Mathematical Measurements

How confident are you when you make guesses about someone's height?

This was a question that one of my teachers asked our class before, and our class had a range of answers from "hardly" to "pretty confident". This question was a precursor to an experiment where we had several student volunteers come to the front of the classroom, and have everyone guess their height in centimeters, then afterwards compared our guesses to their actual height. The results were interesting, with a range of accurate guesses and wildly wrong guesses. What fascinated me the most was the fact that while making their guesses several of my classmates had wrongly assumed that certain volunteers were taller than others, which completely skewed their guesses as to how tall the volunteers were.

When we did this experiment to test our observational skills, I began to think about how important accurate observational skills are, and how I had totally overlooked them before. For example, eyewitnesses are vitally important in our justice system, and they need to provide the police details about suspects so that the police will be able to take the correct person into custody. If an eyewitness gives the police a very inaccurate estimate about the height of the suspect, suggesting that the suspect was average height when he was really above average height, this misinformation can hamper the search for the suspect, or cause them to take the wrong person into custody.

I do not recall learning how to make accurate estimates about lengths when I was in elementary school. I remember learning about the importance of specific measurements, and measuring something correctly, but not how to judge lengths from a distance. As an adult, I wish that I had learned this skill when I was a child.

In order to teach students how to accurately estimate lengths, it's important to teach them several benchmarks to use to base their estimates off of. In Casey's video, she suggests having the students use their hands as one such benchmark for future estimates. One of the things that I really like about this suggestion is the fact that students always have their hands with them while they usually don't have a ruler nearby. One problematic thing about teaching students to use their hands is the fact that elementary students are still growing, and so their hands are also going to grow larger, which will skew their benchmark unless they consciously continue to remeasure their hands regularly to update their benchmark.

There are several ways to teach students about estimation. I really liked the activity on page 36 of this resource that suggested that teachers have students examine several different packaging options for 3D objects, use estimates to make educated guesses about which packaging uses less material, and then measure to test their predictions. I like how this activity goes beyond a 2D concept of distance or length, and ventures into the 3D world, and how it connects this concept with a real world context.