I've been thinking about how in my PreCalc class we prove theorems and then use them to solve problems. However, in Geometry we generally prove things that seem self evident after a few examples or that seem completely arbitrary and we never use them again. To try to change this I want to spend class on Wednesday proving theorems. Whatever theorems they prove, I will allow them to use on the test Friday! (Block schedule plus snow days means I only have two 90 minute periods with Geometry classes this week.)

So far we have found (and proven) the angle sum rule for all polygons, defined concave/convex and done the quadrilateral sort. From there I had students make quadrilaterals on their geoboards (thanks so much to Mimi for inspiring me to use them!) and record at least 3 observations. From those observations students proposed characteristics we should use to describe the shapes and then completed the entire row of this chart:

This went great to start! I was really impressed with how many properties they came up with, and the only instructions I provided were "measure sides, angles, diagonals and record observations." However, there were too many properties for this activity to hold their attention. I knew the good streak was over when I got the dreaded "When are we ever going to need to know this?" (side note: Seriously child? I know you're just looking for an excuse to quit, but we're sorting things by characteristics, that's an important life skill that crops up everywhere!)

So, now I need a follow up that's less tedious and proof is always iffy. The proof cards are helpful, and I don't think I'll even need any new ones since most of these characteristics come from parallel lines and properties of triangles. But somehow I need to get students to want to prove characteristics, because I'm pretty sure they're all totally content with having observed them. Ideas?

p.s. After the test students get to work on this awesome worksheet Fawn put together (originally from Don) since we're studying area after vacation.

Another thought: the proofs in the textbook are all "given properties, prove this is a parallelogram" so I should include something about which proofs are reversible...

ReplyDeleteI did an always, sometimes, never follow-up to this last semester. http://pamjwilson.wordpress.com/2012/10/21/always-sometimes-never-75facts/ Great discussions! This semester, I think I'll provide white boards at each "corner" of the room, and use the claim/support/question thinking routine to guide discussions - they must support their statement OR give an example that causes them to question others' statements. LOVED having "corners" labeld in room, Ss had to choose, and be ready to defend their claim!

ReplyDelete>So far we have found (and proven) the angle sum rule for all polygons

ReplyDeleteInteresting, but it's really 5th or 6th grade math, no?

http://fivetriangles.blogspot.com/2012/04/angles.html