Mathematics and numeracy: a summary of Curriculum Leadership coverage 2005–2009
Mathematical knowledge and numeracy inform decision making in personal and community life, and contribute to the study of several other disciplines; mathematics is also one of the core subject areas to be covered in the forthcoming national curriculum in Australia. This week Curriculum Leadership publishes a summary of material that has appeared in the journal since 2005 on the topic of numeracy or on the subject area of mathematics.
The material is organised under broad topic headings. Within each topic, any relevant feature articles are summarised first, followed by references to Curriculum Leadership's abstracts of articles that were published in other journals.
Numeracy, and mathematics in other subject areas
Numeracy covers the competence and disposition to manage mathematical demands made in the home, workplace and community. Numeracy demands are raised by a number of subjects other than mathematics, at times offering scope for explicit connections with maths as a subject area.
Articles published in Curriculum Leadership
Several articles relate specifically to numeracy. Numeracy across the curriculum describes the Middle Years Numeracy Across the Curriculum Project commissioned by the ACT Department of Education, Youth and Family Services (DEFYS), which sought to help teachers in other content areas identify and meet the numeracy demands raised in their respective teaching areas. The project hightlighted the challenge of how to diagnose a student's particular numeracy problem: it may reflect lack of mathematical knowledge, skills, or disposition to persist; a common problem was students' inability to transfer mathematical knowledge and numeracy skills between maths classrooms and other settings.
Numeracy in the curriculum is also addressed by two articles covering the Numeracy Plan 2006–2008 in New South Wales and the Numeracy Framework for Action in Queensland. Of further interest is an article by Shelley Dole, Tony Wright and Doug Clarke that reports on the commencement of a research project promoting and connecting mathematics and science in the middle years of schooling, with a focus on the topic of proportional reasoning. The project involved teacher educators and middle years teachers in seven government, Catholic and independent schools in Queensland.
Ways of connecting maths and science content are outlined in two articles abstracted in past editions of Curriculum Leadership. In the first, Jeff Marshall, Bob Horton and Joyce Austin-Wade describe an integrated course covering physics and pre-calculus for use in both maths and science classrooms. In the second, Sandra West and Selina Vásquez-Mireles offer science teachers a guide for developing correlated maths and science lessons. They argue that 'correlation' implies almost equal treatment of both subjects during teaching, aligned to relevant curriculum objectives, in contrast to 'integration' as the subordinate inclusion of one subject within another.
The relationship between curriculum reform, assessment and numeracy is examined by Jane Skalicky, who uses a social constructivist approach; the author also describes a case study of a social constructivist approach to assessment of numeracy.
Julia Anghileri reports on a study that evaluated the impact of England's National Numeracy Strategy on students' learning of division. Gains in students' understanding were found to be modest and uneven; gender differences are highlighted and discussed.
In a concrete illustration of numeracy, Lara Scharenguivel and Bin Deng write on how the data analysis experts help human rights advocates to interpret and apply human rights data through the use of statistical techniques and ICT.
General approaches to the teaching and learning of mathematics
In the following material, traditional methods are contrasted with the need for a deeper conceptual understanding of maths, as well as the additional need for maths that is more closely relevant to the workplace and society. The value of inquiry-based learning is a prominent theme in this section.
A Curriculum Leadership article by Liz Woodham describes England's NRICH website, which offers resources for a problem-based, process-oriented approach to teaching at all levels of school maths.
Ian Lowe offers an overview of the Victorian Essential Learning Standards (VELS), the Principles of Learning and Teaching (PoLT) that inform them, and related assessment and reporting mechanisms. The article also refers to the issue of mixed ability classes.
Lynn Arthur Steen makes the case for socially relevant maths as a means to improve teaching and learning within the subject area. This approach is designed to shift the emphasis in mathematics teaching from abstract concepts to approaches that seek to apply topics such as ratios and percentages to complex, data-rich topics like global warming and petrol pricing.
Anne Watson calls for school maths to move closer to professional mathematical practice, and urges a more unified approach to mathematical understandings across year levels. The article attracted a range of responses.
Edward Silver et al investigate the ways in which middle years teachers can encourage a deep conceptual understanding of mathematics among their students.
Also of interest is an abstract of a literature review by Eric Mann on the topic of creativity in mathematics.
Approaches for the primary years
Obstacles to maths learning among primary school students has attracted the attention of several authors. Another important issue has been the application of higher level thinking to maths at the primary level.
Articles published in Curriculum Leadership
In an article on numeracy, maths and learning difficulties, Anne Bayetto describes how Postgraduate Education students at Flinders University are helping to support young people who struggle with mathematics at a primary school in South Australia.
Beryl Exley and Kieran Abel consider the literacy demands involved in mathematics problems commonly posed to early years students. The authors describe recent research undertaken at the Queensland University of Technology into the wording and images used to depict mathematical problems in textbooks for young students.
Katie Makar reports on a study involving the University of Queensland and two primary schools, which examines how expert teachers can engage students in inquiry-based learning, while Joanne Mulligan highlights the possibility and value of helping young children to develop algebraic thinking from the early years of schooling.
David W Carraher et al also argue for teaching algebraic reasoning to primary school age children; they also report on a related study conducted by the authors. Kathy Checkley notes that the USA's National Council of Teachers of Mathematics (NCTM) has prepared standards that teachers can use to help young students to think algebraically. The NCTM standards also emphasise problem-solving, as well as the importance of communication in helping students understand how to apply their mathematical skills.
Scott K. Baker et al describe a study exploring a structured mathematics curriculum in the first year of primary school that included topics such as number sense, geometry, measurement, and mathematical vocabulary. In contrast, John Marshall argues that children best acquire abstract, symbolic understanding by generalising from a range of concrete examples.
Approaches for the secondary years
The previously mentioned article by Liz Woodham describes a publication offering rich mathematical tasks for secondary teachers in England. The articles abstracted in this section focus on the promotion of conceptually challenging secondary mathematics.
Jill Vincent and Kaye Stacey note that Australian students performed well in the 1999 TIMSS Video Study of classroom mathematics practice, but also that, on average, Australian students were not challenged to undertake complex mathematical procedures. The authors examined nine Year 8 textbooks from four Australian states, and found that in all of the textbooks most of the problems were of low procedural complexity.
Kim Beswick reports on a Tasmanian study of how two secondary mathematics teachers successfully created effective constructivist learning environments.
The use of ICT in mathematics teaching and learning
Technology raises issues in terms of the calls it makes for preparation in ICT-based careers, as a way to enhance learning, and as a contributor to a mindset among current students. Curriculum Leadership has featured several article abstracts examining these issues.
According to Alexander Khait, computers raise three key sets of issues for mathematics teaching: a new emphasis on procedures and rules; a shift in the hierarchy of difficulty among maths topics, and the steps by which different aspects of maths are best learnt; and the capacity of computers to make some mathematical ideas less abstract.
Neil Roberts also argues that ICT has changed the teaching emphasis in school mathematics from abstract reasoning to more specific problem solving. He sees a danger in the gradual loss of older teachers to younger teachers with different strengths, or who may be untrained in mathematics.
Merrilyn Goos and Anne Bennison report on a statewide survey of Queensland schools and mathematics teachers that explored the extent of technology use within mathematics classrooms. Margaret Scanlon et al note how games, especially computer games, have attracted academic interest as a means to create stimulating, realistic contexts for maths learning.
Teaching maths through ability grouping
An article by Doug and Barbara Clarke published in Curriculum Leadership argues that ability grouping in mathematics is a major impediment to the mathematical learning of students and their beliefs about themselves as mathematical thinkers. Any benefits realised from ability grouping are only to very high achievers.
Based on the analysis of a Grade 5/6 class familiar with inquiry-based learning, Gaye Williams and Nadia Cavallin support like-ability groups. Steve Thornton et al offer arguments for and against ability grouping, while Paul Turner suggests that it may be useful to differentiate maths instruction not by ability level but according to the different uses that students expect to make of the subject in future careers.
Peter Sullivan et al describe an approach to maths for upper primary and lower secondary students that is designed to meet the distinctive needs of struggling, mainstream, and advanced students while keeping all students involved in common tasks. The approach helps students of varying ability levels enjoy the benefits of whole-class discussion and debate.
The New Publications and What's New sections of Curriculum Leadership provide further information on the learning area of mathematics, and are available in archived editions available via the Back Issues link on this web page.
Many of the issues relevant to mathematics education also pertain to other learning areas. These issues include teacher supply, and ways to overcome obstacles to learning that are related to SES, gender and ethnic background. Curriculum Leadership plans to cover these issues in summary articles appearing in future editions.
Policy statements on mathematics in Australia are available from the Australian Curriculum, Assessment and Reporting Authority (ACARA) and via Education Services Australia's listing of Australian Curriculum Frameworks and Syllabuses.
Key Learning AreasMathematics
Subject HeadingsMathematics teaching
Information and Communications Technology (ICT)
Ability grouping in education