How is the modern education system cheating its own students?

Edition 14: There is no systematic attempt to nurture any of the 15 thinking skills through maths.

Ask anyone which school subject best develops thinking.

Most will say mathematics.

They are not wrong about the potential.

They are entirely wrong about reality.

Mathematics, as it is currently taught in the vast majority of classrooms around the world, does not develop thinking.

It develops procedure-following. And procedure-following, however complex and demanding, is not the same as thinking, any more than reading the notes on a page is the same as making music.

The tragedy is not that mathematics fails to develop thinking skills incidentally.

It is that it fails to do so systematically, across all fifteen dimensions of thinking that a complete education should build.

A subject with more inherent potential to develop the human mind than almost any other has been reduced, through decades of exam-driven instruction, to a sequence of steps to be memorized, applied, and reproduced.

We have taken one of humanity's greatest intellectual achievements and turned it into a collection of recipes.

What the 15 Thinking Skills are, and why mathematics should develop all of them:

In four decades of research, I have identified 15 distinct thinking skills that every educated human being needs to function effectively in life.

They include logical reasoning, abstract thinking, creative thinking, analytical thinking, critical thinking, sequential thinking, spatial thinking, lateral thinking, inferential thinking, evaluative thinking, reflective thinking, systemic thinking, convergent thinking, divergent thinking, and metacognitive thinking.

Mathematics, by its very nature, has the architecture to develop every single one of these.

A well-taught mathematics lesson is simultaneously an exercise in logic, abstraction, creativity, analysis, and inference.

A genuinely mathematical mind can reason sequentially and think laterally at the same time, which can converge on a precise answer while remaining open to divergent approaches for getting there.

This is what mathematics could be in the hands of education. This is rarely what it is.

What the system does instead:

The modern mathematics curriculum is built almost entirely around procedural knowledge, the memorization and application of established methods for solving predetermined categories of problems.

A student is shown a technique.

They practice that technique on variations of the same problem type.

They are assessed on their ability to reproduce that technique accurately and quickly under examination conditions.

At no point in this cycle is the student required to think in any of the fifteen senses that genuine thinking demands.

They are not asked to reason logically because the logic is already embedded in the procedure they have been given.

They are not asked to think abstractly because the abstraction has already been done by the mathematician who designed the method.

They are not asked to think creatively because creativity is not required when the path to the answer is already mapped.

They are not asked to think critically because there is nothing to critique when the method is presented as an unchallengeable fact.

They are asked only to follow. To apply. To reproduce.

This is not thinking. This is compliance, dressed in the language of rigor.

The procedural trap:

There is a deeper problem beneath the surface.

When mathematics is taught as procedure, students develop an implicit belief that every mathematical problem has a known method, and that the method will be provided if they are patient enough, and that their job is to identify which method applies and execute it correctly.

This belief is mathematically false and cognitively catastrophic.

Real mathematics, the mathematics that built the modern world, that underlies every scientific and technological advance is almost entirely the opposite of this.

It is the discipline of encountering problems for which no method yet exists, and constructing one.

It is the practice of reasoning from first principles when the familiar framework no longer applies.

It is, at its core, a creative and deeply human endeavor.

The student trained only in procedure has been given a powerful set of tools and told never to ask what else those tools might build.

The real-world consequence:

A student who has spent twelve years in mathematics classrooms without developing a single thinking skill systematically does not leave school as a mathematical thinker.

They leave as a competent calculator, and in a world where calculation is performed almost universally by machines, the value of that competency is diminishing rapidly.

What does not diminish, what becomes more valuable every year, is the ability to reason, to analyze, to think creatively under uncertainty, to approach an unfamiliar problem without panic and construct a path through it.

These are the thinking skills mathematics should have built.

These are the skills that every employer, every institution, and every domain of adult life demands.

And these are the available skills – inherent in the subject itself – and were never systematically developed.

Meanwhile, students who struggle with mathematical procedure are quietly and incorrectly concluded to be poor thinkers, when in reality they may be extraordinary thinkers whose particular thinking strengths were simply never the ones the procedure-based curriculum required.

We have used mathematics to filter minds when we should have been using it to develop them.

So what should change?

Mathematics teaching must be rebuilt around thinking, not procedure.

This does not mean abandoning rigor; it means redirecting it.

The goal of a mathematics lesson should not be a correct answer.

It should be a thinking process, one that is visible, examinable, and deliberately developed across all fifteen dimensions of thinking skill.

Students must be given problems that do not have predetermined methods – problems that require genuine reasoning, genuine creativity, and genuine tolerance for uncertainty.

They must be assessed not just on whether their answer is correct, but on the quality, originality, and logical coherence of the thinking that produced it.

Teachers must be trained not just in mathematical content, but in mathematical thinking, so that they can model what it looks like to encounter an unfamiliar problem and reason through it, rather than simply demonstrating a technique and asking students to replicate it.

And institutions must accept that a mathematics curriculum which produces students who cannot think mathematically – who freeze when a problem falls outside a familiar category – has failed in its most fundamental purpose, regardless of how impressive its examination results appear.

Mathematics is the language of thinking.

We have been teaching the alphabet and calling it fluency.

"How is the modern education system cheating its own students?" – Edition 14 of an ongoing series based on four decades of research and observation. Do you remember a mathematics problem that genuinely made you think – that had no obvious method and required you to reason from scratch? Or did mathematics, for you, feel like following a recipe you had not written and did not fully understand?