Evaluating the impact of computers on the learning and teaching of calculus
Calculus has held its importance in the core undergraduate mathematics curriculum. The introduction of low cost microcomputers about 1979 has led some people to reconsider the content of the calculus curriculum. This investigation was about how microcomputer technology has been integrated into the teaching and learning of calculus to improve students' understanding. The study mainly focused on whether and how computers could influence students' learning of calculus concepts. The rationale for using microcomputer technology to enhance calculus learning was explored through interviews with teachers. But the main issue of concern here was whether and how, for first year engineering students, computers could influence their learning of calculus concepts. Following a survey conducted with teachers in sixth form colleges and universities, an experiment in realistic classroom environments was conducted because of the desire to obtain an in-depth insight into the impact of computers on students' learning of calculus concepts. Four groups in four different universities were involved in this main study; two served as computer groups (the computer was used in teaching); two served as non-computer groups (the computer was not used in teaching). Calculus (Differential and Integral) was taught over two semesters in all universities. The flow of ideas in this study shows several stages in the design where both quantitative and qualitative approaches were used in the collection and the analysis of data. The reason for combining quantitative and qualitative approaches was to demonstrate convergence in results, and to add scope and breadth to the study. Furthermore, this mixed approach was expected to bring meaningful information about the process of learning because classrooms as a whole, and also individual students and their idiosyncrasies could be analysed using these two approaches. Data was gathered from three sources in the main study. The pre-test was administered prior to the instruction in differentiation and integration and the post-test was given upon the completion of these topics. At the end of the post-test, computer groups were asked to complete a computer attitude questionnaire in order to gain background information. The pre-test and the post-test data were collected using a specially developed diagnostic test. The diagnostic test included 10 questions, some of them having several items dealing with similar content. Each item on the diagnostic test was scored on its own six-point scale, developed by the researcher and checked by a specialist in this field. The data from the pre-test, post-test and computer attitude questionnaire was coded, and analysis of variance and other techniques were used to analyze the results. In a follow-up post-testing, a few students were interviewed from each group in order to substantiate inferences deduced from the quantitative data. A pilot study of the test was performed with two separate samples of 14 and 18 A-level students, which served to check its administration and to improve the final version. Some questions were deleted and others were revised using item analysis information. Among a complex pattern of results reflecting the different teaching approaches, the computer groups did better than the non-computer groups, particularly on questions requiring drawing the graph of a derivative by looking at its function and recognising the graph of a function by looking at the derivative graph. Thus, the use of computers over an extended period of time and their availability when carrying out graphical tasks seem to make an impact on the performance of the students on graphical interpretations. Treatments in each group improved understanding much more so for A-level students than non-A-level students because the weaker students lag behind the rest of the class. In all groups the students showed a remarkable consistency in their errors. These results are interpreted in the light of previous research on understanding of calculus and recommendations are made to teachers and researchers.