"Their main difficulty is that the pace of learning increases, and they have to be more self-reliant," said Alastair Gillespie.
He feels that new maths students are less well equipped in other areas, especially those not studying the subject exclusively. Physics students, in particular, suffer from a decreased emphasis on maths in that subject while at school.
Professor Gillespie said poor skills in basic algebra had been common since the early 1990s, and that students often struggled to carry a reasoned argument. "Also, there is little formal proving in Higher maths. Only in Advanced Higher do students really start proving in a rigorous way."
He said the value of learning by rote should not be forgotten. "It instilled the ability to work accurately. Teaching has changed, and the work done in schools to make things more interesting means the drudgery of such basic skills has been lost."