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Teaching Number: Advancing Childrens Skills and Strategies 2nd Revised edition [Kietas viršelis]

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  • Formatas: Hardback, 264 pages, aukštis x plotis: 242x170 mm, weight: 630 g
  • Serija: Math Recovery
  • Išleidimo metai: 30-Aug-2006
  • Leidėjas: SAGE Publications Inc
  • ISBN-10: 1412921848
  • ISBN-13: 9781412921848
Kitos knygos pagal šią temą:
Teaching Number: Advancing Childrens Skills and Strategies 2nd Revised editionDidesnis paveikslėlis
  • Formatas: Hardback, 264 pages, aukštis x plotis: 242x170 mm, weight: 630 g
  • Serija: Math Recovery
  • Išleidimo metai: 30-Aug-2006
  • Leidėjas: SAGE Publications Inc
  • ISBN-10: 1412921848
  • ISBN-13: 9781412921848
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781412921848.html
Raktažodžiai:
The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance childrens learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing childrens number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes:







a clearly defined purpose detailed instructions, activities, learning tasks and reinforcing games lists of responses which children may make application in whole class, small group and individualised settings a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice



Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each countrys numeracy strategy.



Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.
List of Figures
xiii
List of Photographs
xiv
List of Tables
xv
Contributors xvi
Acknowledgments xvii
Series Preface xviii
Preface xx
Introduction 1(5)
Advancing Children's Strategies and Knowledge in Early Number
6(19)
Individualized Teaching in Mathematics Recovery
25(24)
Whole-Class Teaching
49(18)
General Introduction to
Chapters 5 to 9
67(6)
Teaching the Emergent Child
73(26)
Key Topic 5.1 Number Word Sequences from 1 to 20
74(4)
Copying and Saying Short FNWSs
75(1)
Copying and Saying Short BNWSs
76(1)
Saying Alternate Number Words Forwards and Backwards
76(1)
Saying the Next Number Word Forwards
77(1)
Saying the Next Number Word Backwards
77(1)
Saying the Number Word After
77(1)
Saying the Number Word Before
78(1)
Key Topic 5.2 Numerals from 1 to 10
78(3)
Numeral Sequences, Forwards
78(1)
Numeral Sequences, Forwards and Backwards
79(1)
Sequencing Numerals
79(1)
Numeral Recognition
80(1)
Numeral Identification
80(1)
Numeral Tracks -- 1 to 5 and 1 to 10
80(1)
Key Topic 5.3 Counting Visible Items
81(2)
Counting Items in One Collection
81(1)
Establishing a Collection of Given Numerosity
82(1)
Counting Items in a Row, Forwards and Backwards
82(1)
Counting Items of Two Collections
83(1)
Counting Items of Two Rows
83(1)
Key Topic 5.4 Spatial Patterns
83(2)
Ascribing Numerosity to Patterns and Random Arrays
84(1)
Making Spatio-Motor Patterns to Match Spatial Patterns
84(1)
Making Auditory Patterns to Match Spatial Patterns
85(1)
Key Topic 5.5 Finger Patterns
85(4)
Sequential Patterns for 1 to 5, Fingers Seen
86(1)
Sequential Patterns for 1 to 5, Fingers Unseen (Bunny Ears)
87(1)
Simultaneous Patterns for 1 to 5, Fingers Seen
87(1)
Simultaneous Patterns for 1 to 5, Fingers Unseen (Bunny Ears)
87(1)
Double Patterns for 1 to 5
88(1)
Using Fingers to Keep Track of Temporal Sequences of Movements
88(1)
Using Fingers to Keep Track of Temporal Sequences of Sounds
89(1)
Key Topic 5.6 Temporal Patterns and Temporal Sequences
89(10)
Copying and Counting Temporal Sequences of Movements
90(1)
Copying and Counting Rhythmic Patterns
90(1)
Copying and Counting Monotonic Sequences of Sounds
91(1)
Copying and Counting Arhythmical Sequences
91(8)
Teaching the Perceptual Child
99(27)
Key Topic 6.1 Number Word Sequences from 1 to 30
101(3)
Saying Short FNWSs
101(1)
Saying Short BNWSs
102(1)
Saying Alternate Number Words Forwards and Backwards
102(1)
Saying the Next One, Two or Three Number Words Forwards
102(1)
Saying the Next One, Two or Three Number Words Backwards
103(1)
Saying the Number Word After
103(1)
Saying the Number Word Before
103(1)
Key Topic 6.2 Numerals from 1 to 20
104(5)
Numeral Sequences, Forwards and Backwards
104(1)
Sequencing Numerals
105(1)
Numeral Recognition
105(1)
Numeral Identification
106(1)
Numeral Tracks -- 11 to 15, 16 to 20 and 11 to 20
107(1)
Numeral Rolls 1 to 20, 1 to 50
108(1)
Key Topic 6.3 Figurative Counting
109(2)
Counting Items in Two Collections, with First Collection Screened
109(1)
Counting Items in Two Collections, with Second Collection Screened
109(1)
Counting Items in Two Screened Collections
110(1)
Counting Items in a Row with Some Items Screened
110(1)
Key Topic 6.4 Spatial Patterns
111(2)
Partitioning Visible Patterns to 6
111(1)
Partitioning Flashed Patterns to 6
112(1)
Partitioning Visible Patterns to 10
112(1)
Partitioning Flashed Patterns to 10
112(1)
Combining Patterns Using 4-grids, 6-grids, 8-grids, 10-grids
113(1)
Key Topic 6.5 Finger Patterns
113(3)
Five Plus Patterns for 6 to 10
114(1)
Partitioning Numbers 3 to 10
115(1)
Doubles Plus One
115(1)
Partitioning 10 Fingers
115(1)
Key Topic 6.6 Equal Groups and Sharing
116(10)
Describing Equal Groups
116(1)
Organizing Equal Groups
117(1)
Making Equal Groups
117(1)
Describing Equal Shares
117(1)
Organizing Equal Shares
118(1)
Partitioning into Equal Shares
118(8)
Teaching the Figurative Child
126(41)
Key Topic 7.1 Number Word Sequences from 1 to 100
127(4)
Saying Short FNWSs
128(1)
Saying Short BNWSs
128(1)
Saying One, Two or Three Numbers After a Given Number
129(1)
Saying One, Two or Three Numbers Before a Given Number
129(1)
Counting the Number of Jumps Forwards from a to b
129(1)
Counting the Number of Jumps Backwards from b to a
130(1)
Forwards and Backwards Using the Sequence of Decade Numbers from 10 to 100
130(1)
Key Topic 7.2 Numerals from 1 to 100
131(6)
Sequencing Numerals
131(1)
Sequencing Decade Numerals
132(1)
Sequencing Off-Decade Numerals
132(1)
Ordering 2-Digit Numerals
132(1)
Numeral Recognition
133(1)
Numeral Identification
133(1)
Numeral Tracks in Range 20 to 100
134(1)
Numeral Roll 1 to 100
134(1)
Hundred Square
135(1)
Blank Hundred Square
136(1)
Key Topic 7.3 Counting-On and Counting-Back
137(4)
Counting Items in Two Screened Collections
137(1)
Counting Items in a Row with Some Items Screened
138(1)
Missing Addend Tasks
138(1)
Removed Items Tasks
139(1)
Missing Subtrahend Tasks
139(1)
Subtractive Tasks Using a Row
140(1)
Comparison Tasks
140(1)
Key Topic 7.4 Combining and Partitioning Involving Five and Ten
141(4)
Combining Numbers to 5
142(1)
Partitioning 5
143(1)
Combining 5 and a Number in the Range 1 to 5
143(1)
Using 5 to Partition Numbers in the Range 6 to 10
143(1)
Combining Numbers to 10
144(1)
Partitioning 10
144(1)
Key Topic 7.5 Partitioning and Combining Numbers in the Range 1 to 10
145(3)
Describing and Recording Partitions of a Number
145(1)
Partitioning Using Flashed Ten Frames
146(1)
Partitioning and Recording Using Flashed Ten Frames
146(1)
Combining Two Numbers Using Visible, Pair-Wise Frames
146(1)
Combining Two Numbers Using Visible, Five-Wise Frames
147(1)
Combining Two Numbers Using Flashed Frames
147(1)
Combining Two Numbers Using Flashed Frames and Recording
147(1)
Key Topic 7.6 Early Multiplication and Division
148(19)
Combining and Counting Equal Groups
148(2)
Determining the Number of Equal Groups
150(1)
Determining the Number in an Equal Share
150(1)
Describing Visible Arrays
151(1)
Building Visible Arrays
152(1)
Determining the Number of Dots on Visible Arrays
152(15)
Teaching the Counting-On Child
167(37)
Key Topic 8.1 Number Word Sequences by 2s, 10s, 5s, 3s and 4s
169(4)
FNWSs by 2s, from 2
170(1)
FNWSs and BNWSs by 2s
170(1)
FNWSs by 10s, from 10
170(1)
FNWSs and BNWSs by 10s
171(1)
FNWSs by 5s, from 5
171(1)
FNWSs and BNWSs by 5s
171(1)
FNWSs by 3s, from 3, and by 4s from 4
172(1)
FNWSs by 3s and by 4s
172(1)
Key Topic 8.2 Numerals from 1 to 1,000
173(4)
Sequencing and Naming 100s Cards
173(1)
Naming 3-Digit Numerals Using Arrow Cards
174(1)
Naming 3-Digit Numerals Using Digit Cards
175(1)
Sequencing and Naming Decade Numerals beyond 100
176(1)
Sequencing 3-Digit Numerals
176(1)
Ordering 3-Digit Numerals
176(1)
Sequences of Multiples with Numerals
176(1)
Key Topic 8.3 Incrementing by Tens and Ones
177(4)
Incrementing and Decrementing on the Decade, by Tens
177(1)
Incrementing and Decrementing off the Decade, by Tens
178(1)
Incrementing by Tens and Ones
179(1)
Decrementing by Tens and Ones
180(1)
Key Topic 8.4 Adding and Subtracting to and from Decade Number
181(3)
Adding from a Decade
181(1)
Subtracting to a Decade
182(1)
Adding to a Decade: 1--5
182(1)
Subtracting from a Decade: 1-5
182(1)
Adding to a Decade: 6--9
183(1)
Subtracting from a Decade - 6--9
183(1)
Key Topic 8.5 Addition and Subtraction to 20, Using 5 and 10
184(4)
Building Numbers 6--10
185(1)
Doubles: 3 + 3, 4 + 4, 5 + 5
185(1)
Building Numbers 11--20
185(1)
Doubles -- 6 + 6 to 10 + 10
186(1)
Doubles Plus or Minus 1
186(1)
Addition by Going through Ten
186(1)
Commutativity of Addition
187(1)
Addition by Compensation
187(1)
Subtraction by Going through Ten
187(1)
Key Topic 8.6 Developing Multiplication and Division
188(16)
Determining the Number in Partially Screened Equal Groups
188(1)
Determining the Number in Screened Equal Groups
188(1)
Determining the Number of Groups
189(1)
Determining the Number in Each Group
189(1)
Determining the Number in a Screened Array
189(1)
Determining the Number of Rows
189(1)
Determining the Number in Each Row
190(14)
Teaching the Facile Child
204(32)
Key Topic 9.1 Counting by 10s and 100s
206(3)
Counting by 10s off the Decade
206(1)
Counting by 100s to 1000
207(1)
Counting by 10s beyond 100
207(1)
Counting by 100s off the 100
207(1)
Counting by 100s off the Hundred and off the Decade
208(1)
Counting by 10s beyond 100 off the Decade
208(1)
Key Topic 9.2 2-Digit Addition and Subtraction through Counting
209(6)
Adding Tens to a 2-Digit Number
209(2)
Adding Two 2-Digit Numbers Without Regrouping
211(2)
Adding Two 2-Digit Numbers With Regrouping
213(1)
Subtracting Tens from a 2-Digit Number
214(1)
Subtraction Involving Two 2-Digit Numbers Without Regrouping
214(1)
Subtraction Involving Two 2-Digit Numbers With Regrouping
215(1)
Missing Addend Tasks Involving Two 2-Digit Numbers
215(1)
Key Topic 9.3 Non-Canonical Forms of 2-Digit and 3-Digit Numbers
215(3)
2-Digit Numbers in Canonical Form
216(1)
2-Digit Numbers in Non-Canonical Forms
216(1)
3-Digit Numbers in Canonical Form
217(1)
3-Digit Numbers in Non-Canonical Forms: Hundreds and Tens
217(1)
3-Digit Numbers in Non-Canonical Forms: Hundreds, Tens and Ones
217(1)
Key Topic 9.4 2-Digit Addition and Subtraction through Collections
218(2)
Adding Two 2-Digit Numbers Using Visible Collections
218(1)
Adding Two 2-Digit Numbers Using Screened Collections
219(1)
Missing Addend Tasks Using Visible Collections
219(1)
Missing Addend Tasks Using Screened Collections
219(1)
Subtraction Using Visible Collections
220(1)
Subtraction Using Screened Collections
220(1)
Key Topic 9.5 Higher Decade Addition and Subtraction
220(3)
Using Addition Facts Within the Decade
221(1)
Using Subtraction Facts Within the Decade
221(1)
Using Addition Facts Across the Decade
222(1)
Using Subtraction Facts Across the Decade
222(1)
Key Topic 9.6 Advanced Multiplication and Division
223(13)
Word Problems -- Multiplication
223(1)
Word Problems -- Quotition Division
223(1)
Word Problems -- Partition Division
224(1)
Commutativity with Arrays
224(1)
Combining Two Sets of Equal Groups
225(1)
Partitioning Arrays
225(11)
Bibliography 236(3)
Index 239
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.

 

Garry Stanger has had a wide-ranging involvement in primary, secondary and tertiary education in Australia. He has held positions of Head Teacher, Deputy Principal and Principal, and has been a Mathematics Consultant with the New South Wales Department of Education. He has also taught in schools in the USA. He has worked with Robert Wright on the Mathematics Recovery project since its inception in 1992 and has been involved in the development of the Count Me In Too early numeracy project. His last project before finally retiring was working with Jenny Bednall, Head of Junior School, Trinity South and the thirty teachers at the Trinity College schools in South Australia. 

Jim Martland is a member of the International Board of Mathematics Recovery and Founder of the Mathematics Recovery Council (UK and Ireland). He was a Senior Fellow in the Department of Education at the University of Liverpool. In his long career in education he has held headships in primary and middle schools and was Director of Primary Initial Teacher Training. In all the posts he continued to teach and pursue research in primary mathematics. His current work is with local education authorities in the UK and Canada, delivering professional development courses on assessing childrens difficulties in numeracy and designing and evaluating teaching interventions.