Area and Perimeter
Research for Educational Reform
25
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;
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Volume 9 Number3
Students should develop strategies for estimating the perimeters and areas of shapes as they "measure objects and space" in familiar surroundings
25
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;
26
Volume 9 Number3
Students should develop strategies for estimating the perimeters and areas of shapes as they "measure objects and space" in familiar surroundings
References: Bruner, J. (1960). The process ofeducation. Cambridge, MA: Harvard University Press. Copeland, R.W. (1984). How children learn mathematics: teaching implications of Piaget 's research. New York: Macmillan Publishing Co. 1984. Jensen R. J. (Ed.) (1993). Research ideas for the classroom: early childhood mathematics. New York: Simon & Shuster, Macmillan, 1993. 36 Volume 9 Number3 Outhred, L. N. & Mitchelmore, M. C. (2000). children 's intuitive understanding of rectangular area measurement. Journal of Research in Mathematics Education n, 2, p. 144-167. Piaget, J. & Inheldr, B. (1970). The child 's concept of geometry. New York: Basic Books, 1970. Reynolds, A., & Wheatley, G.H. (1996). Elementary students ' construction and coordination of units in an area setting. Journal for Research in Mathematics Education, 27, 564. 581. National Assessment of Educational Progress (1999). The nation 's report Card. (On-line http://nces.ed.gov/nationsreportcrad/tabIes/LTT1999/ ittintro.asp National Council of Teachers of Mathematics (1997). U.S. mathematics teachers respond to the Third International Mathematics and Science Study: Grade 4 results ( On-line). Available: http:www.nctm.org/new/release /timss-4 '* '-pgO 1 .htm. (July 10, 2001). . (2000). Principles and standards for school mathematics. Reston, VA: NCTM: Author. Sheffield, L&CruikshankD.E. (2000). Teachingand learning elementary and middle school mathematics. New York: John Wiley and Sons. Silver, E.A. & Kenney P.A. (Eds.). (2000). Results from the seventh mathematics assessment of the National Assessment of Educational Progress. Reston, VA: NCTM. Van De Walle, J.A.(1994). Elementary school mathematics, teaching developmentally. New York and London: Longman Publishers.