Perimeter, Area, Volume, and All That: A Study of Measurement

Rationale

During this seminar Area, Perimeter, Volume and All That, I have had the opportunity of reflecting on my teaching practices regarding area and perimeter while thinking about what are the most frequent misconceptions that my students experience during their learning of this particular topic.

In general, students encounter difficulties to relate multiplication arrays with the area of a rectangular figure. Students often confuse the concepts of area and perimeter when transitioning from the use of manipulatives to pictorial representations. In many cases, they assume that rectangular figures with the same perimeter must have the same area and vice versa.

I also consulted the testing data available for the group of students that were in my 3rd-grade grade in 2017 and compared their performance in the area of Geometry and Measurement. At the end of 3rd grade, 7 % of the students performed below standard, and 66% of the students performed above standards. By the end of 5th grade in 2019, the same group of students scored 24 % below standard and only 27% above standard.⁵ Even though these particular test results are probably not enough to establish a solid conclusion about my students’ understanding of area and perimeter, there is a pattern in the way many students solve problems about area and perimeter. Students encounter difficulties to relate multiplication arrays with the area of a rectangular figure. Students with limited understanding of the two concepts may fail to realize that it is possible to have rectangles with the same area but different perimeters as well as rectangles with the same perimeter but different areas.

France Machaba, in his research about the misconceptions in the understanding of area and perimeter published in 2016, ⁶ referred to multiple research studies in the field of mathematics education that have reported that the concepts of area and perimeter are a continual source of confusion for learners. In his report, Machaba suggested that it is perhaps because both area and perimeter involve measurements, or because students are taught formulas for both concepts at about the same time and they get confused due to the lack of conceptual understanding. The confusion between these two concepts results in misconceptions.

I have observed the confusion and misunderstanding in my class, but I do not think area and perimeter should be taught separately. On the contrary, I think it is a powerful instructional strategy to present both concepts simultaneously, but in a way that allows students to understand the contrasting differences between the two.

During our current seminar with Dr. Howe, we learned to approach the distinction between area and perimeter in ways that allow solid comprehension and more in-depth content knowledge. As a result, I plan to develop my unit as a sequence of intentional activities to help my students develop a correct and solid understanding of the relationship between area and perimeter and use appropriate methods to solve problems involving area and perimeter.