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El. knyga: Making Sense of Number: Improving Personal Numeracy

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(University of Technology, Sydney), (University of Queensland)
  • Formatas: PDF+DRM
  • Išleidimo metai: 15-Sep-2021
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781009008297
Kitos knygos pagal šią temą:
Making Sense of Number: Improving Personal NumeracyDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 15-Sep-2021
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781009008297
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Making Sense of Number is a concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent. It includes relevant content to assist pre-service teachers to improve numeracy for the classroom or to prepare for LANTITE and support for practising teachers to develop their numeracy skills.

Making Sense of Number is a concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent. It includes relevant content to assist pre-service teachers to improve numeracy for the classroom or to prepare for LANTITE, as well as support for practising teachers to develop their understanding and skills in numeracy. Making Sense of Number focuses on number sense as a conceptual framework for understanding mathematics, covering foundational areas of mathematics that often cause concern such as multiplication, fractions, ratio, rate and scale. The authors use real-world examples to explain mathematical concepts in an accessible and engaging way. Written by authors with over 30 years' experience teaching mathematics at primary, secondary and tertiary levels, Making Sense of Number is an essential guide for both pre-service teachers and those looking to improve their understanding of numeracy.

Daugiau informacijos

A concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent.
Preface ix
Chapter 1 Reflection on personal mathematics experiences and abilities
1(16)
Introduction
2(1)
What is my mathematical circumstance?
3(4)
Understanding the problem: a personal perspective
4(3)
Been there, done that
7(1)
Understanding the problem: a research perspective
7(2)
What is mathematics anxiety?
8(1)
What is the impact of mathematics anxiety?
8(1)
Why is it important that teachers address their mathematics knowledge and dispositions?
9(1)
Addressing mathematics difficulties
10(5)
Number sense
10(2)
Lifelong learning
12(1)
Growth mindset
13(2)
Conclusion
15(2)
Chapter 2 Mathematics and numeracy: the role of number sense
17(16)
Introduction
18(1)
Numeracy: a real-world reason for learning mathematics
18(7)
What is numeracy?
19(1)
Some everyday examples
20(2)
The central role of context in numeracy
22(1)
Why is numeracy so important?
23(2)
The key ideas of number sense
25(7)
Mental computation
26(1)
Estimation
26(1)
Judging magnitudes
27(1)
Place value
28(1)
Numerical relationships
29(1)
Representational fluency
29(1)
Problem solving
30(2)
Conclusion
32(1)
Chapter 3 The Hindu-Arabic number system
33(17)
Introduction
34(1)
A brief history of the Hindu-Arabic number system
34(2)
Feature number one: place value
36(8)
Placement of digits in place value columns
37(3)
Naming numbers
40(2)
Decimal place value
42(2)
Feature number two: Base 10
44(1)
Feature number three: zero
45(1)
Some things we should not have learned
45(3)
Multiplying and dividing by powers of 10
46(2)
Conclusion
48(2)
Chapter 4 Number facts
50(20)
Introduction
51(1)
Learning the number facts
51(8)
Addition facts
54(1)
Multiplication facts
54(3)
Approaches to learning number facts
57(1)
Why learn number facts?
58(1)
Properties to assist the learning of number facts
59(2)
Working with zero and one
59(1)
Commutativity
60(1)
Auditing number fact knowledge
61(3)
The addition grid
61(1)
The multiplication grid
62(2)
Arrays for learning number facts
64(1)
Putting it all together: the power of number facts
65(3)
Related systems
68(1)
Conclusion
69(1)
Chapter 5 Mental computation
70(17)
Introduction
71(1)
What is mental computation?
71(4)
Why the focus on mental computation?
73(2)
Using number facts to complete mental calculations
75(1)
Properties of numbers and operations
76(4)
Order of operations
76(1)
Distributivity
77(1)
Associativity
78(2)
Estimation and mental computation
80(2)
Choosing strategies to aid mental computation
82(2)
Is the answer to my mental computation reasonable?
84(2)
Conclusion
86(1)
Chapter 6 Additive and multiplicative thinking
87(21)
Introduction
88(1)
Additive and multiplicative thinking
88(3)
Additive thinking
88(2)
Multiplicative thinking
90(1)
Distinguishing between additive thinking and multiplicative thinking
91(5)
Absolute and relative thinking
96(6)
Relative thinking and co-variation
98(1)
Co-variation in nature
99(1)
Confusing relative thinking
100(2)
Making connections
102(4)
Connecting relative thinking to multiplicative thinking
102(2)
Connecting additive to absolute and multiplicative to relative thinking
104(2)
Conclusion
106(2)
Chapter 7 Fractional thinking
108(25)
Introduction
109(1)
Common fractions
109(13)
Common fractions are versatile
111(5)
Why are common fractions useful?
116(1)
Operations with common fractions
117(2)
Equivalent fractions
119(1)
Multiplying fractions
120(1)
Dividing fractions
121(1)
Some possible reasons for difficulty with common fractions
122(1)
Decimals
123(3)
Working with decimals
124(2)
Percentages
126(4)
Working across the three main fraction types
130(2)
Conclusion
132(1)
Chapter 8 Ratio, rate and scale
133(26)
Introduction
134(1)
Ratio
134(8)
Representing ratio
134(2)
Developing ratio understanding
136(2)
Real-world examples of ratio
138(4)
Rate
142(6)
Common rates in everyday life
142(4)
Long-term effects of rates
146(2)
Scale
148(10)
Relative size
149(1)
Reading scales
150(3)
Scale factor
153(1)
One-, two- and three-dimensional scale
154(3)
Not to scale
157(1)
Conclusion
158(1)
Chapter 9 Problem solving
159(20)
Introduction
160(1)
Problem solving and life
160(2)
Problem solving and growth mindset
161(1)
Contributing skills for problem solving
162(4)
The language of problem solving
162(2)
Multiple representations
164(1)
Thinking mathematically
165(1)
Polya's Step 1: Understand the problem
166(4)
Irrelevant facts (red herrings)
167(1)
Too much information
168(1)
Missing information
168(1)
Not understanding all the information
169(1)
Polya's Step 2: Devise a plan
170(7)
Using multiple representations
170(1)
Deciding what operation(s) to use
171(2)
Working backwards
173(1)
Multistep problems
174(2)
Unfamiliar contexts
176(1)
Polya's Step 3: Carry out the plan
177(1)
Thinking about possible outcomes
177(1)
Polya's Step 4: Look back at what you've done
177(1)
An authentic example of problem solving
178(1)
Conclusion 179(2)
Appendix: Answers to learning activities 181(15)
References 196(4)
Index 200
Annette Hilton is an Industry Fellow in the School of International Studies and Education at the University of Technology Sydney. Geoff Hilton is an Honorary Research Fellow at the University of Queensland School of Education.
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