Investigation of the development of operational and conceptual knowledge in the context of equations containing algebraic fractions

The purpose of this research is to examine the development of operational knowledge and conceptual knowledge in equations involving addition and subtraction in algebraic fractions. The research was carried out by 4 ninth grade students who attended two different high schools in Sinop province in 2015-2016 academic year. Firstly, pre-application questions were applied in high school in Sinop center and 4 students were identified. Following the first clinical interview, 7 teaching sessions were held once a week, and the last clinical interview and persistence clinical interview were performed 3 months later. The model of the research constitutes the "teaching experiment" which is one of the qualitative research approaches, the "clinical interviews" and the "document examination" which are made to support this. The obtained data are examined under three headings: to show information of multiple solution strategy in terms of transaction flexibility, to make conscious preferences among these solutions and to implement preferred solution. In the multi-strategy information section, the data were coded and scored and four levels were determined. The content analysis method and the conceptual understanding dimension are analyzed by using descriptive analysis and content analysis method. As a result of the research, the participants have developed operational and conceptual knowledge in this process. As multi-strategy knowledge has developed in operational sense, it has been seen that process flexibility develops, analytical examples play an important role in this, the development of multi-strategy information, and the ability to select the right strategies for the solution have mutually positive effects. The development of multi-strategy knowledge has made mathematical reason for preference. It has been determined that the meanings used in the verbal problems written in the given equations and the errors made when writing the problem differ according to the specific type. The use of the notion of a definite part in the solution of the equations has shown that the two sets of information affects each other positively.