Eight-Grade Students explore Surface Area and Volume Problems: The Role of Representations

PurposesLesson activity; Professional development activity; Student collaboration; Student engagement; Student model building; Representation
DescriptionThe purpose of this RUanalytic is to examine how students use different representations to illustrate their developing understanding of the concepts of surface area and volume.

The events chosen for the RUanalytic focus on the following categories of external representations: manipulative/physical, written symbols, experiential, spoken language and pictures and diagrams (Lesh, Post and Behr 1987).

The video data for this RUanalytic come from a longitudinal study, from first grade to twelfth, and beyond of the development of mathematical ideas and ways of reasoning in students. The National Science Foundation funded the study (funded in part by NSF grants MDR 9053597 and REC-9814846), in the Kenilworth School District.
The events for this study occurred during an extended class session with fourteen eighth-grade students working in groups, who were provided with Cuisenaire rods, paper and pencil. The events for this RUanalytic are taken from the full video of the single session. It details the students’ participation in the activity and respects the chronology in which the students worked on the tasks described below.

Researcher Carolyn Maher presented the following tasks;
1. Find the surface area of one rod.
2. Find the volume of one rod.
3. Find the volume of any number of stacked rods of a particular length.
4. Find the surface area of any number of stacked rods of a particular length.


Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. In C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ; Lawrence Erlbaum.

Goldin, G., Shteingold, N. (2001). Systems of Representations and the Development of Mathematical Concepts. The Roles of Representation in School Mathematics, NCTM 2001 Yearbook. (p. 1-23).

Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. Theories of mathematical learning, 397-430.

National Council of Teachers of Mathematics. (2000). Principles and Standards for school mathematics. Reston VA.
Created on2014-02-24T13:19:33-0500
Published on2015-11-17T09:10:59-0500
Persistent URLhttps://doi.org/doi:10.7282/T3V40X46