Mathematical integration throughout the BE: lecturer expectations versus student knowledge

Background: Students who perform well in high school mathematics often struggle at university with mathematical integration. Failure rates of 30-35% are common across first-year mathematics courses at The University of Queensland, with integration a threshold concept most students do not understand well even at the end of first-year. Do students who perform well at school somehow lose their integration knowledge between the end of high school and the start of university some four months later? Or did they actually not grasp integration at school yet somehow manage to achieve good grades? In order to assess the knowledge of incoming students and thus provide a benchmark against which their performance at university could be assessed, Kavanagh et al (2009) analysed the results of a competency test delivered prior to Semester 1. Whilst there were many positive outcomes of the competency test, which is now implemented every year by a number of national institutions, it highlighted mathematical integration as a difficult concept that many students struggled with. This difficulty was anecdotally reported to occur across the four-year degree program. Purpose: This research identifies the types of integration that are used throughout the engineering degree program, and academics' perceptions and expectations of students' integration skills. It forms the prelude to a teaching and learning initiative to address any deficit in students' ability to understand and apply mathematical integration to a variety of problems. Design/Method: Data on integration techniques used in courses across the four-year engineering degree program were collected via a survey. The same survey was used to obtain lecturers' perceptions of the level of students' integration skills, and whether there would be value in an online competency test for each integration technique used prior to their course(s). The second phase of the research (not reported here) will support students with appropriately timed tests and revision exercises. Results: Integration skills were found to be required across all years and disciplines, with a recurring theme of one-dimensional concepts. Lecturers at all year levels and across all disciplines thought that students' integration skills were either poor or, at best, satisfactory. Actual knowledge, assessed by the presemester competency test and end of semester examinations, supported this. Lecturers of higher level courses were more likely to rate skills as 'poor'. Interestingly, of those who said 'satisfactory', the majority taught courses where not much integration was used. Conclusions: Mathematical integration is a fundamental skill that all engineering students are required to use throughout their undergraduate and professional lives. Therefore it is important that any deficit in this skill be addressed. The next phase of this research will build on the work of Kavanagh et al. (2009), and will see integration competency tests administered before key courses in order to allow lecturers to assess the incoming cohorts' knowledge level, and also to allow students to revise knowledge before the course begins.