Changing attitudes to university mathematics through problem solving

University mathematics is often presented in a formal way that causes many students to cope by memorising what they perceive as a fixed body of knowledge rather than learning to think for themselves. This research studies the effects on students' attitudes of a course encouraging co-operative problem-solving and reflection on the thinking activities involved. The attitudinal questionnaire was shown to the students' teachers who were asked to specify the attitudes they expect from their students and the attitudes they prefer. This was used to give a ‘desired direction of change’ from expected to preferred. Before the course, half the students responded that university mathematics did not make sense. A majority declared negative attitudes such as anxiety, fear of new problems and lack of confidence. During the problem-solving course the changes were almost all in the desired direction. During the following six months of standard mathematics lecturing, almost all changes were in the opposite direction

Thinking mathematically : a framework for developing positive attitudes amongst undergraduates

This thesis tests the hypothesis that problem-solving activities caused positive changes in students attitudes towards mathematics. A pilot test, carried out in a problem-solving course at the University of Warwick, tested possible questions that would indicate change of attitudes. The findings indicate that the course affected students attitudes to mathematics in what was considered a positive manner. Using that experience gained through the pilot study, the main study was carried out at Universiti Teknologi Malaysia (UTM) in which data was collected from 44 students who took the course in problem-solving taught by the researcher. A pre-test, post-test and a delayed post-test (six months later) were administered, which included interviews with selected students and staff. To establish what might be considered a positive change, the staff at the Mathematics Department were asked what attitudes they would expect students have as a result of the mathematics teaching at the University, and then specify the attitudes they would prefer students to have. The direction of change between the two responses were considered to be positive, and this is defined as the "desired direction of change". The results show that the problem-solving course affected students attitudes such that the change, identified as the difference between pretest and post-test results, was largely in the desired direction of change. However, when students return to normal mathematics lectures many of the indicators reverted in the opposite direction; away from what the staff preferred