Measurement seems a weird topic for a high school math teacher. It is generally expected that students can measure things by the time they get to high school. They can use a ruler, a protractor, and various other instruments of measurement. It is what students do with that measurement that is usually the concern of high school math teachers.
There’s more measurement than I thought in high school math. There’s measurement when I teach students to find slope. They are measuring the rate of change. There’s literal measurement in the distance formula, and the Pythagorean Theorem from which it comes. There’s measurement of angles in geometry. There’s measurement in constructions as you copy or bisect lines and angles. These are all geometry topics in my high school. So students get plenty of practice in measurement there.
What surprised me about measurement, was how it builds across the grades. I knew, of course, that students start learning about area in elementary school, but I had not considered how much it built across the grades. My knowledge of curriculum at the high school level is pretty thorough. I know what students are learning in Geometry (see previous paragraph), and Algebra 1 and 2. However I know much less about elementary and middle school learning. I was not aware of the horizon content knowledge (Hill & Ball, 2009), or how the topic builds across grades and classes. It can be difficult from the end of the elementary to secondary path to see how carefully and slowly knowledge has been built for students over time.
According to the Common Core Standards (CCSSI), students begin learning about area in the 3rd grade. They begin by tiling and counting, but then build into multiplying to find area. Students continue to work with area from there all the way to high school. They begin to find area with decimal values. They build from simple areas to surface area and on to volume. They build from area of rectangles to area of other shapes, getting to more complicated shapes as they advance through grades. They find area of rectangles that have sides defined only by variable expressions in algebra. This is where quadratics come from (hence the name quadratics, referring to quadrilaterals). In calculus, area of rectangles is used to define the area under a curve. In statistics, that area helps find the probability of an event. Although area is a simple idea that can be learned relatively early in school, it forms the heart of more complicated mathematics; essentially, area is just a measurement.
Measurement seems like a simple topic at first, yet the way that it builds throughout students’ mathematics learning is fascinating, and also essential.
Hill, H., & Ball, D. L. (2009). The curious – and crucial – case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71.