| Perimeter and area are concepts with which fourth grade students, ages 10 and 11, should be familiar; surface area and volume are topics generally studied formally in fifth or sixth grade and beyond, and often studied in sequence. The goals of this study were to provide evidence that fourth graders are able to (a) understand the concepts of perimeter, area, surface area, and volume and the relationships among them when taught concurrently and (b) solve problems and construct models that require the application of these concepts. Also, the study was designed to assess qualitatively the effects of non-traditional manipulatives (e.g., magnetic cubes, connected cubes, and precut cardstock rectangular shapes) to support the students' understanding of these four concepts. Materials commonly found in elementary mathematics classrooms (e.g., loose cubes, square grids and tiles, and rectangular prisms) were also used.;Nineteen students in a heterogeneous class in a suburban public school participated in eight instructional sessions during which they (a) predicted and verified perimeters, areas, surface areas, and volumes using 2D and 3D models, (b) completed measurement tasks and constructed 3D models, and (c) discussed and wrote about their findings. Students completed culminating construction projects that had specific requirements involving the four concepts.;The pretest and identical posttest consisted of released questions from state and national tests as well as questions that required students to use manipulatives. Results from paired t-tests on the released questions (t = 3.05, df = 18, p <0.01) and on questions that required the use of manipulatives (t = 6.82, df = 18, p < 0.001) indicate a significant whole-class improvement. Challenges that confronted students and factors that contributed to the success of the students' understanding of perimeter, area, surface area, and volume when taught concurrently are summarized in four categories: the use and availability of the manipulative materials; the tasks and exploratory activities that involved the concurrency of the concepts; the consistent use of accurate mathematical terminology; and the establishment of a cooperative learning community. The findings from this study are compared to previous research and theory; recommendations for further research opportunities are suggested. |
