Area and Perimeter: "Which is Which and How Do We Know?" Helene Sherman Tammy Randolph
University of Missouri - St. Louis Fourth grade students participated in three hands-on lessons designed to foster conceptual understanding of area and perimeter, to able to measure them in units and to be able to distinguish them from each other within the same figure. Students worked with a university faculty member and classroom teacher to construct shapes on geoboards, transfer the shapes to dot paper and count units in and around each shape. Students' misconceptions and lack of direct experience were evident in answers on the pretest; conceptual development was improved as evidenced on answers to post test as well as on dot paper drawings. Although formulas were not developed in the lessons, students could explain how measures were found as well as arrive at the correct amount at the completion of the unit Area and perimeters were identified on shapes children constructed and drew, including their initials. Introduction How do students learn to understand, measure and distinguish area and perimeter? Over the past several decades, researchers such as Jerome Bruner (1960) and Jean Piaget (1970), found that conceptual development is possible when students are given opportunities to think, reason and apply mathematics to real world situations at appropriate learning levels; students need to construct their own knowledge in context as they engage in tactile experiences. Because most second to fifth grade school pupils reason at the "concrete operational stage," (Copeland, 1984, p. 12) hands-on learning opportunities are essential to enhancing the children's mathematical thinking. "Students should be actively involved, drawing on familiar and accessible contexts;
Volume 9 Number3
Students should develop strategies for estimating the perimeters and areas of shapes as they "measure objects and space" in familiar surroundings (NCTM, 2000, p. 171). Utilizing manipulatives to foster students' measurement sense of area and perimeter is supported in the NCTM document as well as mathematics education literature (Outhred, L.& Mitchelmore, M., 2000). The concepts of area and perimeter are difficult for students to grasp, as reported in the TIMSS results (NCTM, 1997) since fourth graders scored less well in the area of measurement than they did in topics of whole numbers, data representation, geometry, patterns, relations and function and fractions and proportionality. The National Assessment of Educational Progress (NAEP,1999), reported that only 35.4% of nine-year-oids were successful in finding the perimeter of a rectangle, just 37% could find the area of a rectangle and that fourth and eighth grade students sometimes confuse area and perimeter. Carpenter, T.P.,Lindquist, M.M., Brown, C. A, Kouba, V.L, Silver, E. A. & Swafford, J.O.(1998) found that this lack of understanding continued to affect children in older grades. This article is written to describe a project designed to work with fourth graders on these critically important but confusing measurement and geometry topics. The lessons focused on developing conceptual understanding of area and perimeter, counting their measure and then comparing them in a common setting in order to identify and distinguish them from each other. Project Overview A St. Louis Public School District teacher and a University of Missouri-Saint Louis mathematics education professor worked together during the 2002-2003 school year in a district-university fionded cooperative project to develop and team teach lessons about area and perimeter. Geometry and measurement topics were chosen because the school's intermediate grade students scored at less than desired levels on state and district standardized mathematics tests administered during the previous spring semester. The class
Research for Educational Reform
consisted of 16 males and 11 females and...