Bridging the Gap Between Math Formalism and Natural Language
摘要
Knowledge representations have been successfully used for decades across various subject domains to support understanding and learning. We introduce a novel approach called Natural-Language Conceptual-Graph (NaGra). This approach facilitates the application of knowledge representations for learning support, even in more formal disciplines such as mathematics, where learning content often takes the form of formalisms. In a process of knowledge transposition, the NaGra approach first translates the formal mathematical content into a natural language text. This text is then analyzed using the computational linguistic tool T-MITOCAR, generating a corresponding knowledge map. Building on the theory of mental models and self-regulated learning (SRL), we illustrate how knowledge maps and NaGra texts, when paired with targeted prompts, can serve as instructional scaffolds. These tools are designed to enhance the mathematical understanding of first-year students, particularly those facing challenges during the transition from secondary to university-level mathematics, where the demand for abstraction significantly increases. Through three application examples, we illustrate how this method can be utilized to: (1) translate and visualize a mathematical formalism, (2) make the mathematical prior knowledge structure of a problem more accessible, and (3) make the structure of the relevant prior knowledge areas for a mathematical problem tangible. The conditions for the effective application of this method, as well as its limitations, are discussed.