What Everyone Finds

The Problem-Size Effect

Authored by: N. Jane Zbrodoff , Gordon D. Logan

Handbook of Mathematical Cognition

Print publication date:  December  2004
Online publication date:  August  2005

Print ISBN: 9781841694115
eBook ISBN: 9780203998045
Adobe ISBN: 9781135423667

10.4324/9780203998045.ch19

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Abstract

Research in every area of psychology is driven by landmark findings that inspire theoretical and empirical work. The landmark findings are often counterintuitive and puzzling but they are always robust, pervasive, and easy to replicate—they are the results that everyone finds. They become the benchmark findings that every new investigator must reproduce and every new theory must predict. In the psychology of arithmetic, the strongest candidate for the landmark finding is the problem-size effect: people take longer and make more errors to solve problems like 9 + 7 = 16 with large digits and large answers than to solve problems like 2 + 3 = 5 with small digits and small answers. It occurs with addition, subtraction, multiplication, and division. It occurs in production tasks, in which subjects are given digits and an operation and are asked to produce the answer (e.g., 4 × 5 =?), and in verification tasks, in which subjects are given digits, an operation, and an answer and are asked to say whether the answer is true or false (e.g., 4 × 5 = 24). It occurs with children, adults, and the elderly. It occurs in different cultures and different languages. It has driven research in mental arithmetic for more than 30 years.

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