摘要：“Practice makes perfect” is an old adage. The question is: what is the relationship between theamount of practice and the level of perfection achieved? This paper presents a cyclical teachingapproach used in an undergraduate course that provides initial exposure to mathematical andeconomic reasoning using a problem-based approach involving finite mathematics and basiccompetence in economic principles. Students were assessed in the following areas: problemdefinition, solution formation and implementation, solution evaluation, and monitoring. Studentswere allowed repeated attempts in the form of word problems requiring use of mathematicalmodels to provide evidence that explicit learning outcomes were met. It was found that repeatedcycling through the same, explicitly defined problem solving and mathematical modellingprocess led to a gradual improvement. Detailed criteria were listed under each of the two majoroutcomes and students were provided with a check mark for each skill that was demonstratedand with detailed feedback on their performance. Each student was required to demonstrate eachskill at least twice. The student’s final grade was based on the proportion of abilitiesdemonstrated. Data showed that students improved with repeated cycling, and furthermore, thatstudents continued to demonstrate these abilities in subsequent attempts. The mean data showeda 58% improvement in economics knowledge, a 45% improvement in math modelling, and a33% improvement in problem solving abilities. Individual data showed that even those studentswho demonstrated limited abilities on a first attempt were able to successfully demonstrate theability by the last attempt. The findings suggest cyclical teaching helps to achieve demonstratedoutcomes and that practice does indeed lead to perfection.
