On the topic of making my class a bit more stimulating for the upper end…
Today, I raided the dusty copy of Addison-Wesley Informal Geometry (1986) that was passed down to me from my predecessor who got it from his predecessor that passed it down to him. I figured the book hasn’t been opened in 20 years (or more) so I would check out the contents, and they did not disappoint.
Here’s a look at what I did with them:
We took a look at what it would take to make parallel lines. I felt that they knew the basics of the angle relationships, but I wanted them to get a bit confused and have to really take apart some diagrams and fill in some necessary gaps in the problem in order to answer an open-ended question. These problems do not look for one answer. They are complex and multi-faceted, here is another that we tried:
I was not going to do this last example, but I decided to ask the class if they wanted to do another, and they were all in, they kind of cheered when they knew that we were going to do another. One student even said, “Hey Mr. Seris, I love how socratic you are being today!”. (hint, hint)
The key to this activity is making them say the reason why they have that hypothesis. Several times, students had the right answer and said things like, “well, it just looks that way” (GASP!) and “well, it couldn’t be anything else” (GRRR!). It was important to keep pressing and to get the reasoning out there, making them think about and verbalize WHY, not just what. It helped us to air out the stuffiness of “Converse of the Corresponding Angles Postulate” vs. “Corresponding Angles Postulate” and the like, while at the same time exercising their “fill-in-the-missing-information muscles” through the use of missing angle measures.
During the activity, I was able to adapt it and I had a couple of particularly bright students that I gave the task of justifying why two lines were not parallel. Several students took it upon themselves to try to find the measures to all of the unused angles utilizing what they knew about linear pairs, vertical angles and parallel line angle relationships. This task accomplished more than I could have asked for and the socratic method gave me huge insights into the depth of the knowledge of my students.
Definitely a keeper…