Determining Ways of Thinking and Understanding Related to Generalization of Eighth Graders

Abstract

The main purpose of this study is to determine ways of thinking and understanding of eight graders related to generalizing act. To carry out this aim, a DNR based teaching experiment was developed and applied to 9 eight graders. The design of the study consists of three stages; preparation process in which teaching experiment is prepared, teaching process in which teaching experiment is applied, and analysis process in which continuous and retrospective analyses are carried out. Analysing the data, it was found that students' ways of thinking could be determined as relating, searching, and extending. Ways of understanding belonging to generalizing act could be determined as identification, definition, and influence. It was recommended to add two new categories "relating with an authority" and "searching the same piece" to the generalization taxonomy.

Student Thinking Levels in Solving Open-Ended Geometric-Function Problem by Algebraic Representation Approach

“…While for analyzing thinking levels based on van Hiele theory referred to some literature like Herbst et al [12], Van de Walle et al [13], and Luneta [14]. The finally was analyzing algebraic thinking levels referred to some literature like Oflaz & Demircioglu [16], Özdemir et al [17], [18], and Apawu et al [19].…”

“…In this study, the geometric-function problem has been served is to sketch of derivative function graph, and this problem invited a student to think algebraically than geometrically. Van de Walle et al [13], Oflaz & Demircioglu [16], Özdemir et al [17], [18], and Chimoni & Pitta-Pantazi [24] stated that algebraic thinking is mathematical thinking related to reveal of pattern and investigate a mathematical relationship of geometrical shape, generalized, and used symbol to problem-solving. Based on its statement, the sample in this study have used a symbol as the result of their investigation toward function graph in the problem, and all three students found the completion that was constructed at a base on the symbol commonly said by algebraic representation.…”

“…Furthermore, generalization has done by NI, AN, and PR in determining process the function formula of the graph. All of the function that was constructed by the student is made on the basis of the explicit relationship between two variables, x and y, from the properties of shape, Oflaz & Demircioglu [16] and Warren et al [25] categorized its generalization process through a combination of explicit and visual thinking. However, there was a conversion process of the representation from geometric to algebraic as the consequence in solving the problem by the way.…”