El. knyga: Teaching Number: Advancing Children's Skills and Strategies

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 Groups		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.