This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data. A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems. Existing methods either focus on single-modal or multimodal problems, and they cannot fit each other. A general geometry problem solver should obviously be able to process various modal problems at the same time. In this paper, a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image, which can solve the heterogeneity issue between multimodal geometry problems. A contrastive learning model of multimodal data enhances the semantic relevance between multimodal features and maps them into a unified semantic space, which can effectively adapt to both single-modal and multimodal downstream tasks. Based on the feature extraction and fusion of multimodal data, a proposed geometry problem solver uses relation extraction, theorem reasoning, and problem solving to present solutions in a readable way. Experimental results show the effectiveness of the method.

The COVID-19 emergency necessitated a rapid transition to online teaching by university lecturers. Hence, lecturers need to develop and reorganize their instructions and adjust their teaching roles and activities to the technological demands so as to further facilitate their continuous usage of technological systems after the crisis. Based on the behaviors of lecturers who utilized a particular teaching system—Rain Classroom—during school closure, this study aimed to predict their retention of online teaching beyond lockdown. Classical machine-learning classifiers were adopted to make predictions, most of which had an accuracy greater than 73%. Moreover, through a byproduct of these algorithms—feature scoring—we also aimed to determine the prime activities and roles that have strong relationships with lecturers’ retention dispositions. The domain meaning of feature scoring was revealed based on a specific conceptualization of perceived usefulness and the TAM model, which further enlightened system devisers about strategies to improve technological quality. A coevolution mechanism was thus formed, both providing guidance for lecturers in changing their overt behaviors with respect to online teaching and supporting the customization of system functionalities, so as to foster the mutual adaption of teachers’ pedagogies and artifact affordances. The findings, concerning useful teaching roles (namely, learning assessment, guiding technology usage, and learning support) and activities (such as in-class exercises, monitoring of students’ attendance, formal testing, etc.), are corroborated by evidence from other reports in the literature.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved using machines; however, machines encounter challenges in natural language processing and computer vision. Significant progress has improved existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to poor theorem prediction and poor accuracy in problem solving. In this paper, a formal language graph is constructed using the extracted formal language set and applied to theorem prediction using a graph convolutional network. To better extract the relationship set of diagram elements, an improved diagram parser is proposed. The test results indicate that the improved method has good results when solving interpretable geometry problems.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.