This article describes a study of learning when students used interactive spreadsheet-based computer tutorials in a mathematical literacy course. It foregrounds theories relating to the role of computer technology (and specifically spreadsheets) as a mediator for learning of mathematics. It outlines the application of quantitative methods involving pre-and post-testing of students, both in the computer laboratory and in the lecture sessions, and discusses factors constraining the experimental design and the usefulness of the results. There are indications that the data reveal real differences between the learning experiences in the lecture sessions and the computer laboratories. It appears that in some respects the computer tutorials were more effective in conveying the concepts than the lecture sessions were. A method of analysing and representing the data, that tracks the extent of learning of concepts through the pre-and post-tests, was developed. It allows for the performance of sub-groups of students to be examined separately. This analysis shows that simple definitions of disadvantage (such as having English as a second language) are inadequate to account for the poor performance of students in the lower quartile.
There is a generally acknowledged need for students to be quantitatively literate in an increasingly quantitative world. This includes the ability to reason critically about data in context. We have noted that students experience difficulty with the application of certain mathematical and statistical concepts, which in turn impedes progress in the development of students’ critical reasoning ability. One such concept, which has the characteristics of a threshold concept, is that of proportional reasoning. The main focus of this article is a description of the development of a framework using an adapted phenomenographic approach that can be used to describe students’ experiences in the acquisition of the concept of comparing quantities in relative terms. The framework has also helped to make explicit the elements that constitute a full understanding of the requirements for the proportional comparison of quantities. Preliminary results from using the framework to analyse students’ responses to assessment questions showed that many students were challenged by proportional reasoning. When considering the notion of the liminal space that is occupied en route to a full understanding of a threshold concept, about half of the students in the study were at the preliminal stage of understanding the concept and very few were at the threshold
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