(I know, two posts in one day. Clearly I'm excited about this)
In my geometry class we're currently studying circles and all of their glory. We've focussed mainly on arc and angle measures formed by secants, tangents, and chords, but I decided to switch it up today. Because of the shortened block I gave them a quick lesson that involved circles and Pythagorean Theorem (world's collide). I didn't reteach the Pythagorean Theoem, I didn't review all of our work with circles thus far, and I didn't dive into a big speech about how math is relevant to the real world. I took a page out of Mr. Meyer's 3 Acts just to see what would happen. The result was spectacular.
I drew a cirlce on the board, labeled it 'Earth,' and then drew a tiny mountain on top. "How far can you see if you stand on top of this mountain?" My students proceeded to tell me what information they would need; I told them how tall the mountain was, someone shouted out the radius of the Earth (which surprised me), and they wanted to know what angle they were looking at. I went through the problem, showing how their field of vision forms a tangent line with the Earth (horizon) and they quickely figured out how to calculate this distance.
It was amazing to watch their expressions as we went through this problem. They were more focused during this 15 minute lesson (on a topic they already knew I might add) than they were on anything else in this unit. Sometimes when I'm caught up in the 'I've got to cover all of this' mindset, I forget that students LOVE when the material makes sense to them. I never saw this type of problem until I started teaching, but if I would've seen it as a student the Pythagorean Theorem would've made much more sense, and I would've cared more. My students figured these problems out in a heartbeat and there was no questions of 'When am I ever going to use this?' Granted, they might be on an airplane and wonder how far they can see, but most of them will not get out their calculators and actually figure it out. But they thought it was awesome just knowing that they could if they wanted to.
I need to remember this as a I teach more often. Students crave this kind of thing. If they can see it and use it, they don't care what subject or topic it is. Once they're hooked, they want more. Many of my classroom issues could've been alleviated had I thought about this during previous lessons. My hunt is now to fill in these gaps in my lessons to provide my students with the situations they want. Why would I not give them what they want?