*Robert Goldstone, David Landy, and Ji Y Son*

- Published in print:
- 2008
- Published Online:
- March 2012
- ISBN:
- 9780199217274
- eISBN:
- 9780191696060
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199217274.003.0016
- Subject:
- Psychology, Cognitive Psychology

This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific ...
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This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific principles governing complex systems across superficially dissimilar domains. The second line studies how people solve algebra problems. Consistent with an embodied perspective on cognition, both lines show strong influences of perception on cognitive acts that are often associated with amodal, symbolic thought, namely cross-domain transfer and mathematical manipulation.Less

This chapter describes two separate lines of research on college students' performance on scientific and mathematical reasoning tasks. The first research line studies how students transfer scientific principles governing complex systems across superficially dissimilar domains. The second line studies how people solve algebra problems. Consistent with an embodied perspective on cognition, both lines show strong influences of perception on cognitive acts that are often associated with amodal, symbolic thought, namely cross-domain transfer and mathematical manipulation.

*Nicholas Griffin*

- Published in print:
- 1991
- Published Online:
- March 2012
- ISBN:
- 9780198244530
- eISBN:
- 9780191680786
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198244530.003.0007
- Subject:
- Philosophy, History of Philosophy

This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's ...
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This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's work, ‘An Analysis of Mathematical Reasoning’.Less

This chapter discusses Russell's attempts to fashion a Kantian philosophy of pure mathematics where the concept of quantity played a central role. The chapter also introduces another of Russell's work, ‘An Analysis of Mathematical Reasoning’.

*Michael Siegal*

- Published in print:
- 2010
- Published Online:
- March 2012
- ISBN:
- 9780199582884
- eISBN:
- 9780191702358
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199582884.003.0006
- Subject:
- Psychology, Developmental Psychology

To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are ...
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To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are children's number abilities tied to understanding the meaning of the words that we use for counting? This chapter examines related issues: whether children's early theory of number is limited to the discrete whole numbers that are used for counting or whether they are prompted to accommodate their theory to take into account numerical relations which fill the gap between integers. It also examines children in aboriginal cultures, such as those found in Brazil and Australia, who acquire a language with few words for counting, taking into account their mathematical reasoning.Less

To characterize and act upon the world of objects, children in every culture count. Counting is as natural as walking and talking – an adaptive specialization for numerical problem solving. But are children's number abilities tied to understanding the meaning of the words that we use for counting? This chapter examines related issues: whether children's early theory of number is limited to the discrete whole numbers that are used for counting or whether they are prompted to accommodate their theory to take into account numerical relations which fill the gap between integers. It also examines children in aboriginal cultures, such as those found in Brazil and Australia, who acquire a language with few words for counting, taking into account their mathematical reasoning.