Iterative processes in mathematics education

There are many arguments that reflect on inductive versus deductive methods in mathematics. Claims are often made that teaching from the general to the specific does make understanding better for learners or vice versa. I discuss an intervention conducted with Grade 10 (15-year-old) learners in a small suburb in South Africa. I reflect on the iteration between inductive and deductive reasoning and show a link to transformational reasoning. The intervention, described in this paper, showed that the learners developed a good understanding of the concept of concurrency as a result of the modelling process. There is ample evidence that a lot of work has been done on modelling elsewhere in the world, but not much has been done using the specific iterative process. Furthermore, the intervention was conducted fully, using Sketchpad as a mediating tool. This in itself was a difficult task, but Sketchpad's ability to create conviction within a short period of time was essential in obtaining the results.