Generation of Visual Representations for Multi-Modal Mathematical Knowledge
Lianlong Wu, Seewon Choi, Daniel Raggi, Aaron Stockdill, Grecia Garcia Garcia, Fiorenzo Colarusso, Peter C.H. Cheng, Mateja Jamnik
Abstract
In this paper we introduce MaRE, a tool designed to generate representations in multiple modalities for a given mathematical problem while ensuring the correctness and interpretability of the transformations between different representations. The theoretical foundation for this tool is Representational Systems Theory (RST), a mathematical framework for studying the structure and transformations of representations. In MaRE’s web front-end user interface, a set of probability equations in Bayesian Notation can be rigorously transformed into Area Diagrams, Contingency Tables, and Probability Trees with just one click, utilising a back-end engine based on RST. A table of cognitive costs, based on the cognitive Representational Interpretive Structure Theory (RIST), that a representation places on a particular profile of user is produced at the same time. MaRE is general and domain independent, applicable to other representations encoded in RST. It may enhance mathematical education and research, facilitating multi-modal knowledge representation and discovery.
BibTeX
@article{Wu_Choi_Raggi_Stockdill_Garcia Garcia_Colarusso_Cheng_Jamnik_2024, title={Generation of Visual Representations for Multi-Modal Mathematical Knowledge}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/30586}, DOI={10.1609/aaai.v38i21.30586}, abstractNote={In this paper we introduce MaRE, a tool designed to generate representations in multiple modalities for a given mathematical problem while ensuring the correctness and interpretability of the transformations between different representations. The theoretical foundation for this tool is Representational Systems Theory (RST), a mathematical framework for studying the structure and transformations of representations. In MaRE’s web front-end user interface, a set of probability equations in Bayesian Notation can be rigorously transformed into Area Diagrams, Contingency Tables, and Probability Trees with just one click, utilising a back-end engine based on RST. A table of cognitive costs, based on the cognitive Representational Interpretive Structure Theory (RIST), that a representation places on a particular profile of user is produced at the same time. MaRE is general and domain independent, applicable to other representations encoded in RST. It may enhance mathematical education and research, facilitating multi-modal knowledge representation and discovery.}, number={21}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Wu, Lianlong and Choi, Seewon and Raggi, Daniel and Stockdill, Aaron and Garcia Garcia, Grecia and Colarusso, Fiorenzo and Cheng, Peter C.H. and Jamnik, Mateja}, year={2024}, month={Mar.}, pages={23850-23852} }