Primary Mathematics: Knowledge and Understanding 8th Revised edition [Pehme köide]

  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 246x171 mm, kaal: 460 g
  • Sari: Achieving QTS Series
  • Ilmumisaeg: 02-Mar-2018
  • Kirjastus: Learning Matters Ltd
  • ISBN-10: 1526440520
  • ISBN-13: 9781526440525
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  • Formaat: Paperback / softback, 264 pages, kõrgus x laius: 246x171 mm, kaal: 460 g
  • Sari: Achieving QTS Series
  • Ilmumisaeg: 02-Mar-2018
  • Kirjastus: Learning Matters Ltd
  • ISBN-10: 1526440520
  • ISBN-13: 9781526440525
This highly recommended and well established text helps trainee primary teachers develop and consolidate their knowledge of mathematics.


Secure subject knowledge and understanding is the foundation of confident, creative and effective teaching. To help your students master this, the 8th edition of this established text now comes with a range of online resources:

 

·         Interactive Maths subject knowledge audit: to assess your students' overall performance and ensure they have an accurate picture of their ability.

·         Reflective self-assessment questions: to help consolidate students’ understanding of each chapter topic and monitor their learning as they work through the book.

·         Glossary: building students' knowledge of tricky terminology

 

This 8th edition, covering the whole primary curriculum, also includes updated interactive activities throughout the book engage students in their learning and enable discussion. Using this book in conjunction with the free online resources really makes this the complete package for developing Mathematics subject knowledge.

About the authors xi
Foreword xiii
1 Introduction
1(14)
About this book
2(1)
A Mathematics Subject Knowledge Really Does Matter!
3(1)
The importance of talking mathematics
4(1)
The importance of reasoning for the development of your own mathematical knowledge
5(3)
What do we mean by `reasoning skills' and how do you develop them?
5(2)
The vocabulary of reasoning
7(1)
The Teachers' Standards
8(1)
Curriculum context
9(2)
The Early Years Foundation Stage
10(1)
Mathematics in the National Curriculum
11(1)
Assessment of primary mathematics
11(2)
The Primary Framework for Literacy and Mathematics
13(1)
Outcomes
13(2)
2 Number: place value, addition, subtraction, multiplication and division
15(26)
Introduction
18(1)
Place value
19(3)
The four rules of number
22(11)
Addition
22(1)
Subtraction
23(3)
Multiplication
26(4)
Division
30(3)
Precedence - BODMAS
33(1)
The laws of arithmetic
34(2)
The commutative law
34(1)
The associative law
35(1)
The distributive law
35(1)
Negative numbers
36(5)
3 Number: fractions, decimals and percentages
41(32)
Introduction
44(1)
Fractions
44(8)
Equivalent fractions
47(2)
Comparing fractions
49(1)
Addition of fractions
49(1)
Subtraction of fractions
50(1)
Multiplication of fractions
51(1)
Division of fractions
51(1)
Decimals
52(5)
Addition and subtraction of decimals
54(1)
Multiplication of decimals
54(1)
Division of decimals
55(1)
Converting fractions and decimals
56(1)
Using mental strategies to calculate with fractions and decimals
57(1)
Percentages
57(3)
Calculating percentages
58(2)
Equality
60(1)
Inequalities
61(2)
Recurring decimals
63(1)
Rational and irrational numbers
64(1)
Index form
65(1)
Standard form
66(1)
Ratio and proportion
67(6)
4 Mathematical language, reasoning and proof
73(34)
Introduction
76(1)
Levels of proof
77(2)
Deductive proof
79(3)
Pythagoras' proof
82(2)
The converse of a proof
84(2)
Disproof by counter-example
86(2)
Proof by exhaustion
88(3)
Reductio ad absurdum
91(1)
Proof by induction
92(2)
Mathematical proof versus scientific theories
94(2)
Language in mathematics
96(1)
Vocabulary
97(3)
Refining definitions
99(1)
Structure in mathematics and language
100(2)
The number system
102(5)
5 Algebra, equations, functions and graphs
107(28)
Introduction
109(2)
Algebraic expressions
111(2)
Simplifying algebraic expressions
111(2)
General statements
113(6)
Using algebra to describe sequences
114(2)
Sequences - extension (for those who are interested)
116(1)
Using algebra to prove general statements
117(2)
Linear and simultaneous linear equations
119(3)
Functions and mappings
122(4)
Inverse functions
125(1)
Graphs
126(9)
Gradient of a straight line
128(1)
The y-intercept
129(2)
Finding equations of graphs
131(4)
6 Measures
135(16)
Introduction
137(1)
The stages of development in understanding measures
137(2)
Direct comparison using matching, with no actual measuring
138(1)
Using non-standard units
138(1)
Using standard units
138(1)
Understanding units and measures
139(2)
Mass and weight
141(1)
Volume and capacity
142(3)
Surface area
145(1)
Time
146(5)
The 24 hour clock
147(1)
The abbreviations a.m. and p.m.
148(1)
Interval scales
149(2)
7 Geometry
151(34)
Introduction
153(1)
Polygons
154(8)
Naming polygons
155(1)
Regular or irregular polygons?
155(1)
Reflective symmetry
156(1)
Rotational symmetry
156(1)
Triangles
157(1)
Pythagoras' theorem
158(2)
Quadrilaterals
160(2)
Congruence, 2-D transformations and similarity
162(9)
Congruence
162(1)
2-D transformations
163(1)
Similarity
164(1)
The area of 2-D shapes
165(6)
3-D shapes
171(4)
The Platonic solids
172(1)
Pyramids
173(1)
Prisms
173(1)
Nets
174(1)
Surface area and volume
175(1)
Cartesian co-ordinates
175(3)
Co-ordinates in four quadrants
176(2)
Angles
178(7)
Bearings and compass points
182(3)
8 Statistics
185(28)
Introduction
188(1)
Types of data
189(1)
Discrete and continuous data
189(1)
Collecting, recording and representing data
189(5)
Tables
190(1)
Graphs and diagrams
191(3)
Interpreting data
194(1)
Data prediction
195(3)
Finding and using the mean and other central measures
195(3)
Finding and using measures of spread to compare distributions
198(4)
Box and whisker diagrams
198(2)
The probability scale
200(1)
How can we identify the probability of an event?
200(2)
What is the difference between theoretical and experimental probability?
202(1)
When do I add two probabilities?
203(1)
What about throwing two coins?
204(9)
Self-assessment questions 213(8)
Answers to self-assessment questions 221(12)
Glossary 233(8)
References 241(4)
Index 245
Claire Mooney is an Instructor at the School of Education and Professional Learning, Trent University, Canada. Alice Hansen is the Director of Children Count Ltd where she is educational consultant. Her work includes running professional development courses and events for teachers and teacher trainers, research and publishing. Alice has worked in education in England and abroad. Prior to her current work she was a primary mathematics tutor and the programme leader for a full-time primary PGCE programme at a large university in England. Lindsey Ferrie is a primary school teacher in Carlisle. Sue Fox has had extensive experience of teaching all ages from Reception to Year 6. She was Senior Mathematics Lecturer at St Martin's College, Carlisle. Reg Wrathmell is Senior Lecturer in Mathematics Education at King Alfred's College, Winchester. He has extensive experience as a mathematics consultant and as a provider of in-service courses.