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Abstract
Abstract: In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, “Limit Representation Transformation Test” with a reliability of .908 was administered to 50 preservice teachers attending to a state university in the Central of Turkey. Preservice teachers had most difficulty in solving problems that had verbal representation inputs, especially they achieved low performances in transformation from verbal to numerical representation. Although, in general, they achieved the highest performance in the problem that had numerical representation input, they also achieved very high performances in the problems that had graphical and algebraic representation inputs. Specifically, they performed very well in the problems that required transformation from an algebraic representation to a verbal representation. Moreover, significant positive correlations were found among preservice teachers’ representation transformation competence levels.
Highlights
The concept of limit, which requires strong mathematical thinking skills and is among the fundamental concepts of mathematics, has been conceptualized in two ways: dynamic and static (Cornu, 1991; Tall & Vinner, 1981)
Representations and representation transformation process competencies used in the process of solving limit problems by preservice mathematics teachers were explained in line with the sub-problems of the study
Representations used by preservice mathematics teachers in the process of solving limit problems were determined, and it was observed that they had most difficulty in making transformations in the items with the verbal input representation type
Summary
The concept of limit, which requires strong mathematical thinking skills and is among the fundamental concepts of mathematics, has been conceptualized in two ways: dynamic (informal) and static (formal) (Cornu, 1991; Tall & Vinner, 1981). When the studies on limit concept are examined, it is seen that students conceptualize the limit concept more in informal way (Szydlik, 2000; Tall & Vinner, 1981; Williams, 1991) and stated to have difficulty in conceptualizing it formally (Tall & Vinner, 1981), and only a limited number of students being able to develop a clear understanding of formal definition (Quesada, Einsporn & Wiggins, 2008). This situation may cause the concepts such as derivative, integral, and Taylor series that are built on the formal definition of the limit to be incomprehensible. Goldin and Kaput (1996) defined multiple representations as a characteristic arrangement that allows the symbolization of a thing with images or concrete objects
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