding Answer Current Answer
R - R
W - W
RR R R
RW R W
WR W R
WW W W
Answer Types
!!
Question Difficulty: R & W
Question Difficulty: RW, WR & WW
!
Question Difficulty: RW, WR & WW
! !
Question Difficulty Clusters (8 - 22 - 60)
!
!!- 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)
Markov Chain Analysis (per Question)
!!- 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)
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
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
Which question to pose as next ?
- 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
!!- 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
Graz University of Technology
SOCIAL LEARNINGComputer and Information Services
Graz University of Technology
Behnam Taraghi
Slides available at: http://elearningblog.tugraz.at
behi_at