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본 발표는 지난달 했던 발표의 버전2 입니다. 세부 내용을 업데이트하고, 주요 질문들을 기준으로 내용을 재구조화 하였습니다.

A Survey of Knowledge Tracing: Models, Variants, and Applications

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Introduction

• The reason why representer choose this paper…
  • Compared to other review paper, this paper has more higher level overview
• KT
  • one of the fundamental tasks for student behavioral data anaylsis, aiming to monitor students’ evolving knowledge state during their problem-solving process

Overview

A. Problem Definition

• Knowledge Concepts

  • ex) Reading, Listening, Speaking in TOEFL

• Formulating learning sequence like..

  $$ X={([e_{1}, k_{e_{1}}], a_{1}, r_{1}), ([e_{2}, k_{e_{2}}], a_{2}, r_{2}), …(), …} $$

  • $e_{i}$: exercise
  • $k_{e_{i}}$: exercise’s related to KC
  • $a_{t}$: correctness label
  • $r_{t}$: side information

• The general research problem in Knowledge Tracing

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  Given sequences of learning interactions in online learning systems, knowledge tracing aims to monitor students’ evolving knowledge states during the learning process and predict their performance on future exercises. The measured knowledge states can be further applied to individualize students’ learning schemes in order to maximize their learning efficiency

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• To evaluate the quality of the traced knowledge state by KT model, see how model predicts on student performance is the best option

  • But, KT highlights on more on interpretability and rationality of knowledge state, which is related to the students’ acceptance of the conclusions based on the KT model

Fundamental Knowledge Tracing Models

A. Bayesian Knowledge Tracing

• BKT is a specific form of Hidden Markov Model (HMM)
  • A HMM is an extension of Markov model, which is the simplest form of sequential modeling
    • Adding latent state to represnt unobservable variable
    • in BKT, hidden state is knowledge state and observation is student’s answer (e.g. correct | incorrect)
  • transition probability
    • The probability of moving from one hidden state into the other hidden state
    • for example, in BKT, from not knowing to knowing (learning) or from knowing to not knowing (forgetting)
  • emission probability
    • The probability of observing a particular outcome given the hidden state
    • for example, in BKT, “the probability of answering correctly given the student knows the sill”

• BKT is introduced by Corbett and Anderson (1995)
• BKT has two forms (van De Sande, B, 2013)
  1. Hidden Markov Model form
     • a functional form is an exponential
  2. Knowledge Tracing Algorithm form
     • BKT determine the probability of student’s learning state