Note on Suppes' "Mathematical concept formation."

1967 ◽  
Vol 22 (5) ◽  
pp. 400-401 ◽  
Author(s):  
Lawrence T. Frase
Keyword(s):  
Concept Formation ◽  
Mathematical Concept

scholarly journals Questionable Use of the Mathematical Concept of Equivalence by Psychologists

2014 ◽  
Vol 7 (2) ◽  
pp. 124-126
Author(s):  
Makoto Yamaguchi
Keyword(s):  
Empirical Research ◽  
Equivalence Relation ◽  
Concept Formation ◽  
Mathematical Concept

Psychologists have applied the mathematical concept of an equivalence relation to such topics as concept formation and foundations of language. This line of research is not without controversies, and most researchers have only intuitive understanding of this mathematical concept. In this article, accessible explanations are provided on fundamental issues that have implications for empirical research.

Negative Instances and Mathematical Concept Formation: A Preliminary Study

1971 ◽  
Vol 2 (3) ◽  
pp. 218-227
Author(s):  
Richard J. Shumway
Keyword(s):  
Mathematics Achievement ◽  
Concept Formation ◽  
Inductive Reasoning ◽  
Mathematical Concept ◽  
Syllogistic Reasoning ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Common Error ◽  
The Common ◽  
Preliminary Study

Are there measurable differences in general mathematics achievement, inductive reasoning, syllogistic reasoning, perceptual speed, and tendency to overgeneralize between groups learning mathematical concepts through the use of positive instances (C groups), and groups learning mathematical concepts through the use of both positive and negative instances (E groups)? 84 eighth grade mathematics students in 4 classes served as subjects for 65 days. Analysis of variance and covariance of pre- and posttest means yielded significant differences (p<.05) indicating that the E groups tended to overgeneralize less frequently than the C groups. No other differences in means were significant (p<.05). It appears that the use of negative instances may be a means for controlling the common error of overgeneralization.

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