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Modeling discrete and continuous entities with fractions and decimals
Monica Rapp1, Miriam Bassok1, Melissa DeWolf2
1Department of Psychology.
Journal of Experimental Psychology. Applied
|November 18, 2014
Summary
People align discrete items like marbles with fractions and continuous concepts like distance with decimals. This semantic alignment influences how rational numbers are understood and taught.
Area of Science:
- Cognitive Science
- Mathematics Education
Background:
- Semantic alignment influences mathematical modeling by linking real-world relations to mathematical operations.
- The role of semantic alignment in rational number comprehension (fractions and decimals) is underexplored.
Purpose of the Study:
- To investigate if semantic alignment affects the comprehension and use of rational numbers.
- To explore the connection between the discrete/continuous nature of entities and the choice of rational number representation (fractions vs. decimals).
Main Methods:
- Analysis of mathematics textbook content.
- Two experiments involving mathematics educators and college students.
Main Results:
- Both educators and students align discrete entities (e.g., marbles) with fractions and continuous entities (e.g., distance) with decimals.
- Fractions are associated with non-metric units, while decimals are linked to metric units.
Conclusions:
- The ontological distinction between discrete and continuous entities significantly impacts mathematical cognition and the use of rational number notations.
- Findings suggest implications for improving the teaching of rational numbers by considering semantic alignment and symbolic representation.
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