=Paper= {{Paper |id=Vol-2354/w4paper4 |storemode=property |title=SARLR: Self-adaptive Recommendation of Learning Resources |pdfUrl=https://ceur-ws.org/Vol-2354/w4paper4.pdf |volume=Vol-2354 |authors=Liping Liu,Wenjun Wu,Jiankun Huang |dblpUrl=https://dblp.org/rec/conf/its/LiuWH18 }} ==SARLR: Self-adaptive Recommendation of Learning Resources== https://ceur-ws.org/Vol-2354/w4paper4.pdf

SARLR: Self-adaptive Recommendation of Learning
Resources

Liping Liu, Wenjun Wu and Jiankun Huang

State Key Lab of Software Development Environment Department of Computer Science and
Engineering, Beihang University, Beijing, China
{liuliping,wwj,hjk}@nlsde.buaa.edu.cn

Abstract. Personalized recommendation is important for online students to select
rich learning resources and make their own learning schedules. We propose
SARLR, a new self-adaptive recommendation algorithm of online learning re-
sources. The SARLR algorithm integrates an IRT-based learning cognitive
model named T-BMIRT into the recommendation framework and is able to adap-
tively adjust learning path recommendations based on dynamic of individual
learning process. The experimental results show that the SARLR algorithm out-
performs the existing recommendation algorithms.

Keywords: Online Education, Learning Recommendation, ITS

1 Introduction

With the growing prevalence of online education, students have access to all kinds of
electronic learning resources, including electronic books, exercises and learning videos.
Given the diversity of students’ background, learning styles and knowledge levels, it is
essential to have personalized recommendation tools to facilitate students in choosing
their own learning paths to satisfy their individual needs [1]. Previous studies have in-
troduced personalized learning recommendation algorithms following the two major
approaches including rule-based recommendation and data-driven recommendation.
Most Intelligent Tutor Systems (ITS) such as [2], primarily adopt the rule-based ap-
proach to design their recommendation algorithms, which requires domain experts to
evaluate learning scenarios for different kinds of students and define extensive recom-
mendation rules accordingly. Apparently, such a labor-intensive approach can only be
applied in specific learning domains. For modern online educational systems, designers
often take the data-driven approach by utilizing collaborative filtering methods to im-
plement learning recommendation algorithms. These data-driven recommendation al-
gorithms [3] attempt to identify suitable learning resources for students by comparing
similarity among students and learning objects.
Although the data-driven recommendation approach is more scalable and general
than the rule-based approach, current proposed solutions have common problems in
achieving highly adaptive recommendation towards students’ latent learning state.
They often focus on either searching for similar learning resources based on content or

151
2

identifying similar student groups based on their learning behaviors. The recommended
learning objects or paths fail to consider the impact of difficulty of learning objects and
dynamic change in students’ learning states.
In this paper, we propose a novel learning recommendation algorithm named
SARLR, which attempts to integrate an IRT-based learning cognitive model into the
recommendation framework and to adaptively adjust learning path recommendations
based on dynamics of individual learning process. Specifically, we introduce a tem-
poral, multidimensional IRT-based model named as T-BMIRT, which can accurately
infer student proficiency of multiple latent skills and difficulties of exercise assess-
ments. In addition, the T-BMIRT model incorporates the parameter of video learning,
which can describe the improvement in student skills after their interactions with video
lectures. Based on the T-BMIRT model, the SARLR algorithm can comprehensively
analyze every student’s skill progress at each learning step and recommend to them a
personalized learning path with the matching online video lectures and homework prob-
lems.
The contributions of this paper are the two-fold. First, we introduce the T-BMIRT
model, to estimate students’ latent skill levels and difficulties of learning resources for
recommendation. Second, we propose the SARLR algorithm by integrating the T-
BMIRT model in the adaptive recommendation process of learning resources. The ex-
perimental results confirm that the SARLR outperforms regular recommendation algo-
rithms. Lastly, we present an evaluation strategy for recommendation algorithms in
terms of rationality and effectiveness.

2 Related Work

Data-driven learning recommendation algorithms often utilize common recommenda-
tion methods widely adopted in the e-Commence area, including Collaborative Filter-
ing (CF) and Latent Factor Model (LFM). CF can be further divided into UCF (User-
based Collaborative Filtering) and ICF (Item-based Collaborative Filtering). The core
idea of LFM is to connect users and items through latent features [4].
EduRank [5] is a collaborative filtering based method for personalization in e-learn-
ing. It can generate a difficulty ranking of questions for a target student by aggregating
the ranking of similar students. Although this method is able to rank the available ex-
ercise questions based on their difficulties for similar students, it doesn’t integrate cog-
nitive learning models in its framework for estimating the ability of individual students.
Thus, it can’t generate the matching learning paths for students based on their state of
latent skills.
The most related work to our research in previous studies is the Latent Skill Embed-
ding (LSE) model [6], which also presents a probabilistic model of students and lessons.
Although the LSE model provides a good foundation for designing a recommendation
framework for personalized learning, the paper [6] doesn’t propose a detailed recom-
mendation algorithm. Our T-BMIRT model is more fine-grained than the LSE model
because it defines a video learning parameter to capture student progress through their

152
3

interaction with video lectures. Moreover, we present the SARLR algorithm that uti-
lizes the T-BMIRT model to identify similar students for a target student and recom-
mend their learning paths according to the dynamic state of the target student’s latent
skills. We also extend the recommendation evaluation criteria expected gain by incor-
porating two more metrics including relevance accuracy and difficulty accuracy. These
new metrics can support more comprehensive performance evaluation for learning rec-
ommendation algorithms.
Recently, reinforcement learning has been explored in personalized study planning
in ITS [7-9]. Most of them have not evaluated their approaches in real online learning
scenarios and compared their performance to existing problem selection strategies used
in current systems. Moreover, calculating an optimal personalized learning path in a
POMPD is often time-consuming and even becomes intractable as the dimensions of
the knowledge state and strategy spaces increase. Therefore, our SARLR algorithm
adopts the collaborative filter based approach and we plan to investigate the possibility
of utilizing reinforcement learning in our framework in future work.

3 SELF-ADAPTIVE RECOMMENDATION

Fig.1 illustrates the major components in the SARLR algorithm. First, it uses the T-
BMIRT model to estimate every student’s skill levels and difficulties of learning re-
sources. Second, it searches for similar students based on their skill vectors from the
outputs of the T-BMIRT model. Third, it extracts the learning path of the best student,
whose skill level is the highest among the similar students after learning related
knowledge. Lastly, it recommends the learning path to the target student and sets up
two pre-warning conditions to adaptively adjust his recommended contents. The target
student’s latest behavior data are collected instantly and used as a feedback to update
the T-BMIRT model. Thus, all of the modules form a closed loop, which constantly
optimizes our model.

Students interaction

Students Students Similar Learning Recommend
interaction vectors
Search students
Extract
path
Learning T-BMIRT
resources
Resources vectors
Adjust

Update regularly Update in real time

Fig. 1. The Overall architecture of the SARLR algorithm

3.1 The T-BMIRT model
The T-BMIRT model aims to model students and learning resources to infer students’
latent skills and learning resources’ attributes on multiple knowledge components. We

153
4

define the model based on IRT, T-IRT and MIRT model [10]. In a two-parameter IRT
model, the probability of the student 𝑠 correctly answering the question 𝑞 is given by:
1
𝑝𝑠𝑞 = , 𝑃(𝜃𝑡+τ |𝜃𝑡 ) = 𝜙𝜃𝑡,𝜐2 𝜏 (𝜃𝑡+τ ) (1)
1+𝑒𝑥𝑝⁡[−(𝛼𝑞 (𝜃𝑠 −𝛽𝑞 ))]

Where 𝛼𝑞 is the question discrimination, 𝛽𝑞 is the question difficulty, 𝜃𝑠 is the stu-
dent’s ability value. The Temporal IRT (T-IRT) model [11] extends the original IRT
and MIRT model by modeling a student’s latent skills over time as a Wiener process,
where 𝜃𝑡+𝜏 − 𝜃𝑡 ~𝑁(𝜃𝑡 , 𝑣2 𝜏). The model indicates the ability value of the student at the
next moment is only relevant to his current ability value.
The T-IRT model only considers interactions between students and assessments, ig-
noring their interactions with learning videos. However, we believe that the students'
ability can be significantly improved after completing a learning video. Therefore, in
[12], we introduce a new model T-BMIRT by incorporating learning video parameters
to describe the impact of students’ interaction with learning videos. The major equa-
tions are defined in Eq (2):
𝑑𝑠 1
𝑃(𝜃⃗𝑠,𝑡+τ |𝜃⃗𝑠,𝑡 , 𝑙⃗𝑠,𝑡 ) = 𝜙⃗𝜃⃗𝑠,𝑡+𝑙⃗𝑠,𝑡,𝜐2 𝜏 (𝜃⃗𝑠,𝑡+τ ), 𝑙⃗𝑠,𝑡 = 𝑡 ∙ 𝑔⃗𝑡 ∙ ⃗⃗⃗𝑠,𝑡 ∙ℎ
⃗⃗⃗𝑡
(2)
𝑑𝑡 𝜃
1+𝑒𝑥𝑝(−( ⃗⃗ −‖ℎ ⃗⃗𝑡 ‖))
‖ℎ𝑡 ‖

Where ⃗𝑙𝑠,𝑡 represents knowledge that student 𝑠 gains from the video 𝑡, 𝑔
⃗⃗𝑡 ⁡represents
knowledge of the video 𝑡, ℎ⃗ 𝑡 is the prerequisites of video⁡𝑡, 𝑑𝑠𝑡 is the duration in which
student 𝑠 watches video 𝑡 and 𝑑𝑡 is the total length of the video 𝑡. In Eq (2), both stu-
dent ability and learning video requirements have been expanded from one-dimensional
to multidimensional. We utilize the vector projection method to determine whether the
relevant abilities of the student exceed the relevant skill requirements of the video lec-
tures.
The T-BMIRT model enables us to infer every student’s current ability 𝜃, video
knowledge 𝑔 and video skill requirements ℎ through the student’s responses of assess-
ment questions. The detailed model fitting process of the T-BMIRT can be found in
[12]. An approximation technique makes it possible to train the T-BMIRT in an online
way. As a result, the T-BMIRT can be effectively used in the framework of the SARLR
algorithm to estimate the parameters of learning resources and students’ ability levels.

3.2 Similar Students Search and Learning Path Extraction

SARLR Phase 1 describes the process of searching similar students and extracting a
suitable learning path for a target student. At Step 1, the algorithm identifies the stu-
dents MS with the similar skill levels to the target student 𝑠𝑋 through k-nearest neighbor
search method over the k-dimension tree (kd-tree) structure and k-nearest neighbor
search method. At Step 2-4, the algorithm selects the best student 𝑠𝑏 ∈ 𝑀𝑆 with the
highest ability level at the moment when they complete learning specific knowledge
units. At Step 5, the algorithm extracts the learning path 𝑝 of 𝑠𝑏 to the target student⁡𝑠𝑋 .

154
5

SARLR Phase 1: Search and Extraction
INPUT:
Set of students 𝑆 = {𝑠1 , 𝑠2 , … , 𝑠𝑛 }, target student 𝑠𝑋 ∈ 𝑆
Matrix of abilities 𝐴 = [𝜃𝑠,𝑡 ], where 𝜃𝑠,𝑡 is the ability value of student s at time t
Set of learning resources 𝐸 = {𝑒1 , 𝑒2 , … , 𝑒𝑚 }
The time in this paper is the index of learning resources with the student just completed learning.
OUTPUT: learning path 𝑝
1: search for similar students MS, where 𝑠𝑘 ∈ 𝑀𝑆 and 𝜃𝑠𝑘,𝑡0 is similar to 𝜃𝑠𝑋 ,𝑡0
2: for each 𝑠𝑖 ∈ 𝑀𝑆 do
3: find 𝑠𝑏 = 𝑎𝑟𝑔𝑚𝑎𝑥(𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝜃𝑠𝑖,𝑇𝑠 − 𝜃𝑠𝑖,𝑡0 )), where 𝑇𝑠𝑖 is the time of 𝑠𝑖 completing learning
𝑖
4: end for
5: extract the learning path 𝑝 = (𝑒𝑖1 , 𝑒𝑖2 , … 𝑒𝑖𝑇 ) of 𝑠𝑏
6: return 𝑝

3.3 Adaptive Adjustment
Because each individual student has his/her inherent learning style, even when he fol-
lows the recommended learning path generated in SARLR phase 1, the learning out-
come may not be as good as expected by the recommendation algorithm. In order to
deal with this problem, we set up the two conditions in Eq (3) to initiate the Adaptive
Re-planning phase, which is defined in SARLR Phase 2.
1 1
𝑝𝑠𝑞 = ⃗⃗𝑠,𝑖 ∙𝛼
,⁡𝑝𝑠𝑒 = (3)
1+𝑒𝑥𝑝(−(𝜃 ⃗⃗⃗𝑞 −𝑏𝑞 )) ⃗⃗⃗ ∙ℎ
𝜃 ⃗⃗
𝑠,𝑖 𝑒 ⃗⃗𝑒 ‖))
1+𝑒𝑥𝑝(−( ⃗⃗⃗ −‖ℎ
‖ℎ𝑒 ‖

Eq (3) specifies 𝑝𝑠𝑞 and 𝑝𝑠𝑙 to evaluate the progress of the target student in the learning
path. 𝑝𝑠𝑞 indicates the probability of student 𝑠 correctly answering exercise⁡𝑞, where
⃗⃗⃗⃗
⁡𝜃𝑠,𝑖 ,⁡𝛼⃗𝑞 and 𝑏𝑞 represent the same symbols as the T-BMIRT model in Eq (1-2). 𝑝𝑠𝑒
indicates the degree of knowledge that student 𝑠 can acquire from the video 𝑒, where
𝑞⃗𝑒 represents the level of knowledge required for the learning video.
When 𝑝𝑠𝑞 becomes less than the threshold 𝐶𝑠𝑞 , it means that the difficulty of the ex-
ercise 𝑞 in the recommended learning path has significantly exceeded the student’s
ability. When 𝑝𝑠𝑒 becomes less than the threshold 𝐶𝑠𝑒 , it means that the skill level of
the target student is lower than the requirement of the recommend video 𝑒 , thus he can
only acquire little knowledge from the video. When either condition is met, the SARLR
determines that the original recommended path has to be re-planned to match the stu-
dent’s knowledge state.
SARLR Phase 2: Adaptive Re-planning
INPUT:
Target student 𝑠𝑋 , recommended learning path 𝑝 = (𝑒𝑖1 , 𝑒𝑖2 , … 𝑒𝑖𝑇 )
Result of 𝑠𝑋 interacted with learning resources in 𝑝
OUTPUT: new learning path
1: for each 𝑒 ∈ 𝑝 do
2: if 𝑒 is a video and 𝑝𝑠𝑒 < 𝐶𝑠𝑒 do
3: return SARLR Phase 1 to re-plan path 𝑝
4: else if 𝑒 is an exercise and 𝑠𝑋 failed it and 𝑝𝑠𝑞 < 𝐶𝑠𝑞 do
5: return SARLR Phase 1 to re-plan path p
6: end if
7: end for

155
6

4 EXPERIMENTS

We selected two datasets to perform our experiments, the public “Assistments”, includ-
ing 224,076 interactions, 860 students, 1,427 assessments and 106 skills, and a blended
learning data from our learning analysis platform including 14,037,146 learning behav-
ior data from 140 schools and 9 online educational companies.

4.1 Experiments for T-BMIRT

We divided each data set into two parts, one part only contains single skill assessments,
and the other part contains multiple skills assessments. The IRT, T-IRT are single skill
models, and the MIRT and T-BMIRT are multiple skills models. The dimensions for
models are related to the numbers of knowledge components. The values in Table 1 are
average results of the cross-validation. It shows that T-BMIRT outperforms the other
models on each dataset, especially on the multidimensional dataset.

Table 1. Prediction Results of each model
Assistments Blended learning data
Models One-dimensional Multidimensional One-dimensional Multidimensional
ACC AUC ACC AUC ACC AUC ACC AUC
Frequency method 0.694 N/A 0.683 N/A 0.702 N/A 0.688 N/A
IRT 0.716 0.779 0.701 0.758 0.721 0.784 0.706 0.752
MIRT 0.714 0.771 0.721 0.786 0.718 0.775 0.722 0.783
T-IRT 0.738 0.805 0.712 0.769 0.744 0.801 0.717 0.764
T-BMIRT 0.743 0.815 0.738 0.803 0.757 0.820 0.748 0.816

4.2 Rationality Evaluation

The rationality evaluation verifies whether the algorithm can recommend the suitable
learning resources that meet the student’s needs and ability levels. We set the following
two indicators for it.
𝑝 𝑝
∑𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟𝑖𝑡𝑦(ℎ𝑒 ,𝐾𝐶𝑠𝑥 ) ∑𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟𝑖𝑡𝑦(ℎ𝑒 ,𝜃𝑠 )
𝑖 𝑖 𝑥,𝑖
RCsx = 𝑖
, DCsx = 𝑖
(4)
𝑚 𝑚

Where 𝑒𝑖 ∈ 𝑝 is the learning resources in a recommended path, 𝑚 is the length of the
path, 𝐾𝐶𝑠𝑥 is the knowledge components which 𝑠𝑥 is learning in the current chapter,
function similarity() calculates the adjusted cosine similarity of the two vectors in the
parentheses. The relevance accuracy 𝑅𝐶𝑠𝑥 is used to evaluate whether the difficulties
of the recommended learning resources for the target student 𝑠𝑥 are matched with his
ability. The difficulty accuracy 𝐷𝐶𝑠𝑥 is set to evaluate whether the difficulties of the
recommended learning resources for the target student can match his current ability
levels.
We selected the blending data to do this experiments. Table 2 shows the average of
the 10-fold cross-validation results. It can be seen that the UCF and ICF have a similar
effect, but the UCF works better on the relevance accuracy, while the ICF is better at

156
7

the difficulty accuracy. The LFM performs better than the first two algorithms in terms
of both indicators. The SARLR algorithm performs best among all these algorithms.

Table 2. Results of Rationality Experiment.

Model Relevance accuracy Difficulty accuracy
UCF 0.86 0.77
ICF 0.71 0.83
LFM 0.87 0.84
SARLR 0.97 0.92

4.3 Effectiveness Evaluation

The effectiveness evaluation verifies whether the students’ abilities can be improved
by the recommendation algorithm. We clustered the students into six groups according
𝐸(𝑅𝑆′ ⁡)−𝐸(𝑅𝑆 )
their ability levels. We calculated “expected gain” 𝐺 = by using PCA and
𝐸(𝑅𝑆 )
K-means method to further split the students of the same group into two parts based on
their learning paths [6]. One part is the students whose learning paths are strictly rec-
ommended, denoted as⁡𝑆 ′ , and the other part is the students whose learning path are
randomly selected, denoted as⁡𝑆. 𝐸(𝑅𝑆 ′ ⁡) and 𝐸(𝑅𝑆 ) and indicate that the students’ av-
erage score in the last online assessment. We sorted the six groups of the students as-
cendingly based on their ability levels: group 1 has the lowest skill level, group 2 has a
higher skill level than group 1, and group 6 has the highest.

Table 3. Results of Effectiveness Experiment

Expected gain
Model
1 2 3 4 5 6
UCF -0.04 -0.06 0.07 -0.03 0.08 0.01
ICF 0.05 0.04 -0.03 0.07 -0.02 0.05
LFM 0.04 0.12 0.09 0.10 0.03 -0.05
SARLR 0.11 0.27 0.24 0.23 0.17 0.06
We selected the public data “Assistments” to do this experiments. Table 3 shows that
the SARLR algorithm performs much better than the other three algorithms. Especially
for the students in group 2 to group 5, the SARLR algorithm helps them to achieve
noticeable progress from the recommendation learning paths. It indicates that SARLR
is more effective on improving learning gain of students with average ability levels.

5 CONCLUSIONS

We developed a self-adaptive recommendation algorithm of learning resources
(SARLR) to personalize students’ learning path. It contains the T-BMIRT, a temporal
blended multidimensional IRT model, which performs well on the prediction task of

157
8

multi-dimensional skills assessments, especially when the study process contains learn-
ing video interactions. Based on the T-BMIRT model, the SARLR algorithm adopts a
reasonable recommendation strategy and establishes conditions to adaptively adjust
recommendations towards the dynamic needs of the students. In addition, we extend
the evaluation criteria for personalized learning recommendation in term of rationality
and effectiveness. Experimental results prove that the SARLR algorithm outperforms
the other recommendation algorithms based on CF and LFM.

References
1. Akbulut, Y., Cardak, C. S.: Adaptive educational hypermedia accommodating learning
styles: A content analysis of publications from 2000 to 2011. Computers & Education. 58(2),
835-842 (2012).
2. Vesin, B., Ivanović, M., KlašNja-MilićEvić, A., Budimac, Z.: Protus 2.0: Ontology-based
semantic recommendation in programming tutoring system. Expert Systems with Applica-
tions. 39(15), 12229-12246 (2012).
3. Wu, D., Lu, J., Zhang, G.: A fuzzy tree matching-based personalized e-learning recom-
mender system. IEEE Transactions on Fuzzy Systems. 23(6), 2412-2426 (2015).
4. Jenatton, R., Roux, N. L., Bordes, A., Obozinski, G. R.: A latent factor model for highly
multi-relational data. In: Proceedings of the 25th International Conference on Neural Infor-
mation Processing Systems, pp. 3167-3175. ACM, California (2012).
5. Segal, A., Katzir, Z., Gal, K., Shani, G., Shapira, B.: Edurank: A collaborative filtering ap-
proach to personalization in e-learning. In: Proceedings of the 7th International Conference
on Educational Data Mining, pp. 68–75. EDM, London (2014).
6. Reddy, S., Labutov, I., Joachims, T.: Latent skill embedding for personalized lesson se-
quence recommendation. arXiv preprint arXiv:1602.07029 (2016).
7. Theocharous, G., Beckwith, R., Butko, N., Philipose, M.: Tractable POMDP Planning Al-
gorithms for Optimal Teaching in SPAIS. In: Workshop on Plan Activity, and Intent Recog-
nition (PAIR), IJCAI (2009).
8. Folsom-Kovarik, J. T., Sukthankar, G., Schatz, S. L., Nicholson, D. M.: Scalable POMDPs
for Diagnosis and Planning in Intelligent Tutoring Systems. In: AAAI Fall Symposium: Pro-
active Assistant Agents. AAAI Press, Virginia (2010).
9. Brunskill, E., Russell, S.: Partially observable sequential decision making for problem se-
lection in an intelligent tutoring system. In Educational Data Mining (EDM), pp. 327–328
(2011).
10. Reckase, M.: Multidimensional item response theory. Springer, New York (2009).
11. Ekanadham, C., Karklin, Y.: T-skirt: Online estimation of student proficiency in an adaptive
learning system. arXiv preprint arXiv:1702.04282 (2017).
12. Huang, J.,Wu, W.: T-BMIRT: Estimating representations of student knowledge and educa-
tional components in online education. In: 2017 IEEE International Conference on Big Data,
pp. 1301-1306. IEEE Press, Massachusetts (2017).

158