National NumeracyNational Review Report National Numeracy Review Report May 2008 – May 2008 – May Commissioned by the Human Capital Working Group, Council of Australian Governments National Numeracy Review Report May 2008 Commissioned by the Human Capital Working Group, Council of Australian Governments ISBN: 0 642 77735 7 ISBN (online): 0 642 77736 5 © Commonwealth of Australia 2008 This report is copyright. It may be reproduced in whole or part subject to the inclusion of an acknowledgment of the source and no commercial usage or sale. Reproduction for purposes other than those indicated above, requires the written permission of the Commonwealth. Requests and inquiries concerning reproduction and rights should be addressed to Commonwealth Copyright Administration, Attorney-General’s Department, Robert Garran Offi ces, National Circuit, Barton ACT 2600 or posted at http://www.ag.gov.au/cca The views expressed in this report do not necessarily refl ect the views of the Department of Education, Employment and Workplace Relations. ii | National Numeracy Review Report Table of contents Preface ................................................................................................................................................ vii Executive Summary and Recommendations .............................................................................. xi Chapter 1: Numeracy and mathematics in Australia ................................................................. 1 1.1 Introduction ..................................................................................................................................1 1.2 Numeracy and the school curriculum ............................................................................................2 Numeracy and mathematics .........................................................................................................3 Numeracy and ‘the basics’ ............................................................................................................5 Numeracy across the curriculum ...................................................................................................6 Numeracy and the workplace .......................................................................................................7 Dimensions of a school curriculum for numeracy ..........................................................................9 1.3 Achievement in mathematics ...................................................................................................... 11 International comparative assessments .......................................................................................11 National numeracy benchmarks .................................................................................................13 Excellence and equity .................................................................................................................14 1.4 Participation in mathematics .......................................................................................................18 Time on task ..............................................................................................................................18 Participation at senior secondary level ........................................................................................19 Enrolments in tertiary mathematics courses ................................................................................20 1.5 The teaching workforce ..............................................................................................................21 Primary teachers .........................................................................................................................21 Secondary teachers of mathematics ...........................................................................................22 Teachers of numeracy across the curriculum ...............................................................................23 Technical and Further Education (TAFE) ......................................................................................23 University ...................................................................................................................................23 Chapter 2: Supporting mathematics learning ......................................................................... 25 2.1 Introduction ................................................................................................................................25 2.2 International evidence of good practice ......................................................................................25 2.3 Teachers and teaching ................................................................................................................27 Perspectives on teaching ............................................................................................................27 Characteristics of effective teaching ...........................................................................................28 2.4 The role of language in mathematics learning .............................................................................32 2.5 Assessing student achievement ...................................................................................................34 Table of contents | iii Using test data for school improvement .....................................................................................34 Classroom assessment ................................................................................................................37 School entry assessments ...........................................................................................................41 2.6 The pedagogies of adult numeracy .............................................................................................43 2.7 Computational and information and communication technologies ..............................................44 Computational calculators in mathematics lessons ......................................................................44 Computers in mathematics lessons .............................................................................................45 Graphic calculators and CAS in mathematics lessons ..................................................................45 Delivering mathematics lessons through ICT ...............................................................................46 The role of affect and technology...............................................................................................47 2.8 Ability grouping ..........................................................................................................................47 2.9 Fostering positive student motivation ..........................................................................................50 2.10 Out-of-school support ................................................................................................................51 Involving parents in supporting numeracy learning .....................................................................51 Out-of-school tutoring ...............................................................................................................52 Chapter 3: Addressing the numeracy needs of particular groups of students ................ 53 3.1 Introduction ................................................................................................................................53 3.2 Indigenous and cultural minority students ...................................................................................53 Indigenous education .................................................................................................................53 Socio-cultural factors .................................................................................................................56 Numeracy, language and context ...............................................................................................57 3.3 Interventions to support underperforming students ....................................................................59 Numeracy learning withdrawal programmes ...............................................................................59 In classroom support ..................................................................................................................61 Chapter 4: Teacher education and professional development ............................................ 65 4.1 Introduction ................................................................................................................................65 4.2 Mathematical knowledge for teaching ........................................................................................65 4.3 Pre-service teacher education and prerequisite knowledge ..........................................................68 Assessing pre-service teachers’ mathematical knowledge ...........................................................71 4.4 In-service teacher education .......................................................................................................72 Professional teaching standards in mathematics..........................................................................72 Effective professional development programmes ........................................................................73 4.5 Mathematics curriculum leadership .............................................................................................76