Conceptualization of Approaches and Thought Processes Emerging in Validating of Model in Mathematical Modeling in Technology Aided Environment

Abstract

The aim of the present study is to conceptualize the approaches displayed for validation of model and thought processes provided in mathematical modeling process performed in technology-aided learning environment. The participants of this grounded theory study were nineteen secondary school mathematics student teachers. The data gathered from the video recordings received while participants were solving the given problems, the written responses related to the solution of the problems, the GeoGebra solution files and the observation notes taken by the researchers in the process of problem solving. The constant comparative analysis based on open, axial, and selective coding methods were used for data analysis through the grounded theory. The five substeps were emerged from data analyzing related to the process of the validation of model. It was determined that these steps were covered by discussing the unexpected results in real-life situations, comparing the real life results with the estimation based on the experiences or measurements, the problem data, the situations given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen that the technology-aided environment enriched the cognitive processes in validating step. With the help of this research's results, it was constructed a detailed description related to the cognitive processes which can be displayed for validating of model in mathematical modeling. It was considered that the study would bring a different perspective to the researchers towards the process of mathematical modeling.