Negative Instances and Mathematical Concept Formation: A Preliminary Study

1971 ◽  
Vol 2 (3) ◽  
pp. 218 ◽  
Author(s):  
Richard J. Shumway
Keyword(s):  
Concept Formation ◽  
Mathematical Concept ◽  
Preliminary Study

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.

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.

scholarly journals Character Education Through Realistic Mathematics Learning Based On Ethnomathematics

2021 ◽  
Vol 5 (2) ◽  
pp. 211
Author(s):  
Salafudin Salafudin ◽  
Muhamad Sugeng Sholahuddin ◽  
Heni Lilia Dewi ◽  
Alimatus Sholikhah
Keyword(s):  
Character Education ◽  
Mathematics Learning ◽  
Mathematical Concept ◽  
Thinking Skills ◽  
Design Development ◽  
School Students ◽  
Realistic Mathematics ◽  
Before And After ◽  
Preliminary Study ◽  
Character Building

Mathematics is a discipline that can improve thinking skills. However, in reality, the mathematics thinking skills of elementary school students are still low. This is because the mathematics learning used is not optimal and still uses conventional learning. In the process of mathematics learning, there is an integration of character values with mathematics material. Character building through mathematics learning has not been done relatively. The current mathematical concept can be related to cultural activities called ethnomathematics. Through ethnomathematics, mathematics learning becomes more realistic. The purpose of this research is to build students’ character and improve student’s mathematic learning achievement through developing student worksheets with a mathematical approach based on ethnomathematics. The methods of the research were research and development by using steps including preliminary study, design, development, and dissemination. The result of the research is student's worksheets fulfill valid, practical, and effective criteria. The result of the validity of teaching media shows that the average number is 96 % with very good criteria. The effectiveness test shows that there is a distinction of student’s achievement before and after the treatment and the student’s achievement on average is increased. Based on the analysis of student's answers on student worksheets, four characters are built through the learning process with a realistic mathematic approach based on ethnomathematics, such as creativity, independence, curiosity, and nationality. Keywords: character building, realistic mathematics learning, ethnomathematics.  

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