The role of relational preference in early proportional reasoning

2022 ◽  
Vol 93 ◽  
pp. 102108
Author(s):  
E. Vanluydt ◽  
L. Verschaffel ◽  
W. Van Dooren
Keyword(s):  
Proportional Reasoning

Hypothesis Testing on a Proportional Reasoning Task by Children at Different Piagetian Stage Levels

1986 ◽  
Vol 9 (1) ◽  
pp. 91-104
Author(s):  
Gerald E. Gruen ◽  
Stuart I. Offenbach ◽  
Thomas Keane
Keyword(s):  
Sex Differences ◽  
Hypothesis Testing ◽  
Proportional Reasoning ◽  
Strong Relationship ◽  
Older Children ◽  
Reasoning Task ◽  
Cognitive Limitations ◽  
The Relationship ◽  
Age And Sex

The relationship between 7-, 9-, and 11-year-old children's performance on a battery of selected Piagetian measures and on a proportional reasoning task was examined. The proportional reasoning task, modeled after an hypothesis-testing probe procedure, was devised to identify the hypotheses and strategies children use when making proportional judgments. As expected, a strong relationship between stage level and (1) the complexity of hypotheses used, (2) the use of the proportional hypothesis, and (3) the overall use of logical hypotheses was found. Generally, only formal-operational children responded proportionally. Contrary to expectations, children were not responsive to feedback, i.e., they tended to generate and maintain the same hypothesis across trials regardless of feedback. The role of children's cognitive limitations, as well as how salient the feedback was, were discussed as possible explanations for this finding. Age and sex differences on the proportional reasoning task also were found. Possible directions for extension of this study to older children and adolescents were discussed.

International Perspectives: The Triple Jump: A Potential Area for Problem Solving and Investigation

1998 ◽  
Vol 4 (2) ◽  
pp. 104-108
Author(s):  
Doug Clarke
Keyword(s):  
Problem Solving ◽  
Proportional Reasoning ◽  
International Perspectives ◽  
Key Concepts ◽  
Potential Area

Many teachers comment that interesting appucations of ratio are hard to find. Teachers also find that many students have difficulty with proportional reasoning in general, and ratio in particular. In this article, I talk through a process that led to the discovery of the role of ratios and percentages in discussions about triple jump performances, and to a range of tasks that provide important information about students' understanding of key concepts in mathematics.

Discriminating Numbers Allows for Better Decisions

2020 ◽  
pp. 153-168
Author(s):  
Ellen Peters
Keyword(s):  
Decision Making ◽  
Proportional Reasoning ◽  
Number System ◽  
Approximate Number System ◽  
Intuitive Sense

This chapter, “Discriminating Numbers Allows for Better Decisions,” focuses on the role of our intuitive sense of numbers in decision making. Humans have evolved beyond these intuitions about quantities to know modern numeric abstractions. However, the evolutionarily old approximate number system (ANS) nonetheless remains pivotal to human decisions. Just as non-human animals use the proportional reasoning and estimation skills that come from the ANS, so do humans. The chapter introduces three systematic properties of the ANS that can explain differences in how people make decisions. These numeric intuitions, independent of objective ability, relate to having superior numeric memory and (usually) more accurate perceptions of value. Sometimes, however, the ANS’s reliance on proportional reasoning can produce what looks like worse decisions. The Appendix to this chapter describes ANS measures.

Proportional Reasoning

2016 ◽  
Vol 224 (4) ◽  
pp. 266-276 ◽  
Author(s):  
Ruth Stavy ◽  
Reuven Babai ◽  
Arava Y. Kallai
Keyword(s):  
Magnetic Resonance Imaging ◽  
Reaction Time ◽  
Magnetic Resonance ◽  
Functional Magnetic Resonance Imaging ◽  
Proportional Reasoning ◽  
Automatic Processing ◽  
Functional Magnetic Resonance ◽  
Resonance Imaging ◽  
Natural Numbers

Abstract. Comparison of ratios is difficult for children and adults. We studied the role of salience and congruity in comparison of ratios using reaction time and functional magnetic resonance imaging (fMRI). Participants were asked to decide which of two mixtures of red and white paint drops (presented in Arabic numerals) was darker. In congruent trials the mixture with more red drops was darker and in incongruent trials it was lighter. Half of the trials were red salience (more red than white drops in both mixtures) and half of them were white salience. Interaction between congruity and salience was observed. Behaviorally, accuracy was higher and reaction time of correct responses (RTC) was shorter in congruent red salience and incongruent white salience conditions. For these conditions higher activation in a fronto-parietal numerical network was observed in fMRI. These findings suggest that automatic processing of natural numbers supports or suppresses the comparison of ratios as a function of congruity and salience.

Aptitude and Experience Influences on Proportional Reasoning during Adolescence: Focus on Male-Female Differences

1983 ◽  
Vol 14 (1) ◽  
pp. 30-46
Author(s):  
Marcia C. Linn ◽  
Steven Pulos
Keyword(s):  
Sex Differences ◽  
Spatial Ability ◽  
Field Dependence ◽  
Proportional Reasoning ◽  
Formal Reasoning ◽  
Course Experience ◽  
Mathematics And Science

This study investigated the role of aptitudes and experience in sex-related differences in proportional reasoning. Subjects were 778 7th, 9th, and 11th graders. Fewer than half the subjects consistently displayed proportional reasoning, with females slightly less successful than males. Sex-related differences in proportional reasoning were not accounted for by various measures of spatial ability, field dependence-independence, or Piagetian formal reasoning. Course experience in mathematics and science did not explain the differences. A single-aptitude explanation for the observed sex differences in proportional reasoning seems unlikely, and many additional influences of experience remain to be investigated.

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