Global trends in the teaching of mathematics

By Annie Facchinetti

“After 30 years of doing such work, I have concluded that classroom teaching … is perhaps the most complex, most challenging, and most demanding, subtle, nuanced and frightening activity that our species has ever invented … The only time a physician could possibly encounter a situation of comparable complexity would be in the emergency room of a hospital during or after a natural disaster.” Lee Schulman, The Wisdom of Practice

If there was a perfect way to teach mathematics, we would have discovered it by now. But there are so many variables, from student motivation, personality and ability, to teacher capacity, training and knowledge, to school funding and resourcing – it is rarely simple to find the ideal learning pathways and approaches for our students. This is particularly evident in Australia’s waning performance in international comparative testing. As of 2017, Australia ranked a dispiriting 39 out of 41 middle-income countries for quality education on the United Nations Children’s Fund report card. This echoes the results of the most recent round of Programme for International Student Assessment (PISA) results, which found that, although still above the OECD average, Australia’s performance in maths has declined since 2006.

In response to such concerns, the Australian Curriculum, Assessment and Reporting Authority (ACARA) recently released a series of studies comparing the Australian Curriculum with curricula of three jurisdictions that have experienced greater success in measures such as PISA: British Columbia in Canada, Finland and Singapore, although in a literature review of comparative education, ACARA noted that some caution needs to be exercised when evaluating the suitability of successful practices in one country for use in another due to differing socio-cultural, philosophical and operational factors. There are, however, some general principles that the reports surface that are transferable to an Australian context.

While the mathematics sections of the studies are largely affirming, identifying high levels of breadth, depth and rigour in the Australian Curriculum for primary levels, one area that is addressed more explicitly in all three of the comparative curricula is that of personalised learning. The British Columbia Curriculum acknowledges the “central place of the student” in its design (p.28) and recognises the role of teachers in catering to the range of abilities and capacities within a cohort. The Singapore Curriculum goes a step further, allocating students to a standard course at their Primary 5 and 6 levels if they are progressing adequately or to a Foundation Mathematics course if they need more time to acquire the basics. At the other end, the Finnish Curriculum aspires to offer higher performing students the opportunity to explore content in greater depth.

Personalising learning can be challenging for teachers due to time constraints and a lack of professional development in how to successfully implement a differentiated program in a primary maths classroom. With a growing recognition of the importance of catering for students at their point of need, resources such as Oxford Maths have been developed to offer explicit pathways for students who are working at standard and for those who require more support with the underlying concepts relating to a specific topic. Oxford Maths also includes a range of activities and challenges to extend the most capable learners in a class. This is supported by resources such as Peter Sullivan’s Open-ended Maths Activities and Challenging Mathematical Tasks, which allow students to access activities at their current level of understanding. The latter also includes enabling and extending prompts to cater for the full range of abilities within a class.

Another key point in the British Columbia Curriculum is the importance of reasoning and problem solving in the teaching of mathematics. The Singapore Curriculum likewise advocates understanding over rote learning of facts and processes, encouraging students to use different strategies based on reasoning and connections between concepts. Peter Sullivan’s books in particular target the development of these capabilities, fostering critical thinking by engaging students in activities that demand higher order responses. Oxford Maths also incorporates whole class, small group and individual activities that promote problem solving and the use of analytical skills, building students’ abilities to flexibly apply their learning in different situations.

An interesting point in the comparison of the Australian Curriculum with the Finnish Curriculum is the emphasis that the latter places on the use of concrete materials, not just in the lower levels, as is apparent in the Australian Curriculum, but also in Years 3 to 6. This enables students to more confidently and securely move from concrete to abstract concepts in mathematics. This philosophy underpins Oxford Maths, which even in Year 6 uses a variety of materials and resources to engage students in rich learning experiences to enhance their understanding.

Another similarity between the Australian Curriculum and the Finnish Curriculum is consideration of the attitudes of learners. The Finnish National Core Curriculum aspires to foster positive attitudes and a sense of self-efficacy in mathematics students. The rationale for the Australian mathematics curriculum has a comparable aim, suggesting that students should become “self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences” (ACARA, n.d.). Oxford Maths seeks to enable all students to experience success in each maths lesson, using a combination of targeted activities and collaborative tasks that allow students to learn from and challenge each other.

Teacher competency is a final key theme that emerged from ACARA’s comparison studies. In both British Columbia and Finland, the observation was made that successful curriculum delivery “is reliant on the ability of teachers to provide learning programs to provide the skills and understandings which are described in the key content area [or Big Ideas]” (p.72). A program such as Oxford Maths provides comprehensive methodology, organisational information and appropriate learning activities to support classroom teachers to effectively nurture both the content and the mathematics skills required by today’s learners.

Australia has a unique context that requires an approach and resources that are designed specifically for our students. We can, however, learn from international success stories and adapt effective practices to suit our own settings and students. Personalised learning, focusing on understanding underlying concepts and not taking away concrete materials too early are all evidence-based strategies that have a place in our mathematics programs and are an integral part of many of Oxford University Press’s Australian-designed resources.

ACARA. (2018a). International Comparative Study: The Australian Curriculum and the British Columbia New Curriculum. Sydney: ACARA. Retrieved from

ACARA. (2018b). International Comparative Study: The Australian Curriculum and the Finnish National Core Curriculum. Sydney: ACARA.

ACARA. (2018c). International Comparative Study: The Australian Curriculum and the Singapore Curriculum. Sydney: ACARA.

ACARA. (2017). Literature review: contemporary approaches to comparative education research. Australian Curriculum, Assessment and Reporting Authority.

ACARA. Rationale.

PISA 2015 key findings for Australia – OECD. (2018).

Singhal, P (2017) “UN agency ranks Australia 39 out of 41 countries for quality education”, The Age, 16 June 2017

Explore Oxford University Press Australia and New Zealand’s primary maths and secondary maths resources.

 

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