Open letter to Mr. David de Carvalho, CEO of ACARA, and the ACARA Board

The following is an open letter about the draft changes to the maths component of the Australian Curriculum. You may view a list of signatories here.

Open letter to Mr. David de Carvalho, CEO of ACARA, and the ACARA Board

On 29 April 2021, the Australian Curriculum, Assessment and Reporting Authority (ACARA) released its draft revisions to the Australian Mathematics Curriculum, with a consultation period ending on 8 July 2021. We are a group of mathematicians, mathematics educators, educational psychologists, parents and members of the public who take an active interest in mathematics education and in the curriculum. We agree that the Mathematics Curriculum desperately requires reform; it is repetitious, disconnected, unambitious and is lacking in critical elements. We are pleased that efforts to reform the curriculum are underway. We are profoundly concerned, however, with the structure of the current draft and with many of the proposed changes within.

The primary source of our concerns is the proposal to replace the four Proficiencies in the current Curriculum with the draft’s thirteen “Core Concepts”, grouped under three “Core Concept Organisers”. The Proficiencies – understanding, fluency, reasoning and problem-solving – are well-understood and provide a clear structure for teaching mathematics. In contrast, the Core Concepts are often poorly defined and overlapping, vary massively in scope and breadth, and their groupings into Core Concept Organisers, including the faddish “Mathematising”, are a mostly arbitrary and at times contradictory categorisation. The critical element of “thinking and reasoning”, for example, has somehow been reduced to just another concept among thirteen, sharing equal value with wordy descriptions of simple ideas. The end effect is a framework of little practical value as a guiding structure.

The Core Concepts are confused and confusing, but it is clear that they represent a push toward a central role for “problem-solving” and inquiry-based learning. Solving problems is obviously a core aspect of mathematical practice, is an important goal for mathematics education, and is already listed as one of the four Proficiencies in the current curriculum. The issue with the draft curriculum is that its “inquiries” are unanchored by clear and specific content, by underlying knowledge and skills. Moreover, the “problems” suggested to be “solved” are mostly exploratory and open-ended, effectively unsolvable and of questionable pedagogical value, and with little or no indication of the specific desired learning outcome. Insufficient attention is given to carefully constrained problems facilitating the practicing and subsequent extension of already mastered skills. Making things worse, the inclusion of inquiry methods in the content descriptors results in the descriptors being almost useless as determiners of actual content. This obscures the key ideas and basic skills to be learned, which are the foundational elements essential for any effective mathematical practice, including for problem-solving.

The draft is not so much pushing problem-solving as it is pushing for learning through activities referred to as “solving problems”, but which are actually ill-defined explorations. We do not believe that a curriculum document should mandate a specific method of mathematics teaching, and it is especially concerning that the draft curriculum is extensively mandating learning through “exploring” and “problem-solving”. There is strong evidence to indicate that methods without a proper balance that includes the explicit teaching of mathematical concepts are less effective, in particular for younger students grappling with new concepts and basic skills. The content of the mathematics curriculum, even for the lower years, is the result of millennia of human endeavour across cultures around the world – it is neither fair nor realistic to expect students to retrace this journey with a few pointers and inquiries in a few hours per week.

The emphasis in the draft curriculum on open-ended inquiry, without the systematic building of coherent knowledge, creates further serious issues. Some indication of these issues is provided in the following paragraphs, but many, many more examples could be given.

The delaying and devaluing of fluency, of “the basics”

The draft curriculum includes some particularly concerning Content descriptors, and rearrangement of material. The learning of the multiplication tables, for example, is first addressed only in Year 4, where it is framed in terms of “patterns” and “strategies”, with no emphasis on mastery. Similarly, the solving of linear equations such as ax + b =c, a foundational skill for all secondary school mathematics, is pushed in the draft from Year 7 to Year 8. There is simply no valid argument for these, and many other, dilutions and delays. Indeed, the draft curriculum has squandered the opportunity to address some glaring problems with the timing and emphasis of content in the current Curriculum.

The loss of natural mathematical connections

Mathematics in the current Curriculum consists of three strands, but the draft has split these into six strands. The very natural Number-Algebra strand, for instance, has become separate strands of Number and Algebra. This is unwieldy, effectively requires a redefinition of “algebra” and, most damagingly, it severs the critical pedagogical link between these two disciplines. Similarly, the strands of Measurement-Geometry and Statistics-Probability have been split into Measurement, Space, Statistics and Probability, for no benefit or good purpose.

Shallow conceptualisation

Notwithstanding ACARA’s repetitive claims to be promoting “deep understanding”, the draft’s overwhelming emphasis on investigation and modelling has resulted in many critical mathematical concepts being underplayed and, in certain cases, not even being named. In Algebra, for example, fundamental terms such as “null factor” and “polynomial” and “completing the square” rate not a single mention. To give an analogy, it is as if a curriculum on Politics failed to mention “sovereignty” or “citizenship” or “separation of powers”.

The devaluing of mathematics

The problem-solving, investigation and modelling that is advocated by the draft curriculum is very heavily weighted towards real-world contexts. Indeed, the definition of “Problem solving” provided in the draft Curriculum’s “Key considerations” section explicitly mentions solving problems relating to the “natural and created worlds”, and pointedly omits references to solving problems stemming from mathematics itself. This approach squanders an excellent opportunity for students to gain an appreciation of mathematics as a beautiful discipline, a discipline which can be its own goal. This devaluing of mathematics is starkly displayed in the description of, and in the very name of, the Space strand. Whereas Geometry is concerned fundamentally with the study of abstract objects and their properties, the Space content is heavily slanted towards the study of real-world contexts. Learning in genuine real-world contexts is much more difficult, because the real world is inevitably full of distractions that cloud the clear principle to be learned.

Mathematical errors and non sequiturs

Some errors in the draft are subtle, but many are not. There is no purpose, for example, in directing students to “investigate … Fibonacci patterns in shells”, since such patterns simply do not exist. Such errors and confusions would typically be caught during a proper review by mathematicians; their existence in the draft curriculum places into serious question the nature and the extent of ACARA’s consultation process.

Finally, we make two points about ACARA’s presentation and promotion of the draft curriculum.

Part of ACARA’s justification for the strong emphasis on problem-solving has been that the mathematics curriculum in Singapore, an education system that performs extremely well in the mathematics component of the Programme for International Student Assessment (PISA), places an emphasis on problem-solving. We seriously question whether the Singaporean sense of “problem-solving” bears even a remote resemblance to ACARA’s use of the term but, in any case, ACARA’s justification fails on its own terms. To begin, there are other education systems that also place a premium on problem-solving but that do not perform at anywhere near the level of Singapore in PISA mathematics. Further, whatever the role of problem-solving in the Singaporean curriculum, this curriculum is also very demanding in terms of fluency with basic skills; no comparable requirements exist in the current Australian Curriculum, and the draft curriculum only pushes to weaken these requirements. The further elimination and weakening of fundamental skills will contribute to the root cause of Australian students’ slipping in international comparisons: the students end up knowing less mathematics.

Secondly, an important aspect of ACARA’s review is that it was intended to be modest in scope, with a focus on “refining” and “decluttering”. The draft curriculum fails in both respects. The radical introduction of the Core Concepts structure and “Mathematising”, the separation into twice the number of strands, the multipurpose nature of the Content, is all the antithesis of modest. This new structure is, inevitably, much clunkier, with massively increased curriculum clutter. The draft curriculum is barely readable.

In brief, the draft curriculum is systemically flawed. It is unworkable, and it fails to capture or to promote the high standard of mathematical knowledge, appreciation and understanding that Australia’s schoolchildren deserve.

The Australian mathematics curriculum requires proper review. Such a review, however, must be undertaken without a pre-ordained outcome, and with the proper participation and consultation of discipline experts. Indeed, ACARA’s own terms of reference for the review specify that the content changes are to be made by subject matter experts, namely mathematicians. It is difficult to imagine that this was the case.

We urge ACARA to remove the current draft mathematics curriculum for consideration and to begin a proper and properly open review, in line with community expectations and with Australia’s needs.

Sincerely,

List of signatories

Due to the ACARA consultation period ending on 8 July, this list is now closed to new signatories

List of Signatories

Dr. Abdullah Al Amin, Teacher, Victoria

Peter Allen, Parent, Melbourne

Remy Alonso, Year 12 Student, Sydney

Julie May Anderson, Primary Teacher (retired), Sydney

Elizabeth Arnold, Grandparent, New South Wales

Greg Ashman, Teacher and PhD Candidate in Instructional Design, UNSW

Kate Atkinson, Professional Experience Coordinator at a School of Education, Victoria

Dr. Santiago Badia, Professor of Mathematics, Monash University

Charles Bagot, Grandparent, New South Wales

Paul Barton, Mathematics Teacher, Fort Street High School

Dr. Nigel Bean, Adjunct Professor of Applied Mathematics, University of Adelaide

Tamsin Beckett, VET Coordinator and Senior Mathematics Teacher

Mike Beckingsale, Preservice Mathematics Teacher, Brisbane

Deborah Bell, Grandparent, New South Wales

Brian Bellia, Concerned Citizen, New South Wales

Jane Bergamin, Teacher

Cathy Billingham, Teacher, Queensland

Kylie Birch, Teacher, Canberra

Dr. Peter Blain, Uncle, Hobart

Alex Blanksby, Teacher/Tutor, Melbourne

Luke Bohni, Mathematics Teacher, Victoria

Kirstin Bourne, Senior Education Consultant, Victoria

John Boyce, Teacher, Victoria

Douglas Bransgrove, Head of Mathematics, St Peters Lutheran College

Dr. Thomas Britz, Senior Lecturer of Mathematics, UNSW

Dr. Peter Brown, Hon. Senior Lecturer in Pure Mathematics, UNSW

Dr. Tim Brown, Professor of Statistics (retired)

Derek Buchanan, Mathematics Teacher, Sydney

Adam Bulman, Specialist Mathematics Teacher, Melbourne

Russell Bunce, Secondary School Teacher, Victoria

Dr. Michelle Burg, Mathematics Teacher, Canberra

Luke Burgess, Teacher, Melbourne

Merryn Burt, Learning Enhancement Coordinator (Teacher), Melbourne

Ray Bush, Parent, Sydney

Nigel Cadogan, Mathematics and IT Teacher (retired), Sydney

Dr. Grant Cairns, Associate Professor of Mathematics (retired)

Andrew Calvert, Secondary Teacher, New South Wales

Carolyn Campbell, Parent and Grandparent, Queensland

Ben Cannon, Parent, Sydney

Nicola Carr-White, Teacher and Postgraduate Student, Western Australia

H Chang, Parent, Melbourne

Dr. Brian Chapman, Theoretical Biophysicist, Federation University

Tania Charters, Parent, New South Wales

Tony Collins, Teacher, New South Wales

Joanne Cox, Parent, Sydney

Jonathan J. Crabtree, Elementary Mathematics Historian, Melbourne

Michael Cujes, Parent and Mathematics Teacher, Brisbane

Marcella Dalton, Parent, Victoria

Julia Davies-Duff, Inclusive Access Consultant, Canberra

James Dawes, Teacher, Western Australia

Dr. Garry Delmenico, Parent, Melbourne

Giuseppe De Simone, Parent, Melbourne

Wendell De Zilva, Parent, Sydney

Winston De Zilva, Student, Sydney

James Dobson, Learning Specialist & Foundation Teacher, Tylden Primary School

Dr. Anthony Dooley, Professor of Mathematics, University of Technology Sydney

Anthony Dowse, Retired Teacher, Victoria

Eleanor Drayton, Teacher, Melbourne

Dr. Jerome Droniou, Professor of Mathematics and Head of the Applied & Computational Section of the School of Mathematics, Monash University

James Durrant, Parent, Perth

Damien Edgar, Teacher, Melbourne

Peter Edwards, Parent, Western Australia

Shannon Emanuel, Teacher, Adelaide

Dr. Andreas Ernst, Professor of Mathematics, Monash University

Peter Fanning, Retired Secondary Educator, Queensland

Michael Farr, Psychologist, Queensland

Dr. David Finlay, Professor Emeritus, Victoria

Tony Finney, Mathematics Teacher, Queensland

Belinda Fisher, Parent, Melbourne

David Fisher, Parent, Melbourne

Dr. Mark Fisher, Mathematician and Data Scientist, Melbourne

Dr. Nicholas Fisher, Visiting Professor of Statistics, University of Sydney

Alice Fiumara, Parent, New South Wales

Dr. Mark Flegg, Parent and Senior Lecturer in Applied Mathematics, Monash University

Wendy Forsyth, Director of Curriculum, Hobart

Dr. James Franklin, Honorary Professor, School of Mathematics and Statistics, UNSW

Andrew Fraser, Parent, Melbourne

Dr. Anna Foeglein, Mathematician in private industry

Sharron Fowler, Parent, Western Australia

Danny Fowles, Teacher and Numeracy Specialist, Wedderburn College

Daley Gallagher, Teacher and Curriculum Leader Assistant, Queensland

Kevin Gardner, Parent, South Australia

Helen Garland, Primary Teacher, New South Wales

Christy Gentz, Parent, Queensland

Trish Ghirardello, Specialist Mathematics Teacher

Kenneth Giblin, Instructional leader, Westdale Public School

Dr. Gary Glonek, Associate Professor of Statistics (retired)

Fay Gourlie, Grandparent, New South Wales

Dr. Lucy Gow, Mathematics Teacher, Victoria

Peter Gray, Parent, Victoria

Alan Grinton, Secondary Teacher (retired), Victoria

Dr. Joseph Grotowski, Professor of Mathematics, the University of Queensland

Kate Gurjian MEd (LD), Specialist Educator & Principal, Time to Shine Australia, Sydney

Dr. Tony Guttmann FAustMS FAA, Emeritus Professor of Mathematics, University of Melbourne

Yvonne Hanks, Parent and Grandparent, Victoria

Phil Hanson, Parent, Queensland

Linda Harvey, Parent, Victoria

Rod Hayes, Parent, Victoria

Margaret Head, Concerned Citizen, New South Wales

Rebecca Hernandez, Teacher, Brisbane

Nicholas Hildebrandt, High School Mathematics Teacher, Melbourne

Neil Holden, Mathematics Teacher, Melbourne

Aaron Holder, Teacher, Kangaroo Island

Katherine Holford, Teacher, Victoria

Samantha Hornery, Education Manager Learning Links, Sydney

Tara Houle, Parent and Mathematics Advocate, Canada

Bernadette Hovens, Parent and Speech Pathologist, Melbourne

Linda Huber, Teacher, Canberra

Bryn Humberstone, Head of Mathematics, Brighton Grammar School

Dr Rosemary Humberstone, Teacher, Melbourne

Alison Hyde, Specialist Learning Support Teacher

William Ifield, Business Owner, New South Wales

Martin Imber, Grandparent, Melbourne

Katie Jackson, Teacher, New South Wales

Annette Janes, Grandparent, Queensland

Luke Janicke, Pre-Service Teacher, Murdoch University

Maree Johnston, Teacher, Queensland

Natalie Johnston, Parent, Victoria

Daphne Jones, Grandparent, Tasmania

John Jones, Parent, Victoria

Dr. William Jones, Research and Development Manager (retired), Tasmania

Geoffrey Joseph, Grandparent, Tasmania

Anthony Keatch, Teacher, Melbourne

Richard Kelleher, Teacher, Melbourne

Leanne Kelly, Parent, Queensland

John Kermond, Secondary School and University Mathematics Teacher

Cathryn Killin, Head of Mathematics, New South Wales

Dr. Paul A. Kirschner, Emeritus Professor of Educational Psychology, Open University of the Netherlands

Zina Kiss, Primary School Teacher and Parent, Canberra

Dr. Fima Klebaner, Professor of Statistics, Monash University

Brian and Anne Knee, Grandparents, New South Wales

Jana Kovarik, Parent, Queensland

Stephan Kubicki, VCE Mathematics Teacher, Victoria

M. Kudva, Grandparent, Sydney

Rod Langlands, Teacher, Perth

Rosine La Spina, Grandparent and Retired Teacher, Canberra

Tempe Laver, Parent, Brisbane

Norm Lee, Grandparent, Melbourne

Dr. Vicki Likourezos, Mathematics Education, UNSW

Linda Lill, Concerned Citizen, New South Wales

George Lilley, Teacher, Melbourne

Christine Lorriman, Grandparent and Retired Primary Teacher, New South Wales

Dr. Bettina Lythgoe, Head of Mathematics, Victoria

Dr. Amanda Mabbett, Parent and Scientist, South Australia

Douglas Maclennan, Grandparent, Sydney

Judy Maclennan, Grandparent, Sydney

Susan Macrse, Parent, Brisbane

Michael Malone, Head of Teaching & Learning, Hillston Central School

Jennifer Mastorakis, Learning Specialist and Teacher, Melbourne

Dr Alasdair McAndrew, Associate Professor of Mathematics, Victoria University

Elizabeth McCarthy, Mathematics Learning Advisor, Victoria University

Lorna McClory, Teacher and Numeracy Leader, Bacchus Marsh College

Carole McCluskey, Principal, Merrijig Primary, Victoria

Parnell Palme McGuinness, Parent, Sydney

Tracey McMinn, Education Consultant and Instructional Coach

Dianna McTavish, Intervention Teacher, Victoria

Ross Mendan, Parent, Melbourne

Dr. Stacey Mendan, Mathematics Teacher, Presbyterian Ladies’ College

Peter Mengede, Parent, Brisbane

Brayden Mertz, Student, Victoria

Dr. Guy Metcalfe, Adjunct Professor of Mechanical Engineering, Swinburne University of Technology

Yvonne Meyer, Parent, Melbourne

Ruth Middleton, Teacher, New South Wales

Richard Milne, Grandparent, Victoria

Ashleigh Mitchell, Secondary Mathematics Teacher, Queensland

Robert Monay, Curriculum Developer (retired), Melbourne

Dion G. Morgan, Parent, Victoria

Trish Morgan, Managing Director, Teach This, Queensland

Michael Morrell, Head of Mathematics, Queensland

Dr. Bryony Nayagam, Associate Professor, Melbourne

Dr. David Nayagam, Parent, Melbourne

Dr. Jayden Newstead, Postdoctoral research fellow, University of Melbourne

Brett Newton, Teacher, Melbourne

Louise Newton, Learning Area Leader for Mathematics and Technology, Victoria

Jackie Nieuwenhuizen, Literacy teacher in private practice, Victoria

Dr. Yuri Nikolayevsky, Associate Professor of Mathematics, LaTrobe University

Dr. Paul Norbury, Professor of Mathematics, University of Melbourne

Meaghan O’Callaghan, Leader of Year 9 Mathematics, Victoria

John O’Donnell, Parent and retired academic

Peter O’Donnell, Former mathematics teacher, Melbourne

Daniel Oliver, Teacher, Tasmania

Dr. Todd Oliynyk, Professor of Mathematics, Monash University

Peter Ormerod, Grandparent, New South Wales

Geoff Orrin, Senior Mathematics Teacher (retired), Victoria

Nick Pacitti, Teacher and former Head of Mathematics, Melbourne

Michael Palmer, Teacher, Mill Park Secondary College

Dr. Phillip Parker, Senior Lecturer in Chemistry and Biochemistry, Melbourne

Sabine Partington, Head of Teaching & Learning, Haileybury

Anthony Pasinati, Teacher and Head of Mathematics, Melbourne

Zalie Perry, Parent, Victoria

Howard Petts, Teacher, New South Wales

Matthew Philips, Teacher, New South Wales

Nadine Phillips, Secondary School Mathematics Teacher, Melbourne

Donna Pinkiewicz, Parent, Tasmania

M. Pollock, Parent, Melbourne

Dr. Burkard Polster, Associate Professor of Mathematics, Monash University

Daniel Potaczala, Mathematics Teacher, Sydney

Libby Prince, Secondary Mathematics Teacher (retired)

Ezekiel Prlja, Parent, Queensland

Ying Qin, Parent, Melbourne

Omair Raza, Teacher, Northern Territory

Kelli Reeves, Teacher, Queensland

Joanne Richards, Teacher, Victoria

Rebecca Rizzo, Teacher, Canberra

Patrick Robertson, Mathematics Teacher, Melbourne

Dana Roles, Teacher of Senior School Mathematics, Hazel Glen College

Erin Rollason, Learning Intervention Coordinator, Melbourne

Dr. Marty Ross, Mathematician, Melbourne

Dr. Daniel Ross, Philosopher, Melbourne

Dr. Anne Rouse, Psychologist

Sarita Ryan, Head of Campus, Alice Miller School

Dr. Tian Sang, University of Melbourne

Lynnette Saville, Concerned Citizen, New South Wales

Andrea Schaul, High School Mathematics Teacher, Queensland

Ben Schutz, Mathematics Teacher, Melbourne

Ingrid Sealey, Director of Teach Well, Western Australia

Dr Jan Seiler, Teacher and Parent, Tasmania

Bronwyn Self, Teacher

Denise Sheehan MSped, Special Education Coordinator, Canberra

Chris Sheldon, Retired Teacher and Grandparent, Queensland

Ron Sheldon, Retired Teacher and Grandparent, Queensland

Katrina Sheraton-Yu, Director PosAbility Psychology and Learning Clinic, Psychologist and Special Education Consultant

David Simpson, Head of Department, Melbourne

Dr. Ian Sloan Professor of Mathematics, UNSW

Conrad Smith, Special Education Teacher

Raymond Smith, Grandparent, Melbourne

John Smyth, Mathematics Teacher, Victoria

Maree Sommerville, Parent, Melbourne

Douglas Spencer-Roy, Parent, Melbourne

Alana Spizzirri, Teacher, Victoria

Beth Stansfield, Teacher Brisbane

L. W. Stevens, Parent, New South Wales

Wayne Stone, Parent, Sydney

Vernon Stooke, Parent, Victoria

Peter Strantzen, Mathematics Teacher (retired)

Rosemary Sutherland, Mathematics Teacher (retired) and Tutor, New South Wales

Dr. John Sweller, Emeritus Professor of Educational Psychology, UNSW

David Tattersall, Grandparent and former Teacher, New South Wales

Dr. Wendy Taylor, Mathematics Teacher, Sandringham College

Simon Teague, Assistant Lecturer, Mathematics, Monash University

Leigh Thompson, Teacher and formerly Head of Mathematics, Victoria

Dr. David Treeby, Mathematics Teacher, Presbyterian Ladies’ College

Sarah Trinder, Parent, Victoria

Erin Turner, Deputy Principal and Mathematics Curriculum Leader

Joanne van de Camp, Head of Mathematics, Victoria

Vajal Varghese, Parent, Melbourne

Dr. Ian Wanless, Professor of Mathematics, Monash University

Rod Watson, Mathematics Teacher, Melbourne

Rodney Watson, Parent, Melbourne

Dr. Neville Weber, Emeritus Professor of Mathematical Statistics, University of Sydney

Dr. Alan Welsh, E.J. Hannan Professor of Statistics

Patrick F. Whalen, Mathematics Teacher

Dr. Glen Wheeler, Senior Lecturer in Mathematics, University of Wollongong

Pauline Wilson, Mathematics Teacher, Victoria

Demeke A Wondmagegn, Head of Mathematics and Computer Science, South Africa

Dr. David Wood, Professor of Mathematics, Monash University

Troy Wood, Primary Teacher, Melbourne

Keith Wrigley, Parent, Victoria

Guanghua Wu, Mathematics Teacher, Melbourne

Carlynn Yong, Teacher, Sydney

Stephen Young, Teacher, Victoria

Dr. Nadia Zatsepin, Senior research fellow in Physics, La Trobe University

Edward Nordin Zuber, Head of Mathematics, Sydney