So just what is conceptual understanding of mathematics?

There is substantial anecdotal evidence to suggest that students entering many mathematical sciences courses in HE are less well prepared than previously. At Keele University, we have been using the same diagnostic test to help students in their transition from School to University; the results over the last 15 years show substantial variation but no statistically significant fall in the average mark scored. In a small pilot study we set out to compare students’ mechanical skills with their conceptual understanding in order to understand this apparent dichotomy…