This miniproject attempted to provoke an open discussion of the link between need for deep understanding (conceptual understanding) as opposed to surface learning (methodological understanding). This debate, known in the United States as the Reform Movement, has had a substantial influence on redefining the mathematic curriculum throughout the US for both the reform and so-called traditional colleges.
Specific expected outcomes were:
1. A validated test and questionnaire for investigating the link between conceptual understanding and methodological ability of mathematics students;
2. A number of articles about the causal link between conceptual understanding and methodological ability of mathematics students; and,
3. A final report giving complete details and conclusions of the study.
There had been substantial anecdotal evidence prior to this project to suggest that students entering many mathematical sciences courses in HE are less well prepared than previously. At Keele University, the mathematics department 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 significant fall in the average mark scored. In 2007-2008, a small pilot study was carried out at Keele University to investigate the perceived difference between students’ mechanical skills and their deeper conceptual understanding. The conclusions of the study led credence to the efficacy of providing substantial resources to the many students who struggle with mathematics when they first arrive at university.
The results were of sufficient interest, that funding for a national study was sought from the MSOR.
Results and conclusions of the national study:
1. This project showed that many students transferring to university to read mathematics have not made the leap from procedural knowledge to a conceptual understanding of mathematics as taught in the first year of mathematics degrees at universities in the UK and elsewhere. However, it appears that this deeper level of understanding has been established in many students as they start their second year of a mathematics degree.
2. There is evidence to suggest that some staff teaching first year mathematics have higher expectations regarding their students’ understanding and perceptions in mathematics when they transfer to university.
3. The refocusing of the project in year two to investigate the effect of group working confirmed the higher scores observed in the first year of the project. The value of such collaborative working needs a more detailed investigation to determine whether this improvement is due to pooling of knowledge or improvement in understanding by group discussion.
With the current increase in students opting to study mathematics at university, there is an obvious need to pursue these recommendations if educators are to provide an optimum environment for these students to develop their mathematical skills to fulfil their individual goals.