Using analogical representations for mathematical concept formation

Alison Pease; Simon Colton; Ramin Ramezani; Alan Smaill; Markus Guhe

doi:10.1007/978-3-642-15223-8_17

Using analogical representations for mathematical concept formation

Alison Pease, Simon Colton, Ramin Ramezani, Alan Smaill, Markus Guhe

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

1 Citation (Scopus)

Abstract

We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of "visual" concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.

Original language	English
Title of host publication	Model-Based Reasoning in Science and Technology
Subtitle of host publication	Abduction, Logic, and Computational Discovery
Editors	Lorenzo Magnani, Walter Carnielli, Claudio Pizzi
Pages	301-314
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-642-15223-8_17
Publication status	Published - 14 Oct 2010
Externally published	Yes

Publication series

Name	Studies in Computational Intelligence
Volume	314
ISSN (Print)	1860-949X

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10.1007/978-3-642-15223-8_17

Cite this

Pease, A., Colton, S., Ramezani, R., Smaill, A., & Guhe, M. (2010). Using analogical representations for mathematical concept formation. In L. Magnani, W. Carnielli, & C. Pizzi (Eds.), Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery (pp. 301-314). (Studies in Computational Intelligence; Vol. 314). https://doi.org/10.1007/978-3-642-15223-8_17

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title = "Using analogical representations for mathematical concept formation",

abstract = "We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of {"}visual{"} concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.",

author = "Alison Pease and Simon Colton and Ramin Ramezani and Alan Smaill and Markus Guhe",

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Pease, A, Colton, S, Ramezani, R, Smaill, A & Guhe, M 2010, Using analogical representations for mathematical concept formation. in L Magnani, W Carnielli & C Pizzi (eds), Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery. Studies in Computational Intelligence, vol. 314, pp. 301-314. https://doi.org/10.1007/978-3-642-15223-8_17

Using analogical representations for mathematical concept formation. / Pease, Alison; Colton, Simon; Ramezani, Ramin et al.
Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery. ed. / Lorenzo Magnani; Walter Carnielli; Claudio Pizzi. 2010. p. 301-314 (Studies in Computational Intelligence; Vol. 314).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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Using analogical representations for mathematical concept formation

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