University Students Modeling processes While Engaging in Modeling Activities with and without a Technological Tool

Mathematical modeling is an alternative method for teaching and learning mathematics, where the modeling activities start from real life situations and problems that students need to solve and find models in order to generalize the problems. Performing modeling activities involves performing different learning processes: real life processes, logical processes, communicational and mathematical processes. Thus, engaging in modeling activities is needed in the mathematics classroom. This made me want to experiment with modeling activities with university students who will become teachers and examine the modeling circles in which they engage with in the presence of technology and without it. The researcher chose the participants from the faculty of educational sciences in An-Najah National University. Eighty one students participated in the research in groups of 3-5 students. The groups were built according to the students' will. These groups were given three modeling activities: The giant bird activity, the shoes activity and the bean plants activity. Each group was requested to video their learning while carrying out the modeling activity and give reports regarding the phases through which they went to arrive at the mathematical model. The researchers used the videos and reports to anlyze the groups' modeling cycles and phases during the activities. The current study answered the following three research questions: (1) what are the cognitive psychological modeling phases that university students go through when they use technology? (2) what are the cognitive psychological modeling phases that university students go through when they do not use technology? (3) what are the differences between the modeling phases that university students go through with technology and without it? The research findings show that the groups of university students carried out the three modeling activities using different modeling cycles. Nevertheless, these modeling cycles were similar in including the following phases and processes: real life explanations, logical explanations, arithmetic operations and building mathematical models. Moreover, some groups performed validation of the models they built by applying it to the real life problem that the model came to generalize. The modeling phases and processes of the different groups differed in some of their aspects, namely students' need for additional information, decision making regarding the real life situation, decision making regarding the technological tool to use, and the mathematical processes needed to arrive at the mathematical models. The similarities between the modeling phases and processes of the different groups could be due to the properties of the modeling activity. At the same time, the differences between the groups in their modeling phases and processes could be due to the characteristics of each group regarding the mathematical and technological abilities of its members. The researcher recommends that mathematical modeling be part of the mathematics curriculum, not only in university, but in the different school levels too. This integration of mathematical modeling in the curriculum could be done with or without technology. Moreover, this integration requires that mathematics teachers by prepared to integrate modeling activities in their classrooms, and, at the same time, be prepared to use technology (GeoGebra, applets, spreadsheets, etc.) in their classes in general and in mathematical modeling in particular. The integration of modeling activities and technology in the mathematics classroom will enrich students' learning of mathematics and support their independent learning of meaningful mathematics. The researcher also recommends that additional qualitative studied by performed regarding using mathematical modeling in the classrooms, which will give mathematics teachers a more detailed view of the contribution of this relatively new method to students' learning of mathematical phenomena, concepts and relations