Applying Petri-Net to Construct Knowledge Graphs for Adaptive Learning Diagnostics and Learning Recommendations Author: Jiann-Yun Dai (Department of Industrial Education, National Taiwan Normal University), Kuo-Liang Yeh (Department of Digital Media Design, Cardinal Tien Junior College of Health and Management), Man-Ting Kao (Department of Computer Science, New Taipei Municipal Jhangshu International Creative Technical High School), Yu-Hsi Yuan (Department of Labor and Human Resources, Chinese Culture University), Min-Wen Chang (Department of Industrial Education, National Taiwan Normal University)

Vol.&No.：Vol. 66, No. 3
Date：September 2021
Pages：61-105
DOI：https://doi.org/10.6209/JORIES.202109_66(3).0003

Abstract：
    Because of the increasing heterogeneity among students in classes and schools, determining a student’s basic learning status and ability in each subject and tailoring instruction or adapting remedial teaching to a student’s needs and characteristics have become challenging, especially for those students with learning disadvantages. According to Skinner’s behavioral learning theory (as cited in Gregory, 1987), differences in a student’s learning experiences (such as in understanding concepts) lead to considerable disparities in future learning. Drastic differences in internal cognition and concept structure may exist even among students with the same traditional learning achievements (i.e., scores) (Yu & Yu, 2006). Furthermore, the differences in concept cognition structure between experts and novices may be discoverable by analyzing similarities in students’ conceptual understandings, relationships, or psychological metrics (Brand-Gruwel et al., 2005; Hsu et al., 2012).
    Cognitive diagnostic models, such as the knowledge map, are useful for assessing a student’s conceptual knowledge structures and misconceptions to improve differentiated teaching, learning diagnosis, and remedial teaching (Chu et al., 2014; Hwang, Shi et al., 2011; Hwang, Wu et al., 2011; Ku et al., 2014; Lou et al., 2007; Lwo et al., 2013; Ting & Kuo, 2016). However, most such models have been constructed using only vertical hierarchical structures, wherein spotting multilateral correlations or influences between subjects or concepts proves difficult. Unlike an expert, a student cannot intuitively identify the multilateral correlations between the concepts involved a learning pathway, and analyzing novice learning is challenging and requires considerable time and effort.
    An adaptive mechanism for diagnosing and analyzing students’ dynamic learning behaviors and learning pathways could improve autonomous learning and remedial teaching. However, most existing mechanisms cannot offer adaptive or personalized learning content or pathways to the learner (Singhal, 2012; Ting & Kuo, 2016; Wang et al., 2019). 
    With the advantages provided by information technologies such as big data analytics and artificial intelligence, large-scale heterogeneous data analysis, cloud computing, and Knowledge Graphs (KGs) with directionally linked data structures have been widely applied in recommendation systems to facilitate the representation of knowledge structures and to mine for new knowledge that helps to meets users’ needs (Deng et al., 2019; Fensel et al., 2020; Guan et al., 2019; Jia et al., 2018; Nickel et al., 2016; Noy et al., 2019; Yu et al., 2020). Similar to tree-structured knowledge maps, KGs are based on directional or nondirectional ontological graphs composed of concept nodes and relationship edges and employ the consensus opinions of Subject Matter Experts (SMEs) to generate consolidated KGs or generate KGs automatically from large mined data sets or text. The associated reasoning mechanism is used to make inferences based on the existing concepts and relationships among them. Among all the graph-building options, Petri-Net possess the most robust capabilities for graphical workflow presentation and pathway analysis (Peterson, 1981; Tan & Zhou, 2013). They have long been widely applied in adaptive learning and learning pathway recommendation.
    According to information published by the Taiwan Bureau of Foreign Trade and Taiwan Electrical and Electronic Manufacturers’ Association in 2020, the electrical and electronics industry accounted for 50.59% of Taiwan’s total export value in 2019. The foundational electricity course is an important core course for future electrical and Electronic Engineering (EE) study and can be the first obstacle for novices because of the intricate relationships among its knowledge concepts. Also, significant differences may exist in individual understandings of concept structures (Dai, 2015).
    To address the aforementioned challenges in learning diagnostics and remedial teaching, this study was based on learning theories such as the conditions of learning, constructivism, and scaffolding theory and utilized Petri-Net to achieve the following goals:
    1. Use a Petri-Net to construct a KG visualizing a foundational electricity course.
    2. Conduct a pilot study to identify personal learning pathways, interrelationships among foundational electricity concepts, and misconceptions regarding novices’ learning types.
    3. Use students’ learning history to predict their learning effectiveness when studying future concepts and maximize their learning outcomes.
    4. Recommend an adaptive, calibrated, personalized learning pathway for further remedial teaching and learning.
    In this study, we employed a three-round modified Delphi technique with 18 SMEs to identify 12 subjects, 58 concepts, and 95 corresponding interrelationships within a core foundational electricity course in EE. We utilized a Petri-Net with graphic features to construct a KG we called a  Petri-Net KG.
    After the third round of the modified Delphi technique, all eight SMEs’ Content Validity Indexes (CVI) were 1.00. Cronbach’s α was .75. The SMEs’ opinions regarding the interrelationships of concepts exhibited good internal consistency and reliability, according to 95% confidence intervals. The correlations between concept weights were .83-.96 (p < .01). Intraclass Correlation Coefficients (ICCs) were used to confirm the consistency of SMEs’ opinions on the weights of the interrelationships between concepts. ICC (1) was .072, and ICC (2) was .75. All the SMEs’ opinions exhibited significant and strong correlations and good consistency.
    Using 947 students’ assessment records, learning portfolios, and learning status data (e.g. conditions of learning performance, scores), the reasoning engine was used to employ the KGs for learning transfer analysis. Preliminary exploration case studies were conducted to create Petri-Net KGs personalized for students with three different learning types (insufficiently hardworking, inadequate learning, and abnormal learning) and to determine their learning progress and status. Sato’s student-problem chart was used to classify students’ learning types.
    The major results and findings of this study are as follows:
    1. The most important concept was circuit patterns and characteristics, affecting the learning of the subsequent 12 concepts, and the total impact was 6. Units, vector operations, and voltage— in that order— were the next most important concepts.
    2. The proposed Petri-Net KG provided students with visualized learning scaffoldings that indicate the experts’ consensus cognitive structure. It also clarified any prior concepts requisite for understanding each concept.
    3. By utilizing the weights of the interrelationships between concepts and their prior concepts, the reasoning engine could adaptively diagnose misconceptions and further predict students’ effectiveness in learning subsequent concepts.
    4. Each learning type was associated with a unique cognitive structure. Integrating students’ learning portfolio data into the proposed Petri-Net KG enabled the reasoning engine to recommend an adaptive and personalized learning pathway.
    The aforementioned results have the following implications for future applications and research:
    1. The visualized Petri-Net KG for the foundational electricity course could clearly depict learning types, experts’ consensus knowledge structure, and students’ personal cognitive structures. Additionally, most influential concepts were observable at a glance. Such KGs could be useful for guiding concept recognition and effectively diagnosing misconceptions.
    2. The personalized learning pathways and content recommended by the Petri-Net KG and reasoning engine can be used in a self-tutoring platform. The weighted concept intercorrelations and student learning data can be analyzed to determine students’ cognitive conditions according to an expert KG. Thus, a model or student learning effectiveness can be established to strengthen the effectiveness of autonomous learning or remedial teaching.
    The framework of this course-level Petri-Net KG can be extended and applied to other curricula, disciplines, or educational levels to develop appropriate recommendation systems for competency development.

Keywords：knowledge graph, Petri-Net, foundational electricity, learning recommendation, learning diagnostic

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