Investigation of Elementary Students’ Geometrical Thinking
In order to collect data, two 3D geometry questions were applied to the students. These have been adapted from various studies in the literature (Battista, & Clements, 1996; Ng, 1998). Questions are given below.
1. This is a 10 x 10 x 10 big cube made up of small cubes. How many small cubes are there in this big cube? 2. If this rectangular block is 5 small cubes wide, 15 small cubes tall, and 13 small cubes long, how many small cube are there?
Results of this study revealed that students who solved 3D questions develop three strategies for first question and two strategies for second question. Two of the strategies developed for both questions were same. In strategy A, students conceptualize 3D figures in terms of its layer and in strategy C, students used volume formula just by using rote memorization. That is, students do not know why they multiply the dimensions of the 3D figures while solving the problem. The last strategy (strategy B) is only developed for solving the first question. In this strategy, students conceptualized the 3D figures in terms of its columns. Although both of the questions were similar in terms of their content, students could develop strategy B only for solving first question. The reason is the first question was asked by using figures but second question was just in sentence format. So student could not perceive that 3D figure in second question is formed by columns.
In this study, results revealed that the number of students who could solve the given questions is low and students who solve questions correctly could develop limited strategies. In other words, they can not think the form of figures in a different way so they can not perceive the part of 3D figures from different perspectives.
Keywords: Three Dimensional Geometry, Problem Solving Strategies, Geometrical Thinking
Reyhan Tekin Sitrava
Doctoral Student, Middle East Technical University

Mine Isiksal
Instructor, Education Faculty 
Yusuf Koc
Instructor, Education Department, Indiana Northwest University

Ref: L09P1300