Understanding the formula for rectangular right prisms: a different perspective

Zembat, I. (2007) Understanding the formula for rectangular right prisms: a different perspective. Eurasian Journal of Educational Research, 27, pp. 205-217.

Abstract

Background/Problem Statement: Measurement is the foundation for mathematical ideas without which misconceptions in counting, geometry and fraction models may arise (Wilson & Rowland, 1995). Osborne (1976) described `measure` as an `entity` as opposed to as a `process.` Measuring, on the other hand, is considered as a process consisting of a comparison between an attribute of a physical object and a purposefully selected unit to quantify that attribute (Bright, 1976). One of the key measurement concepts in elementary mathematics is 'volume.' Piaget and Inhelder (1967) identified three different types of volume: occupied, interior, and complementary volume. Coordination of these volume types might play an important role in understanding the volume concept. This study focuses on developing the meaning of interior volume (capacity of a container) only. Purpose/Objective/Research Question/Focus of Study: The purpose of this article is to give a mathematical description of measurement and volume concept, explain an instructional design by focusing on how the volume formula for rectangular right prisms can be constructed, and talk about the ensued developmental process in which students engaged in general. Methods: This study refers to a radical constructivist framework, called Reflection on Activity-Effect Relationship, as an orienting framework. Based on this framework, the author generated an instructional design and conducted an action research on 22 seventh graders of an art school (in the central region of Turkey) who did not previously know the volume formula for rectangular right prisms. During the instruction, the students were put in (homogenous) groups of four based on their mathematics knowledge to work on the given tasks. Although the whole class was videotaped, the focus was mostly on one of the groups during the instruction. The researcher's notes about what transpired in other groups were also taken into consideration as additional data. Once data were gathered, the researcher transcribed/annotated the important pieces of the teaching session. The main purpose in the analysis process was to formulate and verify hypotheses about students' evolving understandings of measurement of volume. Findings/Results/Conclusions/Recommendations: The offered instruction is based on the idea of reflecting on one's own goal directed activity and it offers a way to help learners reflect on their own activities targeting a common goal. The mental activities in which students were engaged when finding the volume of given rectangular right prisms are (1) filling up the base layer (to find the number of unit cubes in a layer) (2) adding up a number of layers until the box is filled (to find the total number of cubes). These activities are purposeful (to figure out the number of cubes that can fit into given boxes) and related to the process of measuring volume (comparison of corresponding attributes of cubes and given transparent boxes). By having students reflect on such a sequence of activities systematically, learners abstracted the underlying ideas for Cavalieri's principle.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Zembat, Dr Ismail Özgür
• Authors: Zembat, I.
• College/School: College of Social Sciences > School of Education > Creativity Culture and Faith
• Journal Name: Eurasian Journal of Educational Research
• Publisher: Ani Publishing
• ISSN: 1302-597X
• ISSN (Online): 2528-8911