Recent thoughts about math education

When we were young, we learned and studied patterns. When we start learning arithmetic and higher math, we (tradtionally) learn sets of instructions. I find this to be 99% wrong. There is a time and place for learning a set of instructions, but not that often.

Math (and/or nature?) is nothing but patterns. We, as humans, learn from patterns. Why not present all math as patterns and let the students discover the "instructions?"

Many of my lessons are progressed by asking, "What is the pattern?" I set my students up with the pattern. They do the work, they look back at the work, and should come to a conclusion about at least one pattern from their work. For example:
Multiply:
a. (x + 3)(x - 4)  b. (y -5) (y + 7) etc...
What patterns do you notice? How can we use this info to work backwards, or to factor?

The students come up with the rules/patterns/steps/etc. for factoring.

I have found my students are more engaged and excited about math since I have been teaching this way. Let me know what you think or find out.

And I cannot leave this post without sharing a short clip from one of my favorite movies and directors. Daren Aronofsky's "Pi" is an outstanding movie, especially for a first full length film. Enjoy!
Watch a short clip here

Listening

Much of school, learning, and life we depend on our listening skills, but do we ever teach the skill? From birth we read to our children, we play music for them, and we ask them to listen to adults, but when do we teach them the skill of listening? Sean Layne talks about how we need to teach the skill of concentration and he has a great method of doing so. His method breaks it down to a simple game, that only uses concentration. How can we do this with listening? How can we show students what it is to listen?

I know that people still play the game telephone and that students can repeat things back to the teacher to "prove" they were listening, but I do not believe that is teaching or proving they are listening. A quick search on yahoo did not pull up much about teaching the skill. And the articles that were there were talking about reading or ESL. This confines listening to just language.

How can we teach listening? This is the question I want to tackle.

Professional days and the Arts

Yesterday was a half day for students and the afternoon was a professional day for the staff. I was excited about this day. I had worked with our arts integration teacher to bring in Sean Layne. What an amazing and powerful day.

I have already taken a handful of classes with Sean and knew that he would be teaching nothing new to me. However, I still learned a metric boatload. We were fortunate to have Sean work with three different grade levels of kids. Seeing him work with students is awesome for many reasons. The first is you validate much of what you have seen in your class (behavior) and the second is you see the potential of your students.
However, I feel as if I need to apologize after seeing Sean work with this group of eighth grade girls. I told Sean that they have all had Tableau with me and should be able to get through the skill building more quickly than the younger grades that haven't had Tableau. Boy, was I wrong. He was not set up for success due to the day. However, there is no excuse for students to act the way they did. If you ever read this Sean, I apologize.

Enough about that. I just have to say. Read, see, take a class about and with Sean. Your teaching will be changed forever.