You may have heard the phrase ‘Ours is not to reason why, just invert and multiply’ when teaching or learning the division of fractions. Probably one of many maths rules you have come across. These rules can be useful when trying to pass an exam (though, if they are helping it’s probably not a great exam in the first place) , but if we’re trying to develop the next generation of STEM graduates, knowing a rule (or 20) isn’t going to cut it, and, in fact, it’s not cutting it. Australian PISA results have slipped from 11th to 29th in mathematics, and we are now sitting below the OECD Average, but what the results reflect is that Australian Students “...are good at knowing the rules of mathematics, but not good at understanding the reasons for those rules.”

The Australian Curriculum, Assessment and Reporting Authority (ACARA) has released its proposed changes to the mathematics curriculum for review, highlighting an increased importance in the development of conceptual understanding by placing problem solving and critical reasoning into the content and achievement strands. This is a welcome development in the teaching of mathematics in Australia. By emphasising the ‘why’s at the outcome level, the curriculum highlights to teachers the importance of not just developing a skill, but ensuring a deep understanding of the overarching concept. More than that, by building the curriculum around the core themes of ‘mathematical structures’, ‘approaches’ and ‘mathematising’, the curriculum ensures that mathematical skills aren’t siloed into domains like number, probability and measurement, but the links between topics are highlighted through the whole of the mathematics curriculum.

The teaching of mathematics globally has increasingly moved towards a thematic, conceptual approach, as distinct from the traditional procedural approach we may remember from when we were at school. This is not a rejection of mathematical fluency, but it is a recognition that traditional mathematical instruction is failing our students. Conceptual understanding is intertwined with procedural fluency. Deep understanding makes solving mathematical problems of all types possible, even when you haven’t seen the style of problem before. It also makes skills easier to learn, and can help ameliorate against common errors. On the flipside you need to have the automaticity of base level skills for the development of further mathematical understanding. Ensuring both are reflected in the curriculum gives Australian students the best chance to build their overall mathematical proficiency.

The development of conceptual understanding is also intertwined with the development of critical thinking and reasoning skills. Mathematics is not just a pen and paper, algorithm based subject, but a subject that allows for deep exploration, experimentation, and application in the real world. Allowing students to ask questions, to solve problems in multiple ways, and practise hands on experimentation allows students to begin to own their knowledge, and ideally have their own ‘Aha!’ moment where they discover a fundamental rule. Importantly though, these skills aren’t ‘mathematics’ skills, they’re important across the curriculum, and they give educators the chance to break out of the mathematics silo and get students to apply mathematical principles to applications in different subjects.

In today’s world where at any given time you have a calculator, mathematics education is more about asking questions, correlating information, and navigating through vast amounts of data. Emphasising conceptual understanding and critical thinking in the mathematics curriculum is a welcome update by ACARA. Not just for mathematical proficiency, but for the overall development of students. It continues the progress in ensuring mathematics isn’t a domain restricted set of rules, but it is a comprehensive part of how we view the world. At Matific, we place both the development of conceptual understanding and critical thinking as key parts of our pedagogy. It lays the foundation for a lifetime of learning, ensuring that mathematics isn’t a test of our memory, but the development of understanding. It gives students the confidence to apply mathematical principles in new situations, increases their curiosity and engagement, and eventually ensures that we develop full rounded students.

To find out more about how Matific can help you develop conceptual understanding and critical thinking in your students, contact us at australia@matific.com.