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

Introduction

“With many under served, underachieving minority students; her students invariably believe they are bad at math, and if you looked at their past performance, you might be tempted to think so too.”¹ While this quote is not about me or my students, I was able to relate to it. I teach first grade at Ross/Woodward a public school in New Haven, CT. The majority of my students are Hispanic and African American with more than half of them qualifying for free lunch. My young students come to first grade with misconceptions and fears about mathematics. A goal of mine for the last three years has been to help my students overcome these fears and feel confident in math. “I am passionate about equity. I want to live in a world where everyone can learn and enjoy math, and where everyone receives encouragement regardless of the color of their skin, their gender, their income, their sexuality, or any other characteristics. I would like to walk into math classrooms and see all the students happy and excited to learn.”² Unfortunately, as a girl, I was not encouraged in math while I was in school. I did not feel confident in my math abilities until I became a teacher myself. For a long time math has been treated as an elite subject. Girls and other minority groups are often not expected to be “good” at math. This is unacceptable, all students regardless of race and gender can achieve in mathematics. I realized that a lot of the fears that I had surrounding the topic from when I was in school could be projected onto my students. This math anxiety was likely to stay with my students long after they left my classroom. I realized that in order for my students to feel confident in and enjoy mathematics it would need to be rigorous and relevant to them.

One major misconception that my students have when they come to first grade is that in order to be good at math you have to be fast at math. They directly correlate this to fact fluency in addition and subtraction. “Another serious problem we face in math education is that people believe that mathematics is all about calculating and that the best mathematical thinkers are those who calculate the fastest. Some people believe something even worse- that you have to be fast at math to be good at math.”³ Students who are not fast at math facts often feel less confident in math and therefore, do not enjoy it as much as other school subjects. We spend most of the year focusing on addition and subtraction. However, the focus of these units is strategies and not speed. The strategies are presented to my students to get them into the right mathematical mindset. I want them to realize that math is much more exploratory than they think. This is the basis of my curriculum; exploratory yet rigorous math.

Measurement is a great subtopic of mathematics that can be exploratory for students. In first grade, students primarily study how to measure length. I began to think about how I could make this more engaging for my students. I realized that perimeter is a linear measurement and began to think about implementing this concept into my classroom. “It makes sense to start by discussing that most basic, most fundamental of measures: distance.”⁴ When we measure length, we are actually measuring distance. I decided I would begin to use this term when teaching length to my students. I determined that if my students could measure distance and perimeter, then they could explore area as well.

“Our brains need help when thinking about areas because so much of our early learning about numbers and measurement is linear. There are no tools in the set of school mathematical instruments to measure area: areas are almost always the result of calculations.”⁵ Students learn how to measure length first since it is linear. Measuring distance is easily related to counting as students count the distance between zero and the edge of the object they are measuring. Area is more complex, which is why it is saved for later grades. However, with the proper exploratory activities and strategies young students can complete tasks related to area. Area is commonly taught with multiplication. In first grade we begin to explore “repeated addition”, this is the beginning of multiplication. I realized that my students could complete area tasks if they were related to repeated addition. 

Area and perimeter are not expectations for first grade, however, they can be related to other tasks that are incorporated in first grade. With the proper guidance, manipulative work, discussions, and tasks, I knew my students could explore area and perimeter. These concepts would prepare them for higher grades and standardized testing. I was excited to give my students a strong foundation in these concepts and provide them with opportunities that they would enjoy at a rigorous level.