The Modelling Strategies Used by the Pre-service Teachers in Fermi Problems: The Task of Automatic Irrigation System

This study aims to explore pre-service teachers’ solution spaces and model strategies in the mathematical modelling tasks involving estimations. A case study method was employed in the research. 119 pre-service teachers participated in the study. The data were collected in two weeks. The pre-service teachers created groups consisting of four or five individuals according to their wishes. Thus, 26 different groups emerged. The modelling problem was designed by the researcher by considering containing the reality, authenticity, closeness, openness, and modelling competencies criteria. The data collection tools consisted of the worksheets and presentation records of the pre-service teachers. The deduction and induction analysis methods were used together in the data analysis. According to the obtained findings, it was determined that the pre-service teachers used five different modelling strategies. In the problem given within the scope of the number of elements that could fit in a surface, the “reference point” was used most; on the other hand, the “concentration measures” were used least. It is found that taking the area covered by a sprinkler model as a reference rather than the area occupied by sprinklers in the solution spaces produces more realistic results. The solutions spaces created within these strategies was used to detail the modelling process. It is significant for teachers who will apply a similar modelling problem to know the created different modelling strategies and solution spaces. It is thought that the solution spaces will provide a source for teachers to keep track of the information related to their students.