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      Natural Number Bias in Arithmetic Operations With Missing Numbers – A Reaction Time Study


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          When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational numbers), and operation congruency (operations were either consistent – e.g., a product is larger than its operand – or inconsistent with natural number arithmetic). In a response-time paradigm, 77 adults viewed equations and determined whether a number could be found that would make the equation true. The results showed that the NNB affects evaluations in two main ways: a) the tendency to think that missing numbers are natural numbers; and b) the tendency to associate each operation with specific size of result, i.e., that multiplication makes bigger and division makes smaller. The effect was larger for items with small numbers, which is likely because these number combinations appear in the multiplication table, which is automatized through primary education. This suggests that students may count on the strategy of direct fact retrieval from memory when possible. Overall the findings suggest that the NNB led to decreased student performance on problems requiring rational number reasoning.

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          Cognitive arithmetic: a review of data and theory.

          The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.
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            Scientific knowledge suppresses but does not supplant earlier intuitions.

            When students learn scientific theories that conflict with their earlier, naïve theories, what happens to the earlier theories? Are they overwritten or merely suppressed? We investigated this question by devising and implementing a novel speeded-reasoning task. Adults with many years of science education verified two types of statements as quickly as possible: statements whose truth value was the same across both naïve and scientific theories of a particular phenomenon (e.g., "The moon revolves around the Earth") and statements involving the same conceptual relations but whose truth value differed across those theories (e.g., "The Earth revolves around the sun"). Participants verified the latter significantly more slowly and less accurately than the former across 10 domains of knowledge (astronomy, evolution, fractions, genetics, germs, matter, mechanics, physiology, thermodynamics, and waves), suggesting that naïve theories survive the acquisition of a mutually incompatible scientific theory, coexisting with that theory for many years to follow. Copyright © 2012 Elsevier B.V. All rights reserved.
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              Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias


                Author and article information

                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                15 June 2020
                : 6
                : 1
                : 22-49
                [a ]Early Education Department, University of Western Macedonia, Florina, Greece
                [b ] Massachusetts Institute of Technology , Cambridge, MA, USA
                [c ]Centre for Instructional Psychology and Technology, KU Leuven , Leuven, Belgium
                Author notes
                [* ]3rd km. Florina – Niki, 53100, Florina, Greece. kchristou@ 123456uowm.gr
                Author information
                Copyright @ 2020

                This is an open-access article distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                : 23 May 2019
                : 23 December 2019
                Empirical Research

                operation,misconception,multiplication makes bigger,rational numbers,natural number bias


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