Poster at EC-TEL conference 2014, Graz

1. Adaptive Learner Profiling Provides the Optimal
Sequence of Posed Basic Mathematical Problems
Behnam Taraghi1 Anna Saranti1 Martin Ebner1
Arndt Großmann2 Vinzent M¨uller2
1Graz University of Technology,
M¨unzgrabenstrasse 35/I, 8010 Graz, Austria
2UnlockYourBrain GmbH,
Franz¨osische Str. 24, 10117 Berlin, Germany
http://www.unlockyourbrain.com/en/
Introduction
Main Idea and Goal
I Sequence of posed questions has an
influence to the learning process
I Pose the questions in a sequence so
that they will be correctly answered
Modules and Dependencies
1. Learner profiling uses implicit feedback
: the learner’s answering behaviour
2. Cluster learner profiles according to
learning similarity
3. Adaptive optimal questioning sequence
4. UnlockYourBrain : Basic mathematical
questions
Figure 1: Application modules and adap-tation
through feedback.
Dataset
Table 1: The size of the cleaned and reduced final dataset. The minimum sample sizes base on
a confidence level of 95% and a confidence interval (margin error) of 2%.
Addition Subtraction Multiplication Division
Minimum sample size 2400 2398 2398 2398
#Users 102722 38708 46357 47558
#Questions (unique) 667 155 268 204
#Questions (totally) 4228439 611312 1191450 1086256
Question Classification
I Answering behaviour of the users determines the relative difficulty of a
question
I 8 di↵erent answering possibilities define the dimensions used in the
K-Means classification algorithm
I 13 clusters for addition, 10 for subtraction and 11 for multiplication and
division operations
I Sort the clusters according to the difficulty level of the questions they
contain
Table 2: Answer types for a question in regard to di↵erent number of answering options
#Options Answer types
2 R W
3 RWRW WW
4 RWRWWWRWW WWW
5 RWRWWWRWWWWWRWWWWWWW
Dimension 1 2 3 4 5 6 7 8
Methodology
I Minimum Sample Size - Confidence Level:
A confidence level of 95% with a confidence interval of 2% means that
one can be sure with a probability of 95% that the actual probability values
lie within ±2% of their calculated values.
I Classification Algorithm: K-Means
J =
X
i
X
k
rik k xi − μk k2 (1)
where:
rik =
⇢
1 if argminj k xi − μj k 0 otherwise
(2)
I Markov chain for modelling the learning process as a sequence of alternating
question - answer type pairs
P(Xn+1 = xn+1|Xn = xn, ..., X1 = x1) =
P(Xn+1 = xn+1|Xn = xn, ..., Xn−k+1 = xn−k+1)
(3)
Model of Learning Process of one User as a Markov Chain
Figure 2: Markov Chains model of one user profile. The states in blue denote the posed
question clusters and the states in red are the eight answer types. In the upper part of the figure
all possible transitions of the model are displayed. The lower part shows a possible sequence
(1) ! (2) ! (3) ! (4) ! (5) of user’s answering behaviour comprised by the question
answer pairs C1 ! WR ! C9 ! WWWW ! C2 ! R.
Adaptive User Profiling
I Cluster the users according to the build Markov chain models
I Use of the application by the user will change the transition probabilities
I Reclassification : Change the number of question’s clusters as well as their
contents
Optimal Sequence of Questions
I Consider those neighbours of the user who exhibit the same (matched)
subsequence in their history
I Search in the history of user’s neighbours for successful subsequent part of
their sequences
I Matched neighbours and optimum subsequence are recalculated
Figure 3: Subsequence matching between user and its neighbours. At time step k the subse-quence
MS is found as a match in the sequences of neighbour users one and two. The improve-ment
of neighbour user one is greater and happens faster than the improvement of neighbour
user two, hence in the next step the application will pose the first question Q1 to the user. The
matching procedure will continue in the next time step with a (shifted by one) new matching
subsequence.
Behnam Taraghi, Anna Saranti, Martin Ebner, Arndt Großmann, Vinzent M¨uller