Why Mathematics Becomes So Difficult: The Challenge of Solving New Problems
Many parents notice a striking change in their child’s relationship with mathematics during the teenage years. A subject that once felt manageable, even enjoyable, can suddenly become a source of stress, confusion, or avoidance. Homework takes longer, tests feel unpredictable, and confidence often declines, sometimes quite sharply.
This shift is frequently misunderstood. It is tempting to attribute it to a lack of effort, motivation, or aptitude. In reality, one of the most important reasons mathematics becomes harder in adolescence is that the nature of the subject itself changes. As students progress through secondary school, mathematics increasingly focuses on solving unfamiliar problems, rather than applying well-rehearsed methods.
Understanding what makes this kind of problem solving so demanding can shed light on why so many capable teenagers struggle and why those struggles are not a sign of failure.
A fundamental shift in what maths asks of students
In the early years of schooling, mathematics often rewards repetition and accuracy. Pupils are taught a method, practise it extensively, and are assessed on how reliably they can reproduce it. Success comes from recognising a familiar type of question and applying a known sequence of steps.
As students move through secondary education, this approach gradually gives way to something more complex. Mathematics begins to ask pupils to:
Decide which method might be appropriate
Combine ideas from different areas of the curriculum
Adapt known techniques to unfamiliar situations
Justify or explain their reasoning
Problems no longer announce themselves clearly. There may be no obvious starting point, and the solution method is rarely identical to anything practised before.
For many teenagers, this feels deeply unsettling. A common complaint is, “We were never taught this,” when in fact they were taught the underlying concepts. What they were not taught was how to recognise when and how to use them in a new context. Mathematics, at this stage, becomes less about following instructions and more about making judgements.
The often invisible work of interpretation
One reason novel problems are so difficult is that much of the work happens before any calculation begins. To solve an unfamiliar mathematics problem, a student must first interpret it. This involves:
Reading carefully and precisely
Deciding which information is relevant
Ignoring distracting or unnecessary details
Translating a real-world or verbal situation into mathematical form
This process is cognitively demanding and often underestimated. Word problems, for example, are not simply tests of mathematical knowledge; they also require strong language comprehension and logical reasoning. A single misunderstood phrase can derail an entire solution.
From the outside, it can look as though a student “doesn’t understand the maths”, when in reality the difficulty lies in making sense of the situation the maths is meant to represent.
Novelty, uncertainty and the emotional cost of not knowing
Unfamiliar mathematical problems introduce something that many teenagers find deeply uncomfortable: uncertainty. Teenage brains are still developing, particularly in areas related to emotional regulation and decision-making. When a pupil encounters a problem they do not immediately know how to approach, the brain may interpret that situation as a threat rather than a challenge. This can trigger a stress response that interferes with working memory and logical reasoning, making it even harder to think clearly.
In practice, this can look like:
Freezing or blanking during tests
Rushing into an incorrect method
Giving up quickly when the answer is not obvious
Adolescence is a time when self-image is particularly fragile, and repeated experiences of confusion can quickly erode confidence. Mathematics, with its clear right and wrong answers, leaves little room to hide uncertainty. As a result, some students disengage, not because they do not care, but because caring feels risky. Avoidance can become a form of self-protection.
The role of executive function
Solving new problems places heavy demands on executive function, the mental skills responsible for planning, organising, monitoring progress, and adjusting strategies.
A student tackling an unfamiliar problem must:
Hold several pieces of information in mind at once
Decide on a plan of attack
Keep track of multiple steps
Notice when an approach is not working and change direction
These skills develop gradually throughout adolescence and into early adulthood. It is therefore entirely possible for a teenager to understand individual mathematical concepts but struggle to coordinate them effectively under pressure.
Speed versus understanding
In many education systems, mathematics is taught and assessed at pace. Lessons move quickly, curricula are dense, and timed examinations are common. While this can encourage fluency, it can also disadvantage students who need more time to think.
Novel problem solving is rarely quick. It often involves:
Pausing to understand the situation
Trying an approach that may not work
Reflecting and revising
When speed is prioritised, careful thinkers may conclude that they are “bad at maths”, even when they are engaging deeply with the material. The system can unintentionally reward rapid recognition over thoughtful reasoning, despite the fact that true mathematical understanding depends on the latter.
Struggle is not a sign of failure
It may surprise parents to learn that professional mathematicians spend much of their time feeling unsure. Confusion, false starts and dead ends are not incidental to mathematics; they are central to it.
However, students rarely see this reality. They see finished solutions and efficient methods, which can create the impression that competent mathematicians never struggle. When teenagers encounter difficulty, they may assume that something has gone wrong, rather than recognising that they are experiencing mathematics as it truly is.
A different way of understanding the difficulty
Seen in this light, the challenge of novel problem solving is not evidence that mathematics has suddenly become inaccessible. It reflects:
The increasing cognitive demands of the subject
The developmental stage of the adolescent brain
The emotional weight of working under uncertainty
When a teenager struggles with unfamiliar problems, they are not failing to learn mathematics. They are encountering it at a deeper, more demanding level.
And while that experience can be uncomfortable, it is also the point at which genuine mathematical thinking begins.
