Rationale
Often my fourth graders confuse area and perimeter, both the meaning and how to calculate the two measurements. “The results of the National Assessment of Educational Progress (NAEP) testing indicate clearly that students do not have a very good understanding of formulas. For example in the sixth NAEP, only 19 percent of fourth grade and 65 percent of eighth grade students were able to give the area of a carpet 9 feet long and 6 feet wide.”1
After conducting research2, I have discovered the need to deemphasize the use of formulas A= l × w for a rectangle and P = 2l + 2w or P = l + w + l + w and further develop their conceptual understanding. To me, as a veteran teacher, this seems so obvious. However, in the everyday world of teaching, I know why I often neglect the conceptual development: time! Area and perimeter is always taught toward the end of the year, when as a teacher I am itching to get through the last of the curriculum in order to preserve some time for review before the state assessment. Since I always rush this unit of study, I only use simple shapes as prescribed in the state objectives. Since I do not explore deeply into the relationships between area and perimeter, the students end up with a limited understanding of both concepts. If I expose my students to more complex figures and allow them time to grapple with both area and perimeter of these more varied shapes, I will help them develop a better understanding of these two measurements.
After spending two weeks diving into area, perimeter, and geometry at a high level, one thing is clear: the students need many opportunities to explore geometric shapes in a hands-on manner. They need to perform transformations and turn basic geometric shapes into other shapes. They should decompose them, rotate them around a central point, or make multiple copies to create a different shape. I plan to use a variety of manipulatives throughout the explorations to provide a variety of exposure. Many of the higher-level theorems depend on decomposing and recomposing shapes, so this foundation is really crucial.
The curriculum unit will address the issues I have laid out in the previous paragraph. It will focus on perimeter and area and will utilize many opportunities for covering the surface and measuring around polygons to develop a strong conceptual understanding. In teaching general math, I always strive to connect concepts to students’ prior knowledge. I try to make connections to my previous teachings, but geometry always seems like such an isolated, stand-alone topic. In this curriculum unit I want to intertwine geometry and measurement in a meaningful way. I plan to teach aspects of the curriculum unit throughout the year, thus providing more opportunity to strengthen these two weak areas. According to Van de Walle and Lovin, “The relationship between measurement and geometry is most evident in the development of area and volume formulas for measures of geometric figures.”3
Comments: