Middle Grade Students’ Geometrical Reasoning: Does Volume Depend on Area?

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Geometry is the core of learning mathematics (Clements, 1998), and spatial reasoning is one of the important geometric thoughts (Battista, 1997). It is believed that in order to enhance students’ geometrical understanding and performance, it is critical to identify students’ difficulties and problems that they face while learning geometry. In core of this discussion, in this research study, we aimed to examine 8th grade students’ geometrical reasoning on the relationship between lateral surface area and the volume of the cylinder. Thus, our purpose was to answer the following research question: How do 8th grade students reason their understandings on the relationship between lateral surface area and the volume of the cylinder? With this aim, we collected data at the end of the spring semester of 2007-2008 academic year from eight grade middle school students enrolled in 3 public and 2 private schools in Ankara, Turkey. In order to investigate middle school students’ geometrical reasoning on the relationship between surface area and volume of cylinder, we administered the Cylinder Exploration Task (CET, Merseth, 2003). The analysis of the students’ responses to the questionnaire revealed that in general eight grade students had problem on reasoning about the relationship between surface area and volume of cylinder. Implications for the educational field will be discussed.


Keywords: Geometry, Spatial reasoning, Middle Grade Students
Stream: Curriculum and Pedagogy; Student Learning, Learner Experiences, Learner Diversity
Presentation Type: Paper Presentation in English
Paper: Middle Grade Students’ Geometrical Reasoning


Mine Isiksal

Instructor, Elementary Education Department
Education Faculty, Middle East Technical University

Ankara, Turkey


Aslihan Osmanoglu

Research Assistant, Elementary Mathematics Education Department
Education Faculty, Trakya University

Edirne, Turkey

I completed my undergradute education at Yildiz Technical University, Mathematics Engineering Department. I also attended a Pedagogic Formation course at Istanbul Technical University. Then, I started pursuing my master degree in the field of mathematics education at Ohio University in USA. After completing my masters degree, I took Ph.D. classes for about a year in the University of Michigan, Ann Arbor in the same field. Then, I returned to Trakya University where I worked as a research assistant. Recently, I pursue my Ph.D. degree in elementary mathematics education in the Middle East Technical University where I also work as a research assistant. I am interested in teacher education and professional development, and I study the use of video cases with online discussions in pre-service teacher education in my thesis study.

Yusuf Koc

Instructor, Education Department, Indiana Northwest University
Indiana Northwest, Indiana, USA


Ref: L09P0927