Mathematical research as a way of thinking
Research pathway
One AXIOVUM pathway from a question to a method, a tested argument and a course in which to practise the underlying capability.
Read analysisResearch and analysis
Read our analyses of published research and mathematical arguments. Each analysis includes its sources and limitations.
AI tutors: help, risks and independent learning
Evidence guide
Four studies show why assisted performance and independent learning must be measured separately. This page then offers an evidence-informed way to return the next step of the reasoning to the learner; that routine still needs to be tested.
Read analysisStatistical reasoning with generative tools
Research analysis
Rao and colleagues trace how five students move between a practical question, a graphing plan and AI output—and where those connections become difficult.
Read analysisProof, derivation and mathematical understanding
Curriculum analysis
What should a learner be able to justify after obtaining an answer? Three official course records help separate different mathematical demands.
Read analysisConfidence intervals: coverage and bias
Mathematical analysis
Follow the probability statement behind a confidence interval, then see how a shifted centre changes its coverage.
Read analysisWhen a greedy choice preserves the optimum
Mathematical analysis
An exchange argument explains earliest-finish scheduling—and pinpoints why changing the objective breaks its guarantee.
Read analysis