摘要：“Practice makes perfect” is an old adage. The question is: what is the relationship between the amount of practice and the level of perfection achieved? This paper presents a cyclical teaching approach used in an undergraduate course that provides initial exposure to mathematical and economic reasoning using a problem-based approach involving finite mathematics and basic competence in economic principles. Students were assessed in the following areas: problem definition, solution formation and implementation, solution evaluation, and monitoring. Students were allowed repeated attempts in the form of word problems requiring use of mathematical models to provide evidence that explicit learning outcomes were met. It was found that repeated cycling through the same, explicitly defined problem solving and mathematical modelling process led to a gradual improvement. Detailed criteria were listed under each of the two major outcomes and students were provided with a check mark for each skill that was demonstrated and with detailed feedback on their performance. Each student was required to demonstrate each skill at least twice. The student’s final grade was based on the proportion of abilities demonstrated. Data showed that students improved with repeated cycling, and furthermore, that students continued to demonstrate these abilities in subsequent attempts. The mean data showed a 58% improvement in economics knowledge, a 45% improvement in math modelling, and a 33% improvement in problem solving abilities. Individual data showed that even those students who demonstrated limited abilities on a first attempt were able to successfully demonstrate the ability by the last attempt. The findings suggest cyclical teaching helps to achieve demonstrated outcomes and that practice does indeed lead to perfection.
