Higher Maths: the impossibility of 'teaching to the test'

In a BBC article  published shortly after the 2026 Higher Maths examination which provoked a 15,000-signature petition  protesting its alleged unfairness, an S5 pupil who hopes to study medicine said that she had felt "well prepared" as she had "done four years' worth of past papers."

Explaining that she had "got really upset" while sitting the non-calculator Paper 1, the pupil said: "I thought I was really prepared, and had the impression that I was over-prepared but it was so different to what I'd done before."

This pupil's experience was far from unique, but it drew predictable criticisms, with some teachers pointing to "four years' worth" of past papers as evidence of a shallow revision strategy. Yet blaming the pupils doesn't get to the root cause, and in that respect, the petition has something of a point.

Reality vs perception

Objectively, this year's Higher Maths papers were entirely fair. This has been robustly demonstrated by two separate analyses by Maths.scot  (Paper 1) and by the Scottish Mathematical Council  (both papers).

Yet subjectively, many candidates were genuinely distressed when faced with Paper 1, saying that they found it "totally unrecognisable" and "out of step with every previous paper."

To understand this situation, we must bridge the chasm between the objective reality and a great many pupils' subjective experiences.

Teaching to the test

Several commentaries have suggested that 'teaching to the test' may be the primary reason for candidates' ill-preparedness. James McEnaney, writing in The Herald , claimed that "a lot of what happens in National 5 and Higher courses is just some version of teaching to the test."

Similarly, Dr Stuart Waiton, writing in the Scottish Union for Education Newsletter , warned of "school education coming to be a relatively unthinking form of teaching to the test."

The Scottish Mathematical Council  hinted similarly: "Teachers should embrace clever examination questions which do not mirror routine types but encourage deeper thinking, preparing students with such questions in class whenever possible."

The true nature of Higher Maths

The Higher Maths Specification , published in 2013 by the Scottish Qualifications Authority and inherited by its successor body, Qualifications Scotland , details the course content, how it should be taught, the structure of the two exam papers and how pupils should prepare for assessment.

The specification states that the course is intended to provide "breadth, challenge and application," aiming to "motivate and challenge candidates." Pupils should be prepared to "think logically, provide justification or proof, and solve problems," and to "communicate mathematical information with complex features."

Reasoning skills should include "analysing a situation" and "explaining why a particular solution is appropriate in a given context." Approaches to learning and teaching should include "solving problems and thinking critically," as well as "explaining thinking, and presenting strategies and solutions to others."

In respect of the exams, the specification says: "Candidates draw on and extend the skills they have learned during the course." The papers should "provide opportunities for candidates to apply skills in a wide range of situations, some of which may be new."

With roughly 65% of marks allocated to routine operational skills and 35% dedicated more to reasoning, the exam papers are designed to test higher-order thinking, including some new and unfamiliar contexts, extending the course content and skills.

Therefore, true 'teaching to the test' should mean teaching in such a way that actively prepares students for the actual test, including non-routine questions requiring interpretation, analysis and extension of the taught content.

So what has gone wrong?

The underlying causes of this situation lie not within Higher Maths, but in the structural dismantling of Scotland's previous curricular strength from P1 to S4 over the past two decades.

The Scottish 5-14 curriculum, used from the early 1990s until 2010, was built like a scaffolding system. It split mathematics into clear strands mapped across six strict levels (A to F) with highly specific attainment targets at each level. Progression was gated by teacher judgment backed by a bank of national tests, confirming mastery of each outcome at each level. Because the steps were small and sequential, it was difficult for a student to develop substantial gaps in their knowledge or skills without it being flagged.

Curriculum for Excellence , on the other hand, replaced this tight scaffolding with expansive 'experiences and outcomes' and multi-year 'benchmarks' that frequently favour generic competencies over specific skills. Progression from P1 to S3 is tracked loosely across broad bands as 'Developing', 'Consolidating' or 'Secure'. Under this amorphous framework, a student can easily coast through primary or early secondary education appearing to be 'on track' because they have grasped general concepts, while fundamentally lacking mathematical fluency. Without regular diagnostics and interventions, group work and cross-curricular projects can mask significant learning gaps.

Similarly, the one-year National 5 represents a step backwards from the two-year Standard Grade. The Credit paper was unashamedly rigorous, abstract and targeted solely at upper-quartile ability. Scoring a grade 1 or 2 at Credit meant that you had proven your readiness for Higher Maths.

By contrast, National 5 Maths  emphasises algorithmic drilling and predictable question formats. Teaching approaches imported from National 4 or Applications of Maths further compound these factors. Students can comfortably achieve grade A or B at National 5 by picking up accessible marks across a broad, shallow syllabus, despite substantial deficiencies in their knowledge and skills.

In addition, Standard Grade included mandatory 'investigations'. Students explored open-ended mathematical scenarios by devising conjectures, proving results, communicating findings and suggesting further avenues of research. This required genuinely deep understanding and helped students develop the emotional and cognitive resilience needed to get stuck but work their way out, providing a far superior foundation for Higher Maths than National 5, where no such rigour exists.

Scotland's retrograde curriculum changes have resulted in more S5 pupils being unprepared for the rigours of the relatively unchanged Higher Maths course. Teachers, faced with this reality, do their absolute best. They teach the core content and drill their pupils in past paper question types, thereby helping them gain as many routine marks as possible. As a result, because truly strong mathematical foundations are now rarer, students rely heavily on pattern recognition and familiar wording rather than genuine understanding. The moment an exam introduces even slight changes to layout, focus or vocabulary, widespread confusion follows.

Concluding remarks

True 'teaching to the test' for Higher Maths would include exactly what the Scottish Mathematical Council  says it should: "clever examination questions which do not mirror routine types but encourage deeper thinking."

But Higher Maths teachers cannot build critical thinking on quicksand. The architectural failures of the current curriculum mean that the foundation years (P1 to S4) are no longer designed to build the necessary stamina, deep fluency or problem-solving resilience. When Qualifications Scotland designs an exam that perfectly satisfies the rigorous demands of the Higher specification, they are testing a student body that has been systematically deprived of the structural scaffolding needed to meet it.

What now? If Scotland wants to close the traumatic disconnect between student perception and exam reality, tweaking individual exam papers is not the answer. The solution requires looking backward to move forward. Policymakers must shelve the Hayward proposals , which threaten to further dilute external exams into internal assessments, and inject the systemic rigour of the old 5-14 framework and the unfiltered challenge of Standard Grade Credit back into secondary education.

Until the curriculum is explicitly redesigned to cultivate deep knowledge and mathematical independence over superficial pattern recognition, true 'teaching to the test' will remain an impossible task, and thousands more capable, hard-working students will continue to underperform at Higher.

 

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