Our ‘Mathematics Problem’ has persisted for 30 years. How can we improve the school to uni transition?

The concern extended beyond mathematics degrees to engineering, science, economics and other disciplines requiring a successful transition from school mathematics.

Three decades later, the problem remains. If anything, it has become more significant as universities have expanded participation and mathematically demanding disciplines have become increasingly important to modern economies.

So, what have we actually learned since then?

It was never just a knowledge problem

For many years, the discussion centred on student preparation. Did students know enough algebra or calculus? Were schools teaching enough proof?

These questions remain important, but decades of research have shown that they tell only part of the story. Students are not simply moving into more difficult mathematics. They are moving into a different way of thinking mathematically.

School mathematics already asks students to reason, solve problems and make connections, but the balance of expectations can change significantly at university. Students may be expected to work with greater independence, interpret formal definitions, justify claims in unfamiliar settings, connect ideas across topics and tackle problems with much less guidance.

Many students who achieved excellent results at school discover that some of the habits that previously made them successful need to be extended or adapted. This is not necessarily evidence of poor preparation. It is part of entering a new mathematical environment.

Why does the problem persist?

If we have known about these issues for thirty years, why do they continue? One reason is that there is no single cause of the 'Mathematics Problem'.

Transition to university mathematics is shaped by far more than curriculum content. Assessment practices, classroom expectations, opportunities to explain mathematical thinking, confidence and belonging, access to support, institutional cultures and the purposes mathematics serves in different disciplines all matter.

The transition experienced by a future mathematics major is not necessarily the same as that of an engineering, economics or data science student. Students also arrive with different educational experiences and expectations about learning mathematics.

Perhaps the most important lesson is that transition difficulties emerge from the interaction of these factors rather than from any single weakness in students themselves.

From preparation to handover

This understanding suggests that we may need to change the questions we ask. For many years, discussion has centred on preparation: how can schools better prepare students for university mathematics?

Although preparation matters, the language subtly places responsibility in one direction: schools prepare, universities receive.

Research points towards a different way of thinking. Rather than viewing transition as a gap that students must cross alone, we might think of it as a handover between two parts of an education system.

A successful handover depends on both sides understanding one another's expectations while recognising that school and university mathematics serve different purposes.

This does not mean schools should teach university mathematics, or that universities should expect schools to anticipate every future mathematical demand. Instead, it encourages dialogue about the mathematical practices students encounter, expectations often left implicit, and learning experiences that develop increasing independence.

Teachers have an important contribution to make because they know what students have experienced before university and understand the curriculum and assessment pressures shaping school mathematics.

A genuine handover requires universities to understand where students are coming from, just as schools need to understand where some students may be going.

How the research has changed

Research has evolved alongside this perspective. Early studies focused largely on proof, abstraction and advanced mathematical thinking. Later work examined institutional expectations, teaching practices and the different mathematical cultures students encounter at university.

More recently, researchers have explored confidence, belonging, identity, equity and participation, recognising that successful transition depends not only on what students know but also on whether they see themselves as legitimate participants in new mathematical communities.

Researchers are also studying mathematics beyond mathematics degrees, recognising that service mathematics has its own challenges and that success may look different in engineering, health sciences, economics or data science.

The research has become richer because the questions have become richer.

The next challenge

In a recent visionary paper published in Teaching Mathematics and its Applications, I argue that the field is now ready for another step forward. The next challenge is not simply to identify more barriers or to ask "what works?" through isolated interventions.

Instead, research needs to understand why particular approaches work, for whom and under what conditions. It needs to investigate how schools and universities can collaborate more effectively, how curriculum and assessment shape transition, and how professional learning can strengthen understanding across educational sectors.

Teachers should be part of that work, not simply recipients of its findings. Their knowledge of students, curriculum and class practice is essential if research is to produce realistic ways of improving the transition.

In other words, the next phase of research is as much about designing better transitions with educators as it is about explaining existing ones.

A shared responsibility

There is an encouraging message in all of this. The research is not saying that schools have failed, or that secondary teachers need to squeeze university mathematics into an already crowded curriculum. Nor should universities lower their standards.

Teachers already have many of the tools that matter for transition. When students explain why a method works, compare approaches, make sense of an unfamiliar problem, justify a conclusion or persist when the answer is not immediately obvious, they develop mathematical habits that can travel beyond school.

That does not mean every mathematics lesson should prepare students for university. Most students will not become mathematics majors, and school mathematics has purposes far beyond tertiary preparation.

But teachers can help students understand that learning mathematics is more than becoming proficient at familiar procedures. They can make reasoning, curiosity, uncertainty and explanation normal parts of doing mathematics.

Schools can also open conversations about what mathematics might look like after Year 12. University mathematics is not simply the next chapter of the school textbook. Depending on what students study, mathematics may become more formal and abstract, or be used differently in engineering, science, economics, health or data science.

Knowing that the rules of the game may change can help students make sense of the transition.

Universities have an equally important responsibility. They need to understand students’ school experiences, make new expectations visible rather than assume students know them, and provide opportunities to develop increasing independence.

They also need to listen to school teachers. This is why the idea of a handover matters. A good handover does not require one side to do all the preparation. It requires communication between both sides.

Thirty years after the 'Mathematics Problem' was identified, we need to stop asking “Who needs to fix this?” and instead ask “What can each of us contribute to a better transition?”

Secondary mathematics teachers already have much to contribute. The next step is to create stronger opportunities for schools and universities to learn from one another and turn that shared knowledge into better handovers for students.

References

*Howson, A.G. (1995). Tackling the Mathematics Problem. London Mathematical Society.

Hernandez-Martinez, P. (2026). The secondary-tertiary mathematics transition: A visionary research agenda for the field. Teaching Mathematics and its Application. https://doi.org/10.1093/teamat/hrag018