Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Turkey
Approval Date: 2010
Student: HÜSEYİN CAHİT KAYHAN
Supervisor: ZİYA ARGÜN
Abstract:When someone converts from one kind to another of fractions many kind of mental activities take place. Students use lots of activities in their minds when they perform an action. Such kinds of mental processes become actions that are carried consciously or unconsciously. Since these mental actions are abstract objects, phenomena, images etc. it is considerably difficult to explain these actions. Literature says that, observation of students' mental processes by another person is fairly difficult. Consequently describing mental models, their development and someone else's understanding are very hard and difficult. There are some ways in converting fractions each others. In this study by means of determining students' mental models of fraction converting, firstly it is tried to identify their knowledge about fraction concept. As a topic of primary schools mathematics curriculum, fractions converting provides a good context for emphasizing the importance of mental models in learning a topic. This is important not only with respect to learning but also with respect to getting solid clues for answering how this topic can be taught. Teaching of fraction is started from first grade of primary school until 7th grade. Then, teaching of rational numbers and real numbers follow up this topic. The aim of this research is to identify primary school students' mental models when they are asked to solve problems related to fractions converting to each other and comparing the similarities and differences between these mental models. Hence, problems that were related to attainment targets that exist in primary school (1-8) mathematics program about converting fractions are prepared in this study. Converting one type of fraction to another type was investigated basically under four headings; namely converting improper fractions, mixed fractions, proper fractions and decimal fractions to another type of fractions. Participants of this research were 8 students; four of them were 5th graders and four of them were 8th graders during 2009-2010 school academic year. Qualitative approaches are used in this research. In particularly, case study method is employed. Firstly, it is designed as a single case study then after adding similar cases to the research it turns out to be multiple cases. These cases were composed of 5th and 8th grade students. One of purposive sampling methods, namely maximum variation sampling was employed for describing to participant. Data gathering was accomplished by interviews, documentary sources, and think aloud procedures. Furthermore in order to minimize data loss and later to eliminate differences in interpretation of data, video recording was used. Phenemography techniques were used in order to (a) get concepts and relations that could explain the data related to sub-problems, (b) in depth analysis of gathered data and (c) reveal hidden themes and dimensions. As a result of the research participants mental models were collated under these categories: Procedural knowledge (rule), dividing, whole-part, measuring-comparing, ratio-proportion, simplifying, expansion, equivalence relation and sharing. Data analysis show that there were no big differences among grades in converting fractions but there were important differences among participants levels of understanding. Findings of the research is also important for identifying students' existing misconceptions, pseudo-conception, computational errors and reveal underlying reasons of these findings.