The Origins of Mathematical Knowledge in Childhood

Nonfiction, Reference & Language, Education & Teaching, Educational Theory, Educational Psychology, Teaching, Teaching Methods
Cover of the book The Origins of Mathematical Knowledge in Childhood by Catherine Sophian, Taylor and Francis
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Catherine Sophian ISBN: 9781351541749
Publisher: Taylor and Francis Publication: September 25, 2017
Imprint: Routledge Language: English
Author: Catherine Sophian
ISBN: 9781351541749
Publisher: Taylor and Francis
Publication: September 25, 2017
Imprint: Routledge
Language: English

This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another.

Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research:

  • on children's counting;
  • on their reasoning about continuous quantities such as length and area;
  • on the development of the concept of unit;
  • on additive and multiplicative reasoning; and
  • on knowledge about fractions.

In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible.

The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another.

Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research:

In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible.

The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.

More books from Taylor and Francis

Cover of the book The Ideal of Total Environmental Control by Catherine Sophian
Cover of the book Fifty Key Thinkers on Development by Catherine Sophian
Cover of the book Kristeva and the Political by Catherine Sophian
Cover of the book National Security and the D-Notice System by Catherine Sophian
Cover of the book Etruscan Roman Remains by Catherine Sophian
Cover of the book The European Union and International Development by Catherine Sophian
Cover of the book Homoerotic Sensibilities in Late Imperial China by Catherine Sophian
Cover of the book Modern Military Strategy by Catherine Sophian
Cover of the book Indian Agriculture after the Green Revolution by Catherine Sophian
Cover of the book Readers and Reading by Catherine Sophian
Cover of the book A Dangerous Legacy by Catherine Sophian
Cover of the book Julius Caesar by Catherine Sophian
Cover of the book The Nature of Chinese Politics: From Mao to Jiang by Catherine Sophian
Cover of the book The English Church, 940-1154 by Catherine Sophian
Cover of the book Cyberspace Crime by Catherine Sophian
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy