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Developing Number Knowledge: Assessment,Teaching and Intervention with 7-11 year olds [Kõva köide]

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  • Formaat: Hardback, 312 pages, kõrgus x laius: 232x186 mm, kaal: 730 g
  • Sari: Math Recovery
  • Ilmumisaeg: 04-Nov-2011
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 0857020609
  • ISBN-13: 9780857020604
Teised raamatud teemal:
Developing Number Knowledge: Assessment,Teaching and Intervention with 7-11 year oldsSuurem pilt
  • Formaat: Hardback, 312 pages, kõrgus x laius: 232x186 mm, kaal: 730 g
  • Sari: Math Recovery
  • Ilmumisaeg: 04-Nov-2011
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 0857020609
  • ISBN-13: 9780857020604
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780857020604.html
Märksõnad:
Following the great success of the earlier books, this fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds.  



Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasising computational fluency and the progressive development of students mathematical sophistication. The book is organized in key domains of number instruction, including structuring numbers 1 to 20, knowledge of number words and numerals, conceptual place value, mental computation, written computation methods, fractions, and early algebraic reasoning.



 



Features include:







fine-grained progressions of instruction within each domain; detailed descriptions of students strategies and difficulties; assessment tasks with notes on students responses; classroom-ready instructional activities;



 



This book is designed for classroom and intervention teachers, special education teachers and classroom assistants. The book is an invaluable resource for mathematics advisors and coaches, learning support staff, numeracy consultants, curriculum developers, teacher educators and researchers.

Arvustused

This is the must-have resource our teachers have been waiting for! Developing Number Knowledge transforms an extensive body of research and field testing into a practical guide of assessments and instructional activities designed especially for older elementary students. As an instructional support teacher, I will use this guide when helping teachers plan developmentally appropriate lessons for their struggling students - Jackie Amato, District Math Recovery Leader





Essential reading for every teacher of mathematics in primary or early secondary education, Developing Number Knowledge is a professional development tool with detailed assessment and instructional content for the classroom. It is for teachers working one-to-one, with small groups or whole classes who want their children to make sense of mathematics and become confident, successful mathematicians. With its foundations in research and extensive classroom practice, it will challenge the way you teach! Maths Recovery teachers will welcome this addition to their tool kit - Julia Sheridan



Chair Maths Recovery Council UK and Ireland, Maths Recovery Consultant

List of Boxes
xv
List of Tables
xvi
List of Figures
xvii
List of Photographs
xx
Contents of Resource CD xxiix
Acknowledgements xxiv
About the Authors and Contributor xxv
Series Preface xxvii
Introduction 1(4)
The Purpose of the Book
1(1)
The Background to the Book
1(1)
The Structure of the Book
2(1)
Notes to the Reader
3(2)
PART I
5(20)
1 Professional Learning for Quality Instruction
5(5)
Using the Book for Professional Learning and Development
6(2)
Using the Book for Intervention Instruction
8(1)
Using the Book for Classroom Instruction
8(1)
Using the Book to Promote Parental Involvement
9(1)
2 Instruction in Arithmetic
10(15)
Organizing Instruction in Arithmetic
10(4)
Progressive Mathematization of Arithmetic
14(5)
An Inquiry-based Approach to Instruction
19(6)
PART II
25(174)
3 Number Words and Numerals
25(25)
Domain Overview
25(9)
Significance of Knowledge of Number Words and Numerals
25(1)
Learning Number Word Sequences
26(3)
Learning to Read and Write Numerals
29(1)
Assessment of Number Words and Numerals
30(1)
Instruction in Number Word Sequences
31(2)
Instruction in Numerals
33(1)
Assessment Task Groups
34(4)
A3.1 Numeral Identification
35(1)
A3.2 Writing Numerals
35(1)
A3.3 Number Word Sequences by ls
36(1)
A3.4 Number Word Before, Number Word After
36(1)
A3.5 Number Word Sequences by 10s on the Decuple
37(1)
A3.6 Number Word Sequences by 100s on the Centuple
37(1)
A3.7 Number Word Sequences by 10s off the Decuple
38(1)
Instructional Activities
38(12)
IA3.1 Arrow Cards Draw for Numeral Identification
38(1)
IA3.2 I Read, You Write, We Check, We Build
39(1)
IA3.3 Place Value Houses
40(1)
IA3.4 Choral Chanting
40(1)
IA3.5 What Comes After Nine?
41(1)
IA3.6 Disappearing Sequences
41(1)
IA3.7 Bare Numeral Roll
42(1)
IA3.8 Numeral Roll with Window or Multi-Iid Screen
43(1)
IA3.9 Numeral Grid Sequences
44(1)
IA3.10 Numeral Ladder
45(1)
IA3.11 The Four Kings Game
46(1)
IA3.12 Lovely Lucy
47(3)
4 Structuring Numbers 1 to 20
50(27)
Domain Overview
50(12)
Facility with Addition and Subtraction in the Range 1 to 20
50(2)
Significance of Structuring Numbers 1 to 20
52(1)
Assessment of Structuring Numbers 1 to 20
53(1)
Outline of Instruction in Structuring Numbers 1 to 20
53(1)
Instruction in Structuring Numbers 1 to 10 Using Ten-frames
54(2)
Instruction in Structuring Numbers 1 to 20 Using the Arithmetic Rack
56(6)
Assessment Task Groups
62(5)
A4.1 Combinations up to 10, with Ten-frames
62(1)
A4.2 Doubles
63(1)
A4.3 Combinations with 10
63(1)
A4.4 Partitions of 10
63(1)
A4.5 Partitions of Numbers in the Range 1 to 20
64(1)
A4.6 Addition and Subtraction with a Rack (addends ≥ 10)
64(1)
A4.7 Addition and Subtraction with a Rack (one addend > 10)
65(1)
A4.8 Bare Number Addition and Subtraction (range ≥ 10)
66(1)
A4.9 Bare Number Addition and Subtraction (addends ≥ 10)
66(1)
A4.10 Bare Number Addition and Subtraction (one addend > 10)
66(1)
Instructional Activities
67(10)
IA4.1 Keeping Score with Tally Marks
67(1)
IA4.2 Ten-frame Flashes
68(1)
IA4.3 Go Fish with Mini Ten-frames
69(1)
IA4.4 I Wish I Had on the Bead Rack
70(1)
IA4.5 The Double-decker Bus with the Bead Rack
71(1)
IA4.6 9 Plus Game
72(1)
IA4.7 20 Minus Game
72(1)
IA4.8 Making Six
73(1)
IA4.9 Crackers the Parrot
74(1)
IA4.10 Expression Card Families
74(1)
IA4.11 Bulls-eye Dice
75(2)
5 Conceptual Place Value
77(22)
Domain Overview
77(6)
Learning Conceptual Place Value
77(1)
Assessment of Conceptual Place Value
78(1)
Instruction in Conceptual Place Value
78(4)
Distinguishing Conceptual Place Value from Conventional Place Value
82(1)
Assessment Task Groups
83(6)
A5.1 Preliminary Unscreened Bundling Sticks Tasks
84(1)
A5.2 Incrementing and Decrementing by Tens on the Decuple
84(1)
A5.3 Incrementing and Decrementing by Tens off the Decuple
85(1)
A5.4 Incrementing Flexibly by Tens and Ones
86(1)
A5.5 Incrementing by Hundreds on the Centuple
87(1)
A5.6 Incrementing and Decrementing by Tens across 1000
87(1)
A5.7 Ten More and Ten Less
88(1)
A5.8 One Hundred More and One Hundred Less
88(1)
Instructional Activities
89(10)
IA5.1 Incrementing and Decrementing by Tens with Screened Bundling Sticks
89(2)
IA5.2 CPV Egg Contextual Investigation
91(1)
IA5.3 Read It, Build It, Check It with Arrow Cards and Base-ten Materials
92(1)
IA5.4 Arrow Cards Draw Game with Base-ten Materials
93(1)
IA5.5 Hopping and Leaping on the Empty Number Line
94(1)
IA5.6 Crazy Grid
95(1)
IA5.7 Withdrawing Money from the Automated Teller Machine
96(3)
6 Addition and Subtraction to 100
99(36)
Domain Overview
99(21)
Facility with Mental Addition and Subtraction to 100
99(8)
Foundational Knowledge for Mental Addition and Subtraction to 100
107(2)
Assessment of Addition and Subtraction to 100
109(1)
Outline of Instruction in Addition and Subtraction to 100
110(1)
Instruction Phase 1 Developing Foundational Knowledge
111(3)
Instruction Phase 2 Consolidating Early Strategies
114(2)
Instruction Phase 3 Refining Strategies and Extending Tasks
116(4)
Assessment Task Groups
120(4)
Task Group A6.1 Decuple After and Decuple Before a Number
120(1)
Task Group A6.2 Jump Forward from and Jump Back to a Decuple
121(1)
Task Group A6.3 Jump Forward to and Jump Back from a Decuple
121(1)
Task Group A6.4 Jump Across a Decuple
121(1)
Task Group A6.5 Addition and Subtraction of a Decuple
122(1)
Task Group A6.6 2-digit Addition and Subtraction without Regrouping
122(1)
Task Group A6.7 2-digit Addition and Subtraction with Regrouping
123(1)
Task Group A6.8 3-digit Addition and Subtraction
124(1)
Instructional Activities
124(11)
IA6.1 70 Plus Game
124(1)
IA6.2 Jumping Back to the Decuple with Mini Ten-frames
125(1)
IA6.3 Decuple Tag
126(1)
IA6.4 Adding to 50 Game
126(2)
IA6.5 Jumping Back from a Decuple with Mini Ten-frames
128(1)
IA6.6 48 Plus Game
128(1)
IA6.7 32 Minus Game
129(1)
IA6.8 Higher Decade Addition and Subtraction Patterns
130(1)
IA6.9 Screened Tasks with Two Collections of Mini Ten-frames
131(1)
IA6.10 Interstate Driving Context Notated on the Empty Number Line
131(2)
IA6.11 Add or Subtract 12
133(1)
IA6.12 How Many More to Make 100?
134(1)
IA6.13 How Many More to Make 60?
134(1)
7 Multiplication and Division
135(38)
Domain Overview
135(20)
Multiplication and Division in Formal Arithmetic
135(6)
Learning Multiplication and Division
141(6)
Assessment of Multiplication and Division
147(2)
Instruction in Multiplication and Division
149(6)
Assessment Task Groups
155(7)
A7.1 Multiplication with Repeated Equal Groups
156(1)
A7.2 Grouping Division with Repeated Equal Groups
157(1)
A7.3 Sharing Division with Repeated Equal Groups
157(1)
A7.4 Multiplication with an Array
157(1)
A7.5 Grouping Division with an Array
158(1)
A7.6 Sharing Division with an Array
159(1)
A7.7 Multiplication Basic Facts
159(1)
A7.8 Multiplication with Bare Numbers -- 2-digit x 1-digit
160(1)
A7.9 Division with Bare Numbers -- 2-digit Quotients
160(1)
A7.10 Inverse Relationship of Multiplication and Division
161(1)
A7.11 Commutative Principle
161(1)
A7.12 Distributive Principle
161(1)
Instructional Activities
162(11)
IA7.1 Counting Items in Equal Groups
162(1)
IA7.2 Snack Time
163(1)
IA7.3 Counting Dot Tiles
164(1)
IA7.4 Arrays on the 100-bead Rack
165(2)
IA7.5 Array Bingo
167(1)
IA7.6 Using the Empty Number Line to Model Multiplicative Situations
168(1)
IA7.7 The Multiples Games
169(2)
IA7.8 The Factoring Game
171(2)
8 Written Computation
173(26)
Domain Overview
173(14)
Written Computation Methods: Jotting, Semi-formal Strategies and Formal Algorithms
173(3)
Comparing Semi-formal Strategies and Formal Algorithms
176(2)
Significance of Written Computation Methods in the Curriculum
178(1)
Learning Written Computation
178(2)
Assessment of Written Computation
180(1)
Outline of Instruction in Written Computation
181(1)
Instruction in Jotting
182(1)
Instruction in Semi-formal Written Strategies
183(3)
Instruction in Formal Algorithms
186(1)
Assessment Task Groups
187(4)
A8.1 Multi-digit Tasks in a Context: The School Excursion
187(2)
A8.2 Open-ended Horizontal Bare Number Tasks
189(1)
A8.3 Using a Semi-formal Strategy
190(1)
A8.4 Algorithm Error Analysis
190(1)
Instructional Activities
191(8)
IA8.1 Group Monster
191(1)
IA8.2 Sum of the Century
192(1)
IA8.3 Decomposition with Arrow Cards
193(1)
IA8.4 Palindromization
193(2)
IA8.5 Catch 22
195(1)
IA8.6 Shortcut 100
196(1)
IA8.7 The Prodigal Sum
197(2)
PART III
199(48)
9 Early Algebraic Reasoning
199(13)
Basis for Instruction in Early Algebraic Reasoning
199(2)
Examples of Instruction Linking to Early Algebraic Reasoning
201(3)
Patterns and Functions
204(3)
Building Generalizations from Arithmetic
207(5)
10 Understanding Fractions Peter Gould
212(13)
Chapter Overview
212(1)
A Pathway to Understanding Fractions as Numbers
213(2)
Key Ideas in Understanding Fractions
215(8)
Making Sense of Fraction Research
223(1)
Looking Back
223(2)
11 Connecting the Teaching and Learning of Fractions Peter Could
225(22)
Learning Fractions
225(4)
Introductory Assessment Tasks
229(2)
A Teaching Sequence
231(3)
Looking Back
234(1)
Instructional Activities
234(13)
IA11.1 Finding Half Way
234(1)
IA11.2 Line Up
235(1)
IA11.3 Finding One-quarter of the Way
235(1)
IA11.4 What Fraction of the Length is That?
236(1)
IA11.5 One-half, One-quarter and One-eighth
237(1)
IA11.6 Three-eighths of the Way Across the Board
238(1)
IA11.7 One-third of a Circle
238(2)
IA11.8 Recording Partitioning
240(1)
IA11.9 Building Towers
241(3)
IA11.10 Oops!
244(1)
IA11.11 How Many Are At Your Table?
244(1)
IA11. 12 Keeping Records at the Pancake Place
245(1)
IA11.13 Time for a Break
245(2)
Glossary 247(8)
Appendix: Instructional Settings 255(3)
References 258(11)
Index 269
Dr Robert J. (Bob) Wright holds Bachelors and Masters degrees in mathematics from the University of Queensland (Australia) and a doctoral degree in mathematics education from the University of Georgia. He is an adjunct professor in mathematics education at Southern Cross University in New South Wales. Bob is an inter­nationally recognized leader in assessment and instruction relating to childrens early arithmetical knowledge and strategies, publishing six books, and many articles and papers in this field. His work over the last 25 years has included the development of the Mathematics Recovery Program, which focuses on providing specialist training for teachers to advance the numeracy levels of young children assessed as low-attainers. In Australia and New Zealand, Ireland, the UK, the USA, Canada, Mexico, South Africa and elsewhere, this programme has been implemented widely, and applied extensively to classroom teaching and to average and able learners as well as low-attainers. Bob has conducted several research projects funded by the Australian Research Council including the most recent project focusing on assessment and intervention in the early arithmetical learning of low-attaining 8- to 10-year-olds.

 

 Dr. Pamela D. Tabor holds a Bachelor of Science degree in elementary education and Bible from Kentucky Christian University, a Master of Arts degree in elementary education from East Tennessee State University, and a Doctor of Philosophy in mathematics education from Southern Cross University. Her supervisor was Robert J. Wright, the developer of Mathematics Recovery. She has recently worked as Research and Evaluation Specialist for the US Math Recovery Council in which she has had the pleasure of working with instructional leaders from districts around the US and internationally to think deeply about the impact of Math Recovery in their school contexts. Previously, she spent nearly two decades as a school-based math specialist, interventionist and instructional coach. In that capacity she worked with administrators, teachers of mathematics, teachers of special education, students, and parents to improve the quality of mathematics instruction in a public elementary school in Maryland. She is also a coauthor of the Math Recovery series book Developing Number Knowledge, a contributor of Teaching Number in the Classroom with 48 year Olds, one of the original developers of USMRCs Add+VantageMR Professional Development Courses, and one of the developers of USMRCs Student Numeracy Assessment Progressions (SNAP).