Mathematical reasoning has been neglected in Australian schools, but it is key to people’s ability to be strategic throughout their lives, claim researchers who are working to improve maths education across the nation.
A comprehensive review by the Australian Academy of Science (2015) recommended that national attention be directed to broadening “Australia’s focus from numeracy, to achieving the full set of mathematical proficiencies outlined in the Australian Curriculum: Mathematics.”
The review identified a number of gaps within the existing frameworks of mathematics education, at both primary and secondary levels. It argues that the key to filling these gaps is engaging students in exploratory learning experiences and developing mathematical reasoning.
Mathematical reasoning is the critical skill that enables students to use all other mathematical skills, such as evaluating situations, selecting problem-solving strategies and drawing logical conclusions, and “contributes to the development of children’s ability to be thoughtful, strategic and active in and beyond school”.
“There is great potential for improving the way maths is taught in schools,” claims Dr Sandra Herbert, a Deakin University researcher who has been involved in a program seeking to improve maths education.
“ReSolve: Mathematics by Inquiry” is one of the initiatives from the Australian Academy of Science review. It is an Australia-wide program, aimed at building inquiry-based approaches to teaching maths in schools, initially at primary level, and has overseen the development of resources grounded in the inquiry approach.
“Our resources (Special Topic 5) provide teachers with the skills to understand and assess mathematical reasoning, while also identifying how students are best able to develop it,” explained Dr Herbert.
“Through design research we developed trajectories for students’ growth in reasoning and have created a rubric to assess reasoning for teachers to use in primary classrooms.”
Dr Herbert has over 40 years of experience in the field of mathematics education and is Senior Lecturer in Education (Science and Mathematics) at Deakin’s Warrnambool campus. Her research has focused on Science, Technology, Engineering and Maths (STEM) teaching and learning across primary, secondary and tertiary levels and across a variety of STEM-related subjects. Over the past six years, her research has centred on mathematical reasoning.
“Many maths teachers do not have an adequate understanding of mathematical reasoning themselves because the intricacies of reasoning are hard to grasp,” said Dr Herbert.
“Many teachers tend to think teaching mathematical reasoning is about explaining, but it’s more than explaining. It’s about being able to generalise, analyse and justify, which is learnt through the guided self-discovery that occurs in inquiry learning. Not all maths teachers understand this, but we are doing our best to get the word out.”
She explained that the highest-achieving countries in maths emphasise developing students’ capacity for mathematical formulation throughout school and far earlier in the developmental process, embedding the inquiry-based approach within their national curriculum from early primary levels.
For instance, in Japan, teachers emphasise the real-world value of maths by allowing for more time to work through and explore one or two rich problems in a lesson, rather than on “busy work” on many simple problems.
Similarly, in Singapore, problem solving skills are formulated from early primary school, with systematic curriculum reviews taking place every six years.
Singapore has consistently performed above the global average. However, overarching systemic difficulties in Australia have prevented teachers from assembling holistic and coherent programs for their students.
Dr Herbert is now working with ReSolve to encourage primary teachers to use the resources available from the ReSolve website. She is also working to extend her research into secondary education through a collaboration with Monash University and the Singapore National Institute of Education that will investigate the teaching and learning of mathematical reasoning in early secondary schools in Australia and Singapore.
She recently shared her ReSolve findings at a New Zealand mathematics education research conference, where she encountered strong interest from many other education researchers.
“If you don’t have good maths reasoning, you see maths as a collection of isolated ideas,” she said.
“Mathematical reasoning is the glue that connects these isolated ideas together.”
Published by Deakin Research on 10 July 2018