A reliable knowledge structure is a prerequisite for building efective intelligent tutoring systems(ITS). To achieve an explainable and trustworthy knowledge structure, we propose a specific method for constructing causal knowledge networks. This approach leverages Bayesian networks as a foundation and incorporates causal relationship analysis to derive a causal network. Additionally, we introduce a reliable knowledge-learning path recommendation technique based on this framework, improving teaching and learning quality while maintaining transparency in the decision-making process.
The interconnected knowledge system, comprised of subject
knowledge components, forms the basis of Intelligent
Tutoring Systems (ITS)[
Currently, most studies on knowledge component relationships are focused on correlations rather than causations.
Correlations lack true explainability, as exemplified by the
saying “Storks Deliver Babies”[
In the field of deep learning, correlation discovery has been
extensively studied, yielding many excellent models.
However, the demand for explainability in education renders
most deep learning “black box” models insuficient.
Examples include graph structure learning based on Graph Neural
Networks[
This research aims to explore and understand the relationships between knowledge components, focusing on the nature and causes of these relationships. As previously discussed, correlation does not necessarily imply causation. Thus, relationships identified solely from data cannot be directly defined as causal, as this could be misleading.
The study will focus on discovering causal relationships
(B. Jiang)
tensive manual intervention [
Although these studies have successfully identified prerequisite relationships among knowledge components and considered them as a specific type of causal relationship to optimize teaching or learning sequences, uncovering latent causal relationships from student test data is more critical for adaptive learning systems. This is because learning outcome data can more accurately reflect students’ mastery of content, aligning better with the essence of personalized CEUR
ceur-ws.org
investigate causal relationships among knowledge components through targeted interventions and counterfactual
experiments. The process involves recommending new strong and weak ties, representing the data, and conducting counterfactual
experiments to validate the potential causal structures.
learning [
To capture the causal relationships among learning
concepts, we begin by establishing a foundational knowledge
network using available data. Bayesian
networks—probabilistic graphical models represented through Directed
Acyclic Graphs (DAGs) and Conditional Probability Tables
(CPTs)—are used to model the relationships between
variables, making them ideal for constructing knowledge
network structures due to their directed and probabilistic
nature[
BIC(, , ) = log ( ∣ , ) − || 2 log where ( ∣ , )
is the likelihood of the data given the network with parents Pa( ): network structure and parameters, || is the number of parameters in the model, and is the number of data points.
Next, we compute the likelihood for each node in the
∏
∏ where is the number of nodes, is the number of parent configurations for node , is the number of states of node , and is the number of instances in the data where The log-likelihood component of the BIC score is comlog ( ∣ , )
(∑( − 1) ) log (5)
use the initially obtained network structure 0 to represent the assumed causal relationships between variables. Let the variables in the network be 1, 2, ..., , and their causal relationships are represented by a directed acyclic graph (DAG) as = ( , )
, where is the set of nodes and is the set of directed edges.
To calculate the causal efect of node on node , we
can use Pearl’s back-door criterion [
calculate the causal efect of on , i.e., ( |( = ′), ) . Finally, = ′) ).
By combining insights from both intervention and counterfactual experiments, we construct a comprehensive causal network of knowledge components. This network not only reflects the probabilistic relationships between concepts but also provides a deeper understanding of the causal mechanisms that drive knowledge acquisition and mastery. The resulting causal network serves as a valuable tool for educators and learners alike, ofering a detailed map of the interconnectedness of knowledge and a basis for targeted interventions to enhance learning outcomes.
The causal network serves not merely as a static representation of knowledge interconnectivity but as a dynamic tool for educational planning. Each node within the network, fortified by the robustness of its causal linkages, becomes a critical checkpoint in an individual student’s learning trajectory.
To efectively assess and support learning, it is essential to first construct a comprehensive causal network. This network takes the form of a conceptual map that connects all relevant concepts and topics involved in the learning objectives through their causal relationships. Following this, an initial assessment of students’ understanding is conducted through methods such as quizzes, interviews, or observations to determine their grasp of each knowledge component within the network. The assessment results will help us identify the knowledge components that students have not fully mastered, which are the gaps in their understanding.
By analyzing the interconnections of these unmastered knowledge components within the causal network, we can trace the origins of the knowledge gaps and establish a path leading to the root nodes—the fundamental causes of the students’ dificulties. Throughout this process, we highlight all problematic nodes, which are points where students are likely to encounter challenges and require additional support. After identifying the root nodes, we recommend that learners concentrate on strengthening their grasp of these critical concepts through additional practice, review sessions, or targeted instruction.
Ultimately, we provide learners with a detailed guide that serves as a roadmap for their systematic journey through the causal network, ensuring they address each concept logically and organized. This approach fills in knowledge gaps and builds a solid foundation of interconnected knowledge.
To illustrate this process more clearly, we refer to Fig. 2 in the text, which provides a visual representation of the causal network and the traced path. At the same time, to quickly find the path for students to solve the superficial problem step by step from the root problem, we build upon the network structure obtained in the previous section. By learning path tracing and based on the current mastery status of each knowledge component node, we identify the root problem node and then proceed to find the shortest path to the superficial problem node, obtaining the shortest learning path to facilitate student learning. The specific algorithmic process is illustrated in Algorithm 2. Algorithm 2 Find Shortest Path in a Directed Graph Require: Directed graph , source node , target node Ensure: Shortest path from to in 1: Initialize an empty queue 2: Enqueue into 3: Initialize a dictionary
set [] = 0 and [ ] = ∞ 4: while is not empty do 5: Dequeue a node from 6: for each neighbor of in do 7: Calculate = [] + weight(, ) 8: if < [ ] then 9: [ ] = 10: Enqueue into 11: end if 12: end for 13: end while 14: return [] with all nodes in as keys, for all other nodes
Before learning the causal network of knowledge components, it is necessary to collect data on students’ actual learning processes. This type of data is similar to datasets like Assistment1 and Junyi2. In our current experiments, we have collected data on the learning processes and outcomes of mathematics courses from 77 classes in 19 elementary schools and 7 middle schools across Shanghai, Sichuan, Jiangsu, and Beijing, China. These classes cover four grades, from fourth to seventh. Using common cognitive diagnostic methods such as knowledge tracing and the DINA model, we obtained students’ mastery states of knowledge components. These mastery states, represented as time series data, serve as the foundation for constructing the causal knowledge network proposed in this study. The experimental data were obtained from our self-designed adaptive learning platform3, which served as the data foundation for constructing the network.
Following is an example from a small-scale experiment. For larger-scale experiments and comparisons with other methods, please look forward to our future research publications.
We demonstrate the construction process of a causal knowledge network through a small-scale experiment, with the algorithm workflow shown in Algorithm 3.
The Algorithm 3 begins with a learning performance dataset as input, which is then transformed into a knowledge mastery dataset containing student IDs and corresponding levels of knowledge proficiency. Subsequently, an initial knowledge network is constructed through correlation learning, and the following steps are iteratively executed while the student scores remain stable: the current knowledge network structure’s score is calculated using the Bayesian Information Criterion (BIC), followed by the optimization of the network structure through Hill Climbing search to identify a better network structure D(new), which then updates to D(new). Once the optimization is complete, the algorithm returns a knowledge network D(Bayesian) that has been updated through Bayesian inference, and proceeds
D = D(new) return D(Bayesian)
in D(Bayesian) for
Causality = Refute({id,k() }=1 Output D(Causality) _ , ) Algorithm 3 Constructing Causal Knowledge Networks Input: Learning performance dataset = {id,s() }=1 _ Transform: Learning performance dataset ⇒ Knowledge mastery dataset = {id,k() }=1 _ Initial knowledge network through correlation learning: D while is stable
D(new), score = Algorithm 1({id,k() }=1 _ , D) to traverse each edge of the network, using the Refute function to verify the causality of each edge. Ultimately, the algorithm outputs a knowledge network D(Causality) that has undergone causality analysis.
In the Algorithm 3, the Refute method is used to validate
the reliability of the inferred causal relationships through
interventions, which is the causal efect calculation method
discussed previously. In this process, counterfactual data
can be generated through sampling, perturbation, or other
methods as needed for the experiment to verify the causal
relationships. In the experimental example of this study,
we calculate causal efects using only intervention methods
and determine the strength of the causal relationships to
decide whether to add or remove a particular edge. And
BIC_score comes from [
As shown in Fig. 3, through the refutation experiment on edge (a), we found weak causal efect and low credibility of the correlation relationship, and therefore cannot admit the existence of causal relationships between nodes. In contrast, the refutation experiment on edge (b) revealed a causal efect of about 0.77 and over 95% credibility, indicating a Strong tie between the nodes. The modified network structure was then generated accordingly. Certainly, we can continue to explore the causal relationships between more nodes and update the network, in order to obtain the final causal network.
A well-structured knowledge network can efectively support the development of ITS, enhancing personalization and improving educational quality. However, constructing such knowledge structures has always been a topic of interest, and the relationships between knowledge components can be challenging to elucidate. Most studies define knowledge structures through associative relationships, which do not necessarily represent the true causal links between knowledge components.
During the construction of the causal network, we
perform intervention and counterfactual experiments to
discover and validate causal relationships. In the intervention
process, we establish two new causal connections: Strong
and Weak tie. Incorporating causal connection strength
allows us to assess the nonlinear impact and diferences
in interaction strength[
Constructing causal knowledge component networks
provides foundational insights for knowledge tracing (KT),
learning resource recommendations, learning path planning,
and learning outcome assessment. Specifically, utilizing
feature causality can efectively select data features that
enhance the performance of KT, while the causal relationships
among these features can explain why a particular feature
improves KT prediction outcomes[
However, there are still some limitations and challenges; for example, the structural learning of large-scale Bayesian networks remains a challenging scientific problem, especially when analyzing causal relationships on this basis, which further increases the dificulty. The main challenges are high computational complexity, insuficient data, and uncertainty features. For instance, insuficient data in existing educational datasets, the largest online education dataset, EdNet2, contains over 39,000 knowledge components, with approximately 15,000 in mathematics and 8,000 in science. On average, each knowledge component has only 341 data entries. This amount of data per knowledge component is insuficient for generating large-scale networks.
This paper focuses on constructing a causal knowledge network to investigate the causal relationships among learning concepts to enhance teaching quality and efectiveness. Using Bayesian networks and causal inference methods, a knowledge network based on learning performance data has been established. The relationships between nodes in the network have been validated and refined through intervention and counterfactual experiments. This work provides educators and learners with a comprehensive causal knowledge network that reflects the probabilistic relationships between concepts and provides insights into the causal mechanisms driving knowledge acquisition and mastery. Overall, this research ofers a significant tool and approach for the education domain to promote explainability in educational technology and to provide personalized and efective learning support for learners.
This research was funded by the National Natural Science Foundation of China grant number 61977058, and the Natural Science Foundation of Shanghai grant number 23ZR1418500.