This research presents a case study at a South African University, involving students who had studied mathematics in a pre-undergraduate Foundation Programme (FP) and who were currently in their first year of study in Information Technology (IT) at the same institution. The study investigated a possible relationship between the teaching approach used in the FP mathematics classroom and the extent of students’ abilities to use important mathematical practices, such as using procedures flexibly; using representation; understanding/explaining concepts; questioning; justifying claims; disagreeing; strategising; and generalising, in an undergraduate IT context. Focus group interviews and task-based interviews were used to answer three related questions: “To what extent are students aware of differences in teaching approaches between FP mathematics and undergraduate study?”; “To what extent do students believe that their experiences of the teaching approaches in the Foundation Programme mathematics class have helped them in undergraduate study in other courses?”; and “In what ways are the mathematical practices taught in the Foundation Programme used in undergraduate study in IT?” A bricolage of learning theories was used as a framework for understanding the possible relationships between teaching approach, development of mathematical practices and learning transfer. The students in the focus groups described the teaching approach used in the FP mathematics classes as studentcentred, whereas many of the undergraduate IT lectures and tutorials were described as teachercentred. The students felt that the approach used in the FP mathematics classroom was beneficial to further study, in that it taught them how to become responsible for their own learning and brought about deep understanding of the mathematical concepts learned in the FP. The task-based interviews showed that all students used mathematical practices to solve IT problems to a greater or lesser extent. The use of these mathematical practices was best understood as being influenced by all past cognitive, social and cultural experiences, and was therefore not a case of “transfer” in the traditional sense of the word. Instead, the use of mathematical practices could be described as an extreme case of “cognitive accommodation” from a cognitive constructivist perspective, or a case of “generality” from a situative perspective. Furthermore, an inter-relationship emerged between student-centred teaching, students’ productive disposition towards mathematics, and the extent of “transfer” of mathematical practices to the IT domain. This interesting relationship warrants further investigation.

The purpose of this action research study was to investigate the affects of teaching through a situative perspective with story problems on students' understanding of fraction concepts and operations in my fifth-grade mathematics classroom. Students participated in twelve weeks of instruction. Data was collected in the form of pre and post tests, audiotaped and videotaped recordings of instructional sessions, and student work samples. Data analysis revealed that my students constructed their own knowledge about various fraction concepts and operations because students engaged in discussions, after solving story problems, that developed, extended and restructured their knowledge. One example of this occurred after students had solved an equal-sharing problem. Two students came up with different answers and another student explained why both answers were equivalent. Student work samples and post test results indicated that the one student's explanation was understood, adopted and extended by all the students in my class. The data also revealed that students' pictures typically represented the context and action of the story problems. For example, subtraction problems dealing with length were usually represented by number lines or horizontal rectangles with crossed-out markings to show the subtraction operation. Throughout this research study, I discovered that my students were capable of learning from each other and solving problems for which they have no preconceived algorithm. I also learned that analyzing students' work and listening to their discussions in ways that focused on their thinking, not their answers, provided me with information about what my students were grasping and not grasping.