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

Introduction

Every year when I begin to teach perimeter and area, I look through my resources and the internet for engaging ways to teach these topics to my students. There is no end to the activities out there, from using grid paper to make name banners, to creating a city with rectilinear houses, tiling, or using crackers to create a myriad of shapes. All of these activities look good and the students even seem to really enjoy completing them. Yet, I am never truly satisfied with the level of conceptual understanding and mastery my students ultimately achieve. What am I doing wrong? I’ve come to a decision that perhaps I have put too much emphasis on the activity itself and have not asked myself the harder questions about my goals for the activity and my students’ learning. My district’s math program also is a good resource for activities and background information, yet the topic of measurement, with perimeter and area within the scope, is practiced more through a procedural focus and an isolated topic. The connections to other mathematical topics and my students’ background knowledge are limited, and gaps either begin to form or widen.

Through this unit, I would like to set an emphasis on developing strong lessons with a focus on spending more time in my preparations to make sure my students see this topic of measurement as it relates to mathematics as a whole, and not a separate unit of teaching. I want my students to begin to understand math and not just see it as an arbitrary set of rules and formulas to be memorized with no connection to other parts of their lives. Young children are continuously learning about the world around them and about the ways mathematics is used in their lives. “They show remarkable ability to connect experiences gained from a variety of contexts in order to make increasing sense of what they have observed. An abrupt change occurs on entry to statutory schooling when an emphasis is placed upon more formal and abstract ways of understanding and representing mathematical thought.”¹ To that end, there are many questions that I will need to ask and answer about my own understanding and what I want my students to gain. By determining what skills or knowledge the students have learned prior to my introduction of this topic, I can ultimately decide what knowledge and connections I can draw on to facilitate these new lessons. Identifying what misconceptions students are holding will also help guide instruction. Furthermore, it is essential to distinguish between a misconception and an error, the former needing careful re-teaching while the latter needing focus on precision and sense making.