The focus of some of my out-of-classroom obsessions right now is on building the need for mathematical tools. I'm digging into the fact that many people do well on a daily basis without doing what they think is mathematical thinking. That's not even my claim - it's a fact. It's why people also claim the irrelevance of math because what they see as math (school math) almost never enters the scene in one's day-to-day interactions with the world.

The human brain is pretty darn good at estimating size or shape or eyeballing when it is safe to cross the street - there's no arithmetic computation there, so one could argue that there's no math either. The group of people feeling this way includes many adults, and a good number of my own students.

What interests me these days is spending time with them hovering around the boundary of the capabilities of the brain to do this sort of reasoning. What if the gut can't do a good enough job of answering a question? This is when measurement, arithmetic, and other skills usually deemed mathematical come into play.

We spend a lot of time looking at our electronic devices. I posed this question to my Geometry and Algebra 2 classes on Monday:

The votes were five for A, 5 for B, and 14 for C. There was some pretty solid debate about why they felt one way or another. They made sure to note that the corners of the phone were not portrayed accurately, but aside from that, they immediately saw that additional information was needed.

Some students took the image and made measurements in Geogebra. Some measured an actual 4S. Others used the engineering drawing I posted on the class blog. I had them post a quick explanation of their answers on their personal math blogs as part of the homework. The results revealed their reasoning which was often right on. It also showed some examples of flawed reasoning that I didn't expect - something I now know I need to address in a future class.

At the end of class today when I had the Geometry class vote again, the results were a bit more consistent:

The students know these devices. Even those that don't have them know what they look like. It required them to make measurements and some calculations to know which was correct. The need for the mathematics was built in to the activity. It was so simple to get them to make a guess in the beginning based on their intuition, and then figure out what they needed to do, measure, or calculate to confirm their intuition through the idea of similarity. As another chance at understanding this sort of task, I ended today's class with a similar challenge:

My students spend much of their time staring at a Macbook screen that is dimensioned slightly off from standard television screen. (8:5 vs. 4:3). They do see the Smartboard in the classroom that has this shape, and I know they have seen it before. I am curious to see what happens.

This would be a good task for Activeprompt, depending on whether your students have access to devices.

Completely agree - didn't think of it at the time, but you are spot on.