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E-raamat: Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics [Taylor & Francis e-raamat]

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  • Formaat: 172 pages, 1 Tables, black and white; 38 Line drawings, black and white; 38 Illustrations, black and white
  • Ilmumisaeg: 06-Aug-2021
  • Kirjastus: Routledge
  • ISBN-13: 9780429265815
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  • Taylor & Francis e-raamat
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Using Mathematics to Understand the World: How Culture Promotes Children's MathematicsSuurem pilt
  • Formaat: 172 pages, 1 Tables, black and white; 38 Line drawings, black and white; 38 Illustrations, black and white
  • Ilmumisaeg: 06-Aug-2021
  • Kirjastus: Routledge
  • ISBN-13: 9780429265815
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429265815

Using Mathematics to Understand the World offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world.



Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world.

Internationally renowned experts Terezinha Nunes and Peter Bryant examine research into children’s mathematical development to show why it is important to distinguish between quantities, relations and numbers. Using Mathematics to Understand the World presents a theory about the development of children’s quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children’s mathematical attainment in school. It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world.

This essential text is for all students of mathematics education, developmental psychology and cognitive psychology. By including activities for parents and professionals to try themselves, it may help you to recognize your own quantitative reasoning.

List of figures
viii
List of boxes
x
Foreword xi
Ubiratan D'Ambrosio
1 Mathematical models and thinking
1(19)
Tools of the mind: language and number systems
8(5)
The two meanings of numbers: referential and analytical
13(3)
Where will this voyage take you?
16(2)
References
18(2)
2 Counting, adding and natural numbers
20(29)
The invisible knowledge of cardinal number: counting principles and counting systems
20(2)
Addition as the link between the referential and the analytical meaning of cardinal number
22(3)
Learning the meaning of words, including number words
25(3)
Number systems as mathematical models
28(4)
How children learn the referential meaning of number words
32(3)
How children learn the analytical meaning of number words
35(10)
So what do young children know about numbers?
45(1)
References
46(3)
3 Sharing, dividing and rational numbers
49(35)
The invisible knowledge of rational number: equivalence, order and density of numbers based on division
50(2)
Rational numbers: a model for two sorts of quantity
52(4)
Thinking about extensive quantities smaller than the unit
56(5)
Thinking about intensive quantities
61(6)
Rational numbers, intensive quantities and cultural frameworks
67(1)
Why rational numbers are invisible in everyday life
68(2)
Three reasons why intensive quantities are often invisible
70(6)
School mathematics and the need-to-know
76(2)
References
78(6)
4 Word problems, implicit agreements, quantitative reasoning and arithmetic Knowledge of implicit social rules
84(35)
The age of the captain
85(3)
Suspension of sense making
88(2)
The didactical contract
90(2)
Infer the information from the text
92(1)
Identify the arithmetic operation
93(5)
Show your work
98(1)
Quantitative reasoning, arithmetic and a revised didactical contract
99(2)
The first clause: the aim of using word problems is to promote quantitative reasoning
101(1)
The second clause: problem types are defined by the type of relation between quantities
102(1)
Part-whole problems and additive reasoning
102(4)
Ratio problems and multiplicative reasoning
106(4)
The third clause: explain your reasoning
110(1)
Final comments
110(1)
References
111(8)
5 Promoting quantitative reasoning in elementary school Thinking in action
119(31)
From thinking in action to mathematical models of situations
122(1)
From action to language and paper and pencil
123(4)
Part-whole diagrams
127(4)
Ratio diagrams
131(7)
Understanding the inverse relation between operations
138(2)
Final remarks
140(2)
References
142(8)
6 When what we know is not what we see Mathematical models allow us to know more about the world than we can learn from our sensory experiences
150(13)
Mathematical models create realities
150(1)
Mathematical models require a distinction between the referential and the analytical meaning of numbers
151(1)
Understanding mathematical models depends on two mathematical skills: quantitative reasoning and arithmetic
151(1)
During elementary school, children must learn about two classes of relations between quantities: part-whole and fixed ratio relations
152(1)
Promoting quantitative reasoning involves helping children to representing their own thinking explicitly to themselves
153(1)
Quantitative reasoning requires an explicit understanding of the inverse relation between operations
154(1)
Mathematical models can rely on different types of quantity, different types of measurement and different types of number
154(2)
Final remarks
156(1)
References
157(6)
Name Index 163(6)
Subject Index 169
Terezinha Nunes is a Brazilian Psychologist with a doctorate from City University of New York and a Doctor Honoris Causa from Szeged University. She is Emeritus Professor of Education, Oxford University. She received the 2017 Freudenthal Award for innovative and influential research in mathematics education from the International Committee on Mathematics Instruction.

Peter Bryants research has been on childrens cognitive development and its impact on how they learn to read and write and to do mathematics. He is a FRS and he was the Watts Professor of Psychology at Oxford University for several years.
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