Schools should offer ‘abstract mathematics’ elective to drive critical thinking skills

In my view, this should have been extended to Years 9 and 10 Mathematics as well.

Instead of teaching mathematics, we could teach a critical thinking course with elements of mathematical reasoning in it.

For those students really interested in abstract mathematics, that could be a separate subject chosen on an elective line from Year 9 onwards.

It would also be titled 'Abstract Mathematics' so that students themselves can understand the types of thinking involved.

There would be no expectation that it be practical or relatable. Allowing students to do a thinking course and then opt for additional, further mathematics would be far more conducive to robust student learning.

A critical thinking course could be structured around building skills in deductive and inductive reasoning, logic, visual problem solving and also could be inclusive of some mathematical reasoning.

The mathematical reasoning components would be centred on the type of problem-solving, practical maths useful for living.

Such mathematics would lead to an understanding of concepts such as unit pricing, budgeting, understanding bills, paying off loans, estimating risk, assessing competing priorities on the basis of multiple factors and estimation.

A well-designed course could also add understanding to construction, health care, understanding packaging and commercial decisions, and so on. 

This critical thinking course would be far more useful for all students. Including skills in fact checking, questioning assumptions, interrogating evidence and, applying analytical reasoning in a range of contexts, would be useful and also engaging.

At present we have a crisis in mathematics education. We have far too many students spending time in maths classes disengaged.

If we add up the hours that are spent by students wasting time in classes where they feel disempowered it would shock.

For those interested in the numbers, consider this: a third of students in Year 9 do not meet basic numeracy standards. Yet they attend mathematics classes almost daily.

The effect of compulsory mathematics on the self-esteem and behaviour of a high proportion of students is negative. Surely it is not a goal of our education system to leave students feeling disempowered and incapable.

Moreover, it cannot be the goal of education to invest in timetabled classes that have a deleterious effect on learning.

Instead of two wasted years in the current Year 9 and 10 mathematics courses, there could be in an alternative course that offers mathematical reasoning, logic, and other forms of critical thinking essential to living a full life.

The mathematical content taught after Year 8 is mostly abstract and largely irrelevant post-school.

One of the criticisms of our education system is that much of what is taught is neither relevant nor relatable. Are we content that over 55 per cent of our adult population could not perform mathematics above level 2 out of 5 on the OECD PIAAC numeracy test, despite being able to navigate multiple competing priorities, manage risk, budget, and pay off a mortgage? 

A critical thinking course would be both relevant and relatable. It would provide students with the capacity to critique, to understand their own thinking, to solve problems and apply novel solutions.

It would empower them to inquire and to make inquiry purposeful. What students take from a subject in terms of skills applicable to real world problems they encounter in living would be affirming. 

Critical thinking is, at present, a general capability in the Australian curriculum. The teaching of critical thinking is supposedly embedded in all K-10 subjects.

Yet the constant refrain from teachers is that the curriculum is already too crowded. They report that it is content heavy, and that they are time-pressured.

In this context critical thinking is either not taught or is occasionally taught. We also hear that investment is required in meeting the needs of gifted and high potential students. 

Despite understanding the need for differentiation, for over a decade the education system has failed the test of cognition: do we teach thinking explicitly?

As we learn more about learning, we seem to discover that explicit teaching in a range of circumstances is highly effective. Yet we do not have a thinking course.

This seems counter-productive if a key goal of schooling is to create and develop thinking abilities as a purposeful, not incidental priority.

As in Singapore, perhaps we need to teach less and learn more. Or perhaps we need to be smarter about what we deem a subject. 

A dedicated thinking subject, inclusive of mathematical reasoning, would emphasise the priority of thinking in education. It would add to, and boost, the skills taught in other subjects.

At present in schools there is a deference when it comes to mathematics.

Deference means that teachers in non-mathematics subjects will tend to say the following if confronted with a numeracy issue in their class: “you are meant to do that in maths".

If we had a critical thinking course, deference would be highly unlikely. I would not expect teachers to routinely say, “you are meant to think in that course (but not learn to think in the one I do).” Such a statement would be anathema to their role as educators. 

In terms of cross-curricular integration, critical thinking classes as a standalone subject would also lend themselves to a freeing up timetabling for interdisciplinary studies.

At present, students are far too siloed because schools are too siloed. Those schools shaped around PBL and IBL will argue they already expose students to critical thinking, but they do not necessarily.

They do expose students to seeing problems from multiple perspectives, but they do not routinely steep students in logic, reasoning, guided fact checking and the questioning of assumptions. 

In replacing Year 9 and 10 maths with a compulsory critical thinking course and a separate elective Abstract Mathematics course, Australia would become a world leader in curriculum development.

Currently Australian curricula comes from elements of those seen almost everywhere else. When we have curriculum changes we tend to follow the lead, rather than lead.

In a globalised world there is divergence of curricula. No-one seems brave enough yet to question the relevance of the mathematics most kids everywhere learn. This is despite the evidence pointing to it being largely irrelevant for a high proportion of all learners.  

In my view, separating maths into two components, one of which is abstract and the other embedded in a critical thinking course, would demonstrate that we are a clever country - a responsive and innovative nation understanding the role of education in a changing and complex world.