APGKT Exploiting Associative Path on Skills Graph for Knowledge Tracing Haotian Zhang10000000301339762 Chenyang Bu10000000182030956

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APGKT: Exploiting Associative Path on Skills

Graph for Knowledge Tracing ?

Haotian Zhang1[0000−0003−0133−9762], Chenyang Bu*1[0000−0001−8203−0956],

Fei Liu*1,2[0000−0003−0022−4103], Shuochen Liu1[0000−0003−4724−8989],

Yuhong Zhang1[0000−0001−7031−0889], and Xuegang Hu1[0000−0001−5421−6171]

1Key Laboratory of Knowledge Engineering with Big Data (the Ministry of

Education of China), School of Information Science and Computer Engineering, Hefei

University of Technology, China

2Jianzai Tech, Hefei, China

Abstract. Knowledge tracing (KT) is a fundamental task in educa-

tional data mining that mainly focuses on students’ dynamic cognitive

states of skills. The question-answering process of students can be re-

garded as a thinking process that considers the following two problems.

One problem is which skills are needed to answer the question, and the

other is how to use these skills in order. If a student wants to answer a

question correctly, the student should not only master the set of skills

involved in the question, but also think and obtain the associative path

on the skills graph. The nodes in the associative path refer to the skills

needed and the path shows the order of using them. The associative path

is referred to as the skill mode. Thus, obtaining the skill modes is the key

to answering questions successfully. However, most existing KT models

only focus on a set of skills, without considering the skill modes. We pro-

pose a KT model, called APGKT, that exploits skill modes. Speciﬁcally,

we extract the subgraph topology of the skills involved in the question

and combine the diﬃculty level of the skills to obtain the skill modes

via encoding; then, through multi-layer recurrent neural networks, we

obtain a student’s higher-order cognitive states of skills, which is used to

predict the student’s future answering performance. Experiments on ﬁve

benchmark datasets validate the eﬀectiveness of the proposed model.

Keywords: Educational data mining ·knowledge tracing ·graph neural

network.

1 Introduction

Recent advances in intelligent tutoring systems have promoted the development

of online education and generated a large amount of online learning data [1–3].

?Co-corresponding authors: Chenyang Bu (email: chenyangbu@hfut.edu.cn) and Fei

Liu (email: feiliu@mail.hfut.edu.cn).

Chenyang Bu was supported in part by the National Natural Science Foundation

of China under Grants 61806065 and 62120106008, and the Fundamental Research

Funds for the Central Universities under Grant JZ2022HGTB0239. The source code

is available at https://github.com/DMiC-Lab-HFUT/APGKT-PRICAI2022.

arXiv:2210.08971v1 [cs.CY] 5 Oct 2022

2 H. Zhang et al.

？？

with

complete

thinking

process

with

incomplete

thinking

process

obtain the skill modes Correct

Wrong

Question

Student 1

Student 2

skills mastered by student 1

not obtain the skill modes

G1 G2 G3 G4 G5 G6

Thinking process Skills

Skill modes

(a) Different answers are obtained by two students with different thinking process (detailed in (b) )

(b) Diagram of thinking process

skills mastered by student 2

？

Complete thinking

process of the question

Fig. 1. (a) Instance of students answering questions. Given the same question, Student

1 and Student 2 provide diﬀerent answers. Assuming that the skills mastery of the two

students is similar, the student who cannot obtain the skill modes through thinking

should have a higher probability of answering incorrectly. (b) Detailed thinking process

of a student. Girepresents every thinking state and the arrow connecting two states

represents a state transition, indicating a student’s thinking and associative behavior.

Knowledge tracing (KT) is used to model students’ dynamic mastery of skills

based on their historical learning data and to infer their future answering perfor-

mance, which is a fundamental and essential task in computer-aided educational

systems and online learning platforms [4,5].

Bayesian knowledge tracing (BKT) [6] was the ﬁrst KT model proposed by

Corbett et al. It models students’ cognitive states using the hidden markov model

(HMM) with limited representation capabilities [7]. Subsequently, deep learning

models, such as deep knowledge tracing (DKT) [8], were developed, which model

a student’s learning process as a recurrent neural network (RNN), signiﬁcantly

improving the prediction performance of the traditional Bayesian-based KT.

With the development of graph neural networks (GNN) [9], GNN-based KT

models [10,11], which use the natural graph structure existing in skills to model

students’ cognition, have attracted considerable attention. Although KT models

have developed rapidly in recent years, limitations still exist.

Most of the existing KT models assume that students could obtain the correct

answer only if they mastered all the skills; therefore, they use the cognitive state

of the skills to predict a student’s future answering performance. However, they

ignore the thinking process of students. In addition to mastering skills, two points

need to be considered to predict the future answering performance of a student:

APGKT 3

(1) ﬁnding the skills needed to answer a question among all the skills mastered,

and (2) obtaining a reasonable order of use for these skills. If a student wants to

answer a question correctly, the student should not only master the set of skills

involved in the question but should also think and obtain the associative path

on the skills graph, the nodes in which are the skills to be used, and the path

showing the order of using them. Here, the associative path is referred to as the

skill mode. If students only master the skills (e.g., P1 in Fig. 1(b)), the students

cannot solve the problem because they may not establish an association between

s1and s2; they do not think of using s2to solve the problem. At this time, the

students get stuck in processing the association from G1 to G2 shown in Fig.

1(b). Students may fail to establish an association between s2,s3, and s4as well.

At this time, the student gets stuck in processing the association from G2 to G3

shown in Fig. 1(b). Students who do not master any of the processes in P2 may

fail to solve the problem. Thus, obtaining skill modes is the key to answering

questions successfully. As shown in Fig. 1(a), Student 1 and Student 2 provide

diﬀerent answers for the same question. Assuming that the skill mastery of the

two students is similar, the student who cannot obtain the skill modes through

thinking should have a higher probability of answering incorrectly (as shown in

Fig. 1(a)). Students must use the skills they have mastered, the information in

the question, and their experience to ﬁnd the skills needed to answer a question

and convert the thinking process into answers (as shown in Fig. 1(b)). This study

assumed that students will have a higher probability of getting a question wrong

if they only master the skills without mastering the skill modes.

APGKT is proposed considering skill modes (e.g., P2 in Fig. 1(b)) to improve

performance of KT. The main contributions of this study are as follows:

–This study exploits the associative path on the skills graph for knowledge

tracing (KT). The thinking process (i.e., obtaining the associative path)

has been demonstrated to be indispensable for achieving a correct answer

(detailed in Fig. 1). However, most of the existing KT models only consider

whether the set of skills involved in the question have been mastered when

predicting a student’s future answering performance.

–The proposed APGKT model includes the concept of skill modes and higher-

order cognitive states. Considering the dynamic process of students thinking

and answering questions, the skills associated with a speciﬁc problem are

considered as a whole to consider the organizational association. We com-

bine the cognitive state of the skills and the skill modes into a higher-order

cognitive state to accurately represent the cognitive processes of students.

–Extensive experiments on ﬁve public datasets proved that the prediction

results of our model are better than those of baseline models, owing to the

consideration of the thinking process during KT.

2 Related Work

In this section, related work regarding KT and the existing GNN-based KT

models is introduced.

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APGKT:ExploitingAssociativePathonSkillsGraphforKnowledgeTracing?HaotianZhang1[0000000301339762],ChenyangBu*1[0000000182030956],FeiLiu*1;2[0000000300224103],ShuochenLiu1[0000000347248989],YuhongZhang1[0000000170310889],andXuegangHu1[0000000154216171]1KeyLaboratoryofKnowledgeEngineeringwithBigData(the...

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APGKT Exploiting Associative Path on Skills Graph for Knowledge Tracing Haotian Zhang10000000301339762 Chenyang Bu10000000182030956

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