"Vygotsky’s Zone of Proximal Development (ZPD) stipulates that a student can
solve the problems just beyond his/her knowledge with guidance, and a good
teacher/tutor system should recommend those problems to the student. Based on
this theory, we propose the recommendation heuristic to select the next problem
in the (fuzzy) partial ordering graph."



ZPD-based Recommendation Heuristic  (Adaptive Learning Material Recommendation in Online Language Education)

The difference between assessment and recommendation  is that in the case of assessment the whole knowledge structure is searched and the information about user current knowledge is extracted while in the case of recommendation each problem that user hasn't answered correctly is selected.  The probabilistic function to balance this two is used:

$$ p = \frac {Prob} {M} $$
p is the probability that the assessment will be chosen and 1-p is that recommendation will be used. Prob stands for the amount of problems that user visited totally, and M is the parameter controlling transition between recommendation-favoring and assessment-favoring. 


Balancing Assessment and Recommendation (Adaptive Learning Material Recommendation in Online Language Education)

In the adaptive assessment heuristic framework, a problem is selected to maximize the student's knowledge acquisition. This is formulated as: $$s^{*} = argmax [p_sn_s^+ + (1-p_s)n_s^-]$$ Here, $$p_s$$ is the probability that the user will solve problem $$s$$, $$n_s^+$$ is the number of problems the user can solve correctly, and $$n_s^-$$ is the number of problems the user cannot solve. The probability $$p_s$$ is estimated by: $$p_s = \frac {N^+} {N^+ + N^-}$$

Adaptive Assessment Heuristic (Adaptive Learning Material Recommendation in Online Language Education)

1. Adaptive Assessment Heuristic
2. ZPD-based Recommendation Heuristic
3. Balancing Assessment and Recommendation

San Diego State University

1. Introduction
2. Related Work
3. Modeling Vocabulary Knowledge
4. Adaptive Learning Material Recommendation
5. Evaluation of adaptive recommendation

Adaptive Learning Material Recommendation in
Online Language Education

Distributing exercises on online platform represents a difficult task. In order to achieve this goal several factors should be considered like student ability, exercise difficulty, the similarity of the exercises, the skills that are involved in the exercise. In this paper the authors aimed to create personalized adaptive recommender system that would take into account the skills that students acquired in the previous interaction. They gathered materials from the internet and used **fuzzy partial ordering graph** to organize them. 

Introduction (Adaptive Learning Material Recommendation in Online Language Education)

1. Hierarchical Knowledge Organization
In the previous papers, automatic knowledge organization for the procedural tasks was introduced which was based on the execution trace to solve the specific task and partial ordering between tasks. Partial ordering was applied to the natural language grammar and the skill difficulty was measured in the following manner: 
problem a is considered easier than b if b contains all the concepts that are in a. In the graphs this relation is shown by the edge from a to b. This method can be difficult to use when there are large amount of concepts. In order to eliminate this problem new fuzzy partial ordering graph is proposed. 
2. Knowledge Assessment and Computer Based Test
IRT (item response theory) and CAT (Computerized Adaptive Test)  use user responses in order to update the information about student ability and item difficulty. However they have difficulties when there are fresh items since there is no student responses. "In contrast, our work measures the difficulty of online learning materials by studying the compositionality of domain knowledge and building the hierarchical knowledge structure within the corpus"


3. Educational Recommender Systems
Educational recommender systems are mostly used in the formal learning scenarios like universities.  In such environments experts design material and additionally there are pre-assessments or pre-questionnaires. In the case of online learning (informal learning situation) there is lack of structured data. The authors of this papers try to solve this issue by automatically ordering from the learning material that is retrieved from the Internet.


Related Work (Adaptive Learning Material Recommendation in Online Language Education)

The model performance is evaluated at JRec - Japanese reading text recommendation tool . 380 articles were used form Japanese news website and these articles were split in 4267 sentence and paragraphs. Then hierarchical structure of the vocabulary was analyzed and afterwards fuzzy partial ordering graph was applied to it .  After the sentence appears user should answer whether they understand it or not. Their tool was used by 386 users in 3 days. "In JRec, we tested four different versions: 1) adaptive recommendation (which
balances recommendation and assessment as we discussed in the last section4
) and 2) non-adaptive recommendation (with no assessment incorporated), as
well as 3) assessment-only, and 4) random selection as additional baselines"  As it was found adding adaptivity increased user performance. 

Evaluation of Adaptive Recommendation (Adaptive Learning Material Recommendation in Online Language Education)

To model the relationship between reading materials in adaptive learning systems, a fuzzy partial ordering graph can be used. A practice problem is characterized as a multiset of required concepts. The standard ordering rules are:

1. Problem s1 is harder than s2 (s1 > s2) if s1 covers all required concepts of s2.
2. Problem s1 is directly harder than s2 if s1 > s2 and no intermediate problem s3 exists.
3. The partial ordering is represented as a Directed Acyclic Graph (DAG) where edges represent the "directly harder than" relation.

To address sparse hierarchical structures in domains like vocabulary knowledge, an $$\alpha$$-fuzzily harder relation is applied to increase density: problem s1 is $$\alpha$$-fuzzily harder than problem s2 if s1 covers at least a proportion $$\alpha$$ of s2's required concepts. The parameter $$\alpha$$ is tuned to balance graph density and the likelihood of student comprehension (e.g., setting $$\alpha$$ to 0.8).

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