Analysing problem solving processes of mathematical modelling in the technology aided environment: an explanation on cognitive and meta cognitive structures

In the present study, it is aimed to explain cognitive and metacognitive structures occurred in modelling process within a technology enhanced environment. Cognitive structures in mathematical modelling process within a technology enhanced environment were explained with sub-stages, main components and main stages. In addition, metacognitive structures that affect cognitive activities were explained in the present study, and the difference between cognitive and metacognitive activities was also taken into account. Technology enhanced environment was designed with GeoGebra software, calculator, video, animation, photos and screen capture programme which were given with problem situation. The design of this study is grounded theory which is one of the qualitative research methods. The participants of the study are volunteer twenty secondary mathematics programme freshman students. Before the application, activities related to various mathematical modelling problems and various activities to understand the nature of GeoGebra were carried out with participants within duration of one semester. In data analysis, it was adhered to data analysis of grounded theory, constant comparative analysis, open, axial and selective coding was benefited. An analysis unit of codes in data analysis was generally a sentence but when to show in detail having some difficulties and to form categories sometimes a word or a situation was selected. At the end of the analysis, categories were formed corresponding cognitive and metacognitive activities that can explain modelling process, the relation among categories was explained by stressing the difference between cognitive and metacognitive, and lastly theories relating to technology enriched cognitive and metacognitive structures and models that explain these theories were presented. Solutions were carried out with groups which consisted of three students who want to work with each others. Data were collected from video transcriptions which involve groups' solution processes and thinking aloud for three mathematical modelling problems designed by researchers. Data were also collected from GeoGebra solution files, written solution papers and researchers' memos. Students were supplied with animation, video and photos related to problems and when they want to use a computer with GeoGebra installed beforehand, a computer was also given with problems. According to the findings obtained from the data, nine main components, nine main stages and fifty five sub-stages that explain these nine main stages and relations among them were presented with key features. When metacognitive structures in modelling process were examined, each dimension was explained with a number of categories such as; metacognitive planning dimension with six categories, metacognitive monitoring dimension with four categories, metacognitive evaluation dimension with seven categories and metacognitive prediction dimension with five categories. Metacognitive activities occurred with cognitive activities in modelling process; however, it was not a must for metacognitive activities to occur in the areas of cognitive activities occurred. Metacognitive activities in modelling process played a key role in regulating cognitive activities and irregular transitions among stages. Metacognitive structures occurred in all main stages and specifically had a role in transitions among main and sub-stages. While metacognition was regulating and improving effectiveness of cognitive activities in modelling process, three different terms as metacognitive activity, metacognitive structure, and metacognitive activity groups were seen. Technology has not changed main stages and components in modelling process, but it had both a central and supportive role in forming of sub-stages and metacognitive structures. Animation, video and photos given with the problems were seen as an important factor of appropriate solution strategy in solution process. The complexity of calculations arisen from real world solutions was minimised thanks to technology. The strength of GeoGebra in showing the relationship between algebraic and geometric representations played an active role in making comparisons on a regular basis in process, in realization of the continuous control easily, in increasing awareness, in accessing difficult numerical values and mathematical expressions easily, and in analysing them. In further studies with the help of cognitive and metacognitive activities occurred in mathematical modelling process rubrics can be designed considering cycles to evaluate learning activities on modelling problems. A different classification for mathematical modelling problems and activities can be raised with instructional modelling perspective. Metacognitive activities in process can be examined in detail as in micro levels. The effect of technology on process can be discussed with different dimensions or the effect of various mathematical softwares on process can be explained. Qualitative studies on the effect of group work on mental process and its' differences from the individual modelling process are seen as important research topics for the literature. Learning environment which integrate technology and mathematical modelling and reveal a rich mental process should be designed to ensure the development of education. To this end firstly teachers who can create such learning environments should be trained as individuals who both have knowledge in technology and mathematical modelling. Keywords: Mathematical modelling, Technology Enhanced Mathematical modelling, Cognition, Metacognition, GeoGebra, Mathematics Teacher Candidate, Collaborative Working, Grounded Theory