Research Information System
Thesis Type: Doctorate
Institution Of The Thesis: Bursa Uludağ University, EĞİTİM BİLİMLERİ ENSTİTÜSÜ, Turkey
Approval Date: 2021
Thesis Language: Turkish
Student: Mustafa Çağrı Gürbüz
Open Archive Collection: AVESIS Open Access Collection
Abstract:Students are expected to achieve various purposes by using skills such as problem solving, reasoning, and communication, which are the basis of mathematical thinking of their current knowledge, rather than having much knowledge today. In the study, mathematical thinking is discussed to explain how the student constructs mathematics concepts in his mind. This construction process was followed from the framework of mathematical abstraction. Mathematical abstraction is the creation of a more comprehensive application area of comprehension through the generalization of the concept of mathematics. In other words, it is to extract the essence of the concept. It is quite a difficult situation to observe the formation process of information directly in the students' minds. Effective interventions in the learning process will be easier if it is known how the knowledge is formed, abstracted, and what internal processes go through in the student's mind. In this study, it is aimed to analyze the abstraction processes of secondary school students towards basic algebra concepts. Epistemic actions in RBC + C (Recognizing, Building with, Construct, Consolidation) theory were taken into consideration in the analysis of abstraction processes. In addition, Hypothetical Learning Trajectories were used in the research process to provide better observation of students' abstraction processes. Determining the effects of the experimental application on students' achievements in basic algebra concepts and their reflections on abstraction processes is another aim to be revealed in the research. The research is designed as two-stage and longitudinal to achieve the determined goals. Firstly, design-based research model was used in order to see more clearly the processes of abstraction of the concepts of balance and variable, which are the two basic axioms of algebra, and to support them in abstraction in the process. Design-based research allows students to intervene in the learning environment in order to better understand the abstraction processes of students. In this regard, it is believed that it will be more useful than other types of research. Design-based research focuses on learning studies as well as intervention in the learning environment. The second stage of the research was evaluated as a case study. Design applicability and deficiencies through classroom observations; The abstraction skills of the students were analyzed from the data obtained from semi-structured student interviews. Participants were selected by purposeful sampling among 6th grade students studying at a public school in Nilüfer District of Bursa Province. Data collection was continued when they moved to the 7th grade level with the same students. During the 2016-2017, 2017-2018 academic years, researchers and teachers together carried out research in the mathematics classes. In the research, data was collected by data triangulation, data collection tools compatible with the nature of qualitative research, such as documents, observations, and interviews. Observation and interview data were subjected to content analysis, and learning road maps were subjected to historical analysis. This study shows that students with a high level of success can define the linear relationship between variables and solve equations. It was observed that students were able to coordinate all the information given for situations requiring generalization, such as algebraic expression and linear equation creation, as well as create the concept of linear model in more abstract situations and set a rule for the new linear model. In addition, it has been observed that they can use the methods they have determined to find solutions to contextual problems more consistently. This shows that students who can think abstractly can generalize the data and use algebraic expression as a representation. Explaining the problems faced by students in a mathematical way helped them analyze the process of abstraction. In this study, students' skills of abstracting algebra concepts were revealed by epistemic analysis of problem-solving processes and their explanations in interviews. While the students' algebraic habits of mind had a more vicious thought before the application, it was observed that they realized different ways of thinking in the process, presented different algebraic ways of thinking, and initially converted mathematical situations that they expressed verbally or arithmetically into algebraic explanations. In the study, supportive arguments were found between abstraction skills and algebraic habits. Two mathematical habits have been identified that ensure the development of students in algebra relationships. These are to achieve an abstraction by arranging operations and to generalize using a mathematical language. These habits made it easier for students to switch from arithmetic to algebra. It can be said that students who have the habit of making and creating a functional rule are more advantageous in the process of abstracting algebra concepts. As a new structure and mathematical language are mentioned in the abstraction process, understanding the relations in the abstraction process has enabled students with the habit of forming a functional rule to build more easily. In algebraic habits, students' attempts to abstraction from transactions are generally based on finding and explaining a short path rather than a new language. Research, based on an approach to teaching the two basic axioms of algebra, is important to coordinate efforts to promote effective algebra education and to identify important milestones in students' thoughts. Learning trajectories offers teachers and practitioners a systematic way to integrate them into their educational apps. In-service trainings can be given to the teachers that students can be used as an effective tool in teaching abstraction concepts and the abstraction mechanism can be reflected in mathematics curriculum in a more descriptive and useful manner.