DAGKT Diculty and Attempts Boosted Graph-based Knowledge Tracing Rui Luo1 Fei Liu12 Wenhao Liang1 Yuhong Zhang1

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DAGKT: Diﬃculty and Attempts Boosted

Graph-based Knowledge Tracing

Rui Luo1, Fei Liu1,2, Wenhao Liang1, Yuhong Zhang1,

Chenyang Bu1( ), and Xuegang Hu1( ) ?

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

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

University of Technology, China

2Jianzai Tech, Hefei, China

{chenyangbu,jsjxhuxg}@hfut.edu.cn

Abstract. In the ﬁeld of intelligent education, knowledge tracing (KT)

has attracted increasing attention, which estimates and traces students’

mastery of knowledge concepts to provide high-quality education. In KT,

there are natural graph structures among questions and knowledge con-

cepts so some studies explored the application of graph neural networks

(GNNs) to improve the performance of the KT models which have not

used graph structure. However, most of them ignored both the questions’

diﬃculties and students’ attempts at questions. Actually, questions with

the same knowledge concepts have diﬀerent diﬃculties, and students’

diﬀerent attempts also represent diﬀerent knowledge mastery. In this

paper, we propose a diﬃculty and attempts boosted graph-based KT

(DAGKT)3, using rich information from students’ records. Moreover, a

novel method is designed to establish the question similarity relation-

ship inspired by the F1 score. Extensive experiments on three real-world

datasets demonstrate the eﬀectiveness of the proposed DAGKT.

Keywords: Educational Data Mining ·Knowledge Tracing ·Graph

Neural Network

1 Introduction

In recent years, with the development of intelligent tutoring systems, more users

choose online education because it is more convenient to provide personalized

and high-quality education than traditional classrooms [2]. Knowledge tracing

(KT), which evaluates students’ knowledge mastery based on their performance

on coursework, has attracted great attention and in-depth research.

?This work is supported by the National Natural Science Foundation of China (un-

der grants 61806065, 62120106008, 62076085, and 61976077), and the Fundamental

Research Funds for the Central Universities (under grants JZ2022HGTB0239).

3https://github.com/DMiC-Lab-HFUT/DAGKT

arXiv:2210.15470v1 [cs.CY] 18 Oct 2022

2 R Luo. et al.

Graph-based

knowledge tracing

Limit 1:

Lack of

difficulties

and attempts

Limit 2:

Lack of

question

similarity

relationship

Answer

embeddings Question

embeddings

generate

Answering

logs

Exercise embedding

consist

× × √

Same

Question Student 2

Student 1

generate

Question-KC

graph

input

Limits

Question 1

1+1=?

Question 2

1+2+3+……+100=?

Similar

embeddings

√D

difficulties

attempts

Same

knowledge

concept

q1q1'

Question-KC graph

q2q2'

a1'

a2'

Question-KC graph

(with question similarity

relationships)

CaseⅠ

CaseⅡ

Case Ⅲ

Contribution1 (address Limit 1)

Contribution2 (address Limit 2)

Contributions (Section 3): Proposed model DAGKT

Discrepant

embeddings

Embedding

×Answer

record

Question

Knowledge

Concept

Question

similarity

Fig. 1. The limits and contributions. The limit of lack of diﬃculties and attempts is

addressed shown in Case I and II, and the limit of lack of question similarity relationship

is addressed shown in Case III.

Nowadays, KT models based on graph neural networks (GNNs) present sat-

isﬁed performance, because there are natural graph structures among knowl-

edge concepts (KCs) and questions in KT [9]. Nakagawa et al. [13] proposed

the graph-based KT (GKT) to learn the graph relations among KCs using the

GNN. Graph-based interaction model for KT (GIKT) [18] focuses on the re-

lationships between questions and KCs, obtaining higher-order embeddings of

questions and KCs by the graph convolutional network (GCN) [7]. Question em-

beddings and answer embeddings in KT task [15] are integral parts of exercise

embeddings. Among them, question and answer embeddings represent the infor-

mation of questions and students’ performance on questions, respectively. These

GNN-based KT models obtain satisﬁed performance because better exercise em-

beddings are achieved through question embeddings with graph relationships

using GNNs.

Exercise embedding plays an important role in KT task, because cognition

evaluation in KT relies on students’ performance on exercises. There is rich

information involved in exercises such as stem texts [17] and student behaviors

features [12]. There is still room for improvement for both embeddings, analyzed

from the following aspects, as shown in Case I-III of Figure 1.

First, most existing GNN-based KT models ignore the question diﬃculties

in question embeddings as well as attempts in answer embeddings. Diﬃculties

and the number of attempts are critical as question embeddings and answer

embeddings which reasons are as follows. When two questions q1and q2examine

the same KC, student s1may give diﬀerent answers because q1and q2have

diﬀerent diﬃculties (shown in Case I of Figure 1). And if the number of attempts

is not considered, the model will think that student s2who has tried 10 times

to get it right, and student s3who got it right after only one attempt have the

same experience (shown in Case II of Figure 1). So if diﬃculties and attempts

DAGKT: Diﬃculty and Attempts Boosted Graph-based Knowledge Tracing 3

are not considered models can’t discriminate between questions with the same

KCs, or between answers with diﬀerent attempts.

Furthermore, the question embedding is achieved by GNN aggregating the

information of the surrounding nodes in the question-KC graph, so the question-

KC graph is very important. Most existing graph-based KT models perform

convolution on bipartite graphs and there is no question-question relationship

in the graph (shown in III of Figure 1). Gao et al. [5] hold the view that there

are two kinds of relationships between questions: prerequisite relationships and

similarity relationships. In the ﬁeld of GNN-based KT, few studies put the rela-

tionships between questions into the convolution process (most of them only use

the question similarities in the prediction process, such as [18]). Tong et al. [16]

designed a method of constructing prior support relationships between questions

from students’ answer results illustrating the eﬀectiveness of constructing rela-

tions from students’ answer results. However, most existing studies construct

the question similarity relationship through question text information or prob-

lem embedding distances, without using the students’ answer results. There is

still a need for a method that can use students’ answer results to build similarity

relationships.

To address these two problems, we propose the DAGKT model. Speciﬁcally,

to solve the ﬁrst problem, we design a fusion module to fuse two types of infor-

mation: diﬃculty and attempts. We get the diﬃculties of the questions and the

students’ number of attempts from the datasets and encode them into embed-

dings through the encoder. After that, we put them with question embeddings

and answer embeddings to the fusion module to obtain exercise embeddings that

contain enormous information. Secondly, to address the second question and ob-

tain a good question embedding, we design a relationship-building module that

enriches the question-KC graph so that GCN can generate question embeddings

that combine the information of the question relationships. We use statistical

information combined with the calculation method of the F1 score to calculate

similarity relationships between questions. It is assumed that the two questions

may have a close relationship when students always obtain similar answering

results (correct/incorrect) on the two questions. The F1 score is an indicator

used in statistics to measure the accuracy of binary models. Another way to

say, the F1 score infers to the degree of similarity between predicted and tar-

get values [10]. Therefore, the similarity of questions in this study is calculated

according to the F1 score.

Finally, extensive experiments on real world datasets demonstrate the eﬀec-

tiveness of DAGKT and each module. In summary, our main contributions are

as follows:

–To address the problem that most graph-based KT models cannot clearly

discriminate between questions with same KCs, or between answers with dif-

ferent attempts, DAGKT is proposed with a fusion module. In this module,

the question and answer embeddings are fused with diﬃculty and attempts.

–Furthermore, the relationship-building module is designed to construct the

similarity relationship between questions, inspired by the F1 score. The con-

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DAGKT:DicultyandAttemptsBoostedGraph-basedKnowledgeTracingRuiLuo1,FeiLiu1;2,WenhaoLiang1,YuhongZhang1,ChenyangBu1(),andXuegangHu1()?1KeyLaboratoryofKnowledgeEngineeringwithBigData(theMinistryofEducationofChina),SchoolofComputerScienceandInformationEngineering,HefeiUniversityofTechnology,China2Jianz...

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