Should we replace high school maths with reasoning?

By Mohan Dhall
Representative image // Photo by Antoine Dautry on Unsplash

Learning maths doesn’t add up. The subject, as it currently is drafted and taught, needs to be removed from curriculum. Far too many children are scarred by the subject. It should certainly not be mandatory for Year 11 and 12 students.

Additionally, because of maths and how it is taught, generations of people have defined themselves as “incapable”, “dumb” or “not smart.” I know highly capable adults tell me they are “hopeless at maths.” Yet, these same adults manage finances, work rosters and time. They also carefully and competently manage kitchen measurements, make estimations, divide attention between competing tasks and between family members, based on a hierarchy of priority.

They manage complexity through applying rules, but not formulas.

Yet, these same adults conflate not having passed high school maths with not being able to mathematically reason.

Maths homework

In every school and almost every classroom in each high school nationally there is a significant proportion of children who do not enjoy maths and do not understand the concepts when they are covered by teachers. The word covered has been used instead of ‘taught’, as if children are not learning I contend have not been effectively taught. If they are not learning – and the teachers are otherwise competent – then we have a problem with the subject area.

Having numerical concepts covered in class, they are then required to spend hours weekly doing such relevant and important things as factorising, converting between fractions and decimals, or finding the area of triangles and circles. This homework is ostensibly to reinforce and embed understanding. Instead, many will use Chegg, ChatGPT or another AI tool to do it for them.

Yet, despite maths being a subject given priority in every school curriculum, allocated more hours than every subject other than English still we have a national crisis around the learning of maths. According to PIAAC results, nationally between 30 and 50% of all children leaving high school are either innumerate or functionally innumerate.

Rather than look at the irrelevance of the maths curriculum, authorities focus on its deemed importance. After all, it completes the STEM on the plant of logic-based subjects.

Relevant and relatable?

A fundamental tenet of teaching is that subject matter be made relevant to students and relatable. Alas, the focus in maths includes useless topics like introducing variables as a way of representing numbers using letters, evaluating numerical expressions involving a negative index by first rewriting with a positive index, and determining the equation of a parabola, given a graph of the parabola with the main features clearly indicated.

Whilst giving kudos and affirmation to those students interested in cerebral gymnastics, I have yet to meet any adult who routinely rewrites indices with a negative index as its reciprocal with a positive index. Seems I need to look harder.

Moreover, no adult I know has ever had to find the gradient of the tangent of a line, but they have had to differentiate between lenders and whether to fix or keep interest on the variable rate.

If not maths…then what?

Maths could be replaced with a more relevant and interesting subject such as “Logic, and critical thinking”. The subject would include problem solving and mathematical reasoning but not abstract maths. This would be kept separate. All students could study logic and critical thinking in each of their high school years.

The justification for this

This is a world where students are in danger of silos and echo chambers as a result of social media algorithms. The primary source of information may be via Discord, Instagram, Facebook, Telegram and Twitch. The capacity to critically assess sources of information for their independence and integrity is rapidly being eroded. A study of logic and a focus on inquiry would empower them to understand influences that might otherwise shape them.

Students should have a dedicated subject that seeks to teach reason and the application of logic. Included in this would be mathematical reasoning. Students can be taught how to apply deductive reasoning, inference, justify an argument on the basis of evidence and other reasoning skills. From a mathematical reasoning perspective, the evidence can include data sets (numerical literacy), statistics and alternative representations of data in visual forms.

Relevant, applicable, in-context mathematical principles and rules can be embedded where relevant through the content. This would give it a place and utility. It would not be seen as a separate cerebral activity outside of the bounds of normal life.

Keep abstract mathematics as a separate subject

Abstract maths, for those who deem it purposeful and meaningful for students to learn about the formula for drawing a parabola, can still be taught as an additional subject. This means in addition to students also studying logic and critical thinking.

Abstraction is not of itself irrelevant from a critical thinking perspective, but it can become selfishly cerebral. Nevertheless, it can be useful for higher order thinking in some subjects, including those studied later in university.

The beauty of logic and critical thinking

A course on thinking is the essence of what education should be about. Going to school is not just about learning, but also learning about learning. It is about problem solving and understanding frameworks for addressing real issues that affect life daily. Having a syllabus deal specifically with logic and critical thinking makes it applicable to ALL subject areas. In an age where specialisation creates a danger of not seeing our interconnectedness or understanding interrelationships this of great importance.

(The views expressed are solely those of the author’s)

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