Solving Algebraic Problems with Geometry Diagrams (APGDs) poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects. Problems typically involve both textual descriptions and geometry diagrams, requiring a joint understanding of these modalities. Although considerable progress has been made in solving math word problems, research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs, which limits their ability to effectively solve problems. In this study, a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information. The three-phase scheme begins with the application of the state-transformer paradigm, modeling the problem-solving process and effectively representing the intermediate states and transformations during the process. Next, a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams. Finally, a specific algorithm is designed focusing on diagram understanding, which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram. A method for generating derived relations, which are essential for solving APGDs, is also introduced. Experiments on real-world datasets, including geometry calculation problems and shaded area problems, demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

In traditional education, there is not much difference between assessment tasks designed for learners. However, learners’ learning performance may vary due to a number of factors, e.g., learning ability, academic emotion, and learners’ and teachers’ academic expectations. Considering those factors, accurately recommending personalized assessment tasks for each learner is challenging. To overcome the limitations in the current work, this paper proposed an autonomous-agent-based approach to recommend personalized assessment tasks considering multiple factors. Contributions of the proposed approach contain three aspects: (1) Considering objective factors, the proposed approach dynamically adjusts the assessment tasks recommended for students. (2) Considering subjective factors, the proposed approach can dynamically predict learners’ learning performances by applying autonomous agent-based negotiation. (3) The proposed recommendation algorithm can handle the problems of cold start in the research of typical recommendation algorithms. A set of experiments evaluates the effectiveness of the proposed approach in this paper, and the experimental results show that the proposed approach can accurately and adaptively generate personalized assessment tasks considering objective and subjective factors.

In the era of artificial intelligence, cognitive computing, based on cognitive science; and supported by machine learning and big data, brings personalization into every corner of our social life. Recommendation systems are essential applications of cognitive computing in educational scenarios. They help learners personalize their learning better by computing student and exercise characteristics using data generated from relevant learning progress. The paper introduces a Learning and Forgetting Convolutional Knowledge Tracking Exercise Recommendation model (LFCKT-ER). First, the model computes studentsʼ ability to understand each knowledge concept, and the learning progress of each knowledge concept, and the model consider their forgetting behavior during learning progress. Then, studentsʼ learning stage preferences are combined with filtering the exercises that meet their learning progress and preferences. Then studentsʼ ability is used to evaluate whether their expectations of the difficulty of the exercises are reasonable. Then, the model filters the exercises that best match studentsʼ expectations again by studentsʼ expectations. Finally, we use a simulated annealing optimization algorithm to assemble a set of exercises with the highest diversity. From the experimental results, the LFCKT-ER model can better meet studentsʼ personalized learning needs and is more accurate than other exercise recommendation systems under various metrics on real online education public datasets.