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: $$p_s = \frac {N^+} {N^+ + N^-}$$

San Diego State University

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

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

"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. 


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