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Updated: Jun 11, 2025
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
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Mapping and modeling the semantic space of math concepts
Samuel Debray1, Stanislas Dehaene2
1Cognitive Neuroimaging Unit, Institut National de la Santé et de la Recherche Médicale, Commissariat à l'Energie Atomique et aux énergies alternatives, Centre National de la Recherche Scientifique, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France.
Cognition
|October 6, 2024
Summary
This study maps the space of mathematical concepts using semantic models and human judgments. Educational background influences understanding, revealing a structured map of mathematical knowledge.
Area of Science:
- Cognitive Science
- Computational Linguistics
- Mathematics Education
Background:
- Human cognition in mathematics is underexplored beyond basic concepts.
- Existing research rarely maps the broader landscape of mathematical ideas.
Purpose of the Study:
- To map the full space of mathematical concepts.
- To evaluate distributed semantic models (e.g., GloVe) against human judgments of mathematical semantics.
- To investigate the influence of education on these semantic judgments.
Main Methods:
- Analyzed French and English Wikipedia math content to extract 1000 frequent terms.
- Collected behavioral data on familiarity and semantic similarity judgments.
- Utilized vector embeddings based on co-occurrence statistics to model semantic structures.
Main Results:
- Vector embeddings explained approximately 50% of the variance in human similarity judgments.
- Participant education level significantly modulated familiarity and similarity ratings.
- A partial hierarchy of high-level math concepts was established based on educational influence.
Conclusions:
- A comprehensive map of mathematical concepts is proposed, detailing frequency, familiarity, acquisition grade, and inter-concept relationships.
- Distributed semantic models offer a partial but valuable representation of mathematical semantics.
- Education plays a crucial role in shaping the understanding and organization of mathematical knowledge.
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