Teaching Mathematics In Primary Schools

by Zevenbergen, Robyn; Dole, Shelley; Wright, Robert J.

• ISBN13: 9781741143584
• ISBN10: 1741143586
• Format: Paperback
• Copyright: 2005-04-01
• Publisher: Allen & Unwin

Summary

A systematic, research-based introduction to the principles and practice of teaching mathematics at the primary school level, this inquiry moves beyond traditional lockstep approaches to teaching mathematics to emphasize how students can learn to think mathematically in terms of globalization and new technologies.

Author Biography

Robyn Zevenbergen, and Shelley Dole, are researchers in primary mathematics. Robert J. Wright is the author of Early Numeracy: Assessment for Teaching and Intervention and Teaching Number: Advancing Children's Skills and Strategies.

Table of Contents

About this book	xi
About the authors	xiii
The changing face of primary mathematics	1	(20)
Mathematics education and society	1	(1)
Teaching mathematics in New Times	2	(2)
New models of teaching mathematics	4	(1)
Content and pedagogy	5	(2)
What is mathematics?	7	(3)
Where does mathematics come from?	10	(1)
The mathematics curriculum	11	(4)
Integrating curriculum	15	(2)
Numeracy	17	(4)
Theoretical foundations for contemporary mathematics education	21	(12)
Cognitive theories	22	(3)
Sociocultural theories: the influence of Vygotsky	25	(1)
Socially critical theories	26	(1)
New Times: New Learnings	27	(2)
Theory into practice	29	(4)
Language and mathematics	33	(14)
The language of mathematics	33	(5)
Word problems	38	(4)
Language error analysis	42	(1)
Mathematical literacies	43	(1)
Making pedagogy explicit	44	(3)
Diversity and equity	47	(16)
Cognitive models of difference	49	(1)
Social models of difference	50	(1)
Teachers' beliefs	51	(2)
Home-school differences	53	(3)
Knowledge and worldviews	56	(2)
Implications for school mathematics	58	(5)
Planning for teaching	63	(16)
Planning	64	(1)
Why plan?	65	(1)
Planning: What do I want to teach?	66	(5)
Teaching: How will I teach?	71	(3)
Evaluating teaching: How will I know if it has been a success?	74	(1)
Planning the learning environment	74	(2)
Planning for substantive learning	76	(3)
Assessment	79	(27)
Why assess?	79	(2)
Models of assessment	81	(3)
What to assess	84	(1)
Planning assessment	85	(3)
Assessment tools	88	(10)
Student writing	98	(1)
Tests	98	(1)
Rubrics	99	(1)
Opening up assessment	100	(2)
Communicating results	102	(4)
Working mathematically	106	(15)
Problem solving	107	(6)
Problem posing	113	(1)
Technology for thinking mathematically	113	(2)
Making connections	115	(1)
Communicating mathematically	116	(5)
Early number	121	(28)
Number sense	121	(2)
Pre-number	123	(1)
Subitising: Group recognition	124	(1)
Counting	125	(3)
Conservation of number	128	(3)
Number benchmarks	131	(1)
Types of numbers	132	(1)
Learning about numerals	133	(1)
Numeration and place value	134	(7)
Addition and subtraction	141	(2)
Multiplication and division	143	(6)
Basic facts and mental computation	149	(27)
Working flexibly with number	150	(1)
Basic facts of addition	151	(7)
Tens facts	158	(3)
Basic facts of subtraction	161	(1)
Addition and subtraction: Mental computation	162	(1)
Basic facts of multiplication	163	(7)
Basic facts of division	170	(1)
Mental computation and estimation	171	(5)
Written algorithms	176	(21)
The addition algorithm	178	(3)
The subtraction algorithm	181	(3)
The multiplication algorithm	184	(7)
The division algorithm	191	(4)
Summary	195	(2)
Rational number	197	(36)
Fractions	199	(10)
Decimals	209	(4)
Ratio and proportion	213	(5)
Promoting language and mental images of ratio and proportion	218	(4)
Rate	222	(1)
Percent	223	(4)
Mental computation of percent situations	227	(1)
Increases of more than 100%	228	(2)
Summary	230	(3)
Patterns and algebra	233	(17)
Why study patterns and algebra?	233	(2)
Patterning	235	(6)
Number theory	241	(4)
Early notions of algebra	245	(5)
Measurement	250	(31)
What is measurement?	250	(6)
Teaching measurement	256	(7)
Length	263	(2)
Area	265	(1)
Teaching strategies	266	(2)
Volume and capacity	268	(1)
Mass	269	(2)
Time	271	(3)
Temperature	274	(1)
Money	275	(1)
Making connections between substrands	276	(5)
Chance and data	281	(29)
What are chance and data?	281	(3)
Teaching chance	284	(7)
Data collection, representation and interpretation	291	(10)
Measures of central tendency	301	(3)
Statistical literacy: Interpretation of data representations	304	(1)
Teaching notes for graphing	305	(5)
Space	310	(30)
Visualisation	311	(1)
Van Hieles' levels of geometric thinking	312	(2)
Teaching notes	314	(1)
Spatial concepts: Early activities	315	(1)
Shape and structure	315	(9)
Transformation and symmetry	324	(8)
Location and arrangement	332	(8)
Index	340