DOING MATHEMATICS: A Lesson Format

02/16/2012

6 Comments

 
Ask just about anybody to describe the typical math class and I imagine this is what you will get:

1. Teacher goes over answers from last night's homework
2. Teacher introduces new topic for the day while students take notes
3. Class does a few examples together
4. Students start the new problem set assigned

This format works if your goal is to have students learn (read: memorize) someone else's mathematics. If you want students to create, author, and do their own mathematics, something has to change. Brian Lawler introduced me to a lesson format that helps shift this focus:

1. LAUNCH: set up the task/question for the day
2. EXPLORE: students work collaboratively to explore
3. SUMMARIZE: students display work, ask each other questions, and make connections

More details about this format are available online. It's tempting to be a skeptic when it comes to this new format. Most of us have gone through a very different math experience and the pressure of standardized testing pushes us to cover as much "content" as possible. 

Our class is still breaking apart the "infinite star" problem and today's task was to try to figure out the total area at each iteration. The class came up with this:
…which resulted in this:
…and one student even wrote this:
We can talk all day about skills and testing but this sort of abstraction is at the heart of algebra and is the definition of what it means to "do mathematics."
 


Comments

Dan Meyer link
02/16/2012 4:23pm

So cool. The part that excites me most is the bit where the student defines the active variables and makes the decision to make initial triangle area and not side length the independent variable. That's a moment that students generally don't get to access in classrooms that lean heavily on print curricula.

Reply
Asal Mirzahossein
02/16/2012 5:39pm

I really appreciate the value of abstract thinking and exploration discussed in this blog...

Reflecting back on a conversation we had recently, why don't more teachers encourage their students to engage actively in abstract thinking, instead of doing all of the abstract thinking for them? Do teachers even define abstract thinking for students?

As an English teacher, I see so many clear connections between the discussed lesson formats and the English classroom (Just replace "problem set" with "reading"!) . I happen to be a bit more fortunate to be teaching in a discipline that abstract thinking is welcome, and even possibly encouraged...but not necessarily always practiced. Seeing abstract thinking in your students' work, especially the last piece, is exciting and affirming.

Thank you for all the great work you are doing in your classroom :)

Reply
Scott Meyer
02/19/2012 1:55pm

I enjoyed math in school. I was under the "old school" of memorizing the formulas. I did fairly well. I wish that I had a teacher like you. I think that I would have learned more having to think about the solutions instead of memorizing the solutions. Keep it up!

Reply
ihor link
02/23/2012 12:35pm

Nice activity. What programming environment was the student using? Also, I think Brian may have learned about the lesson format from the Connected Math folks (not that it was original with them.)

http://connectedmath.msu.edu/components/teacher.shtml#cmp

It's been my mantra with teachers for most of my career. My three are:
1. Set the stage
2. Do the activity
3. Debrief

Reply
Bryan Meyer link
02/23/2012 10:05pm

In some ways, I think this lesson format is the single most important change in order to help teachers engage their students in DOING mathematics. In thinking about planning for lessons in this way, you (the teacher) necessarily have to think about designing things that force students to be active. Recently, I have been thinking about how important it is to "perplex" in step one (the one you titled "set the stage").

Reply
Ihor link
02/24/2012 5:22pm

Yes, perplex works if you have the right chemistry with the kids. I always tried to spark their interest first with some form of "neat phenonmena" that got them scratching their heads and kept their interest through the investigation stage (doing the activity), so that when we debrief some light bulbs go off. Whether it is the kind of perplexment that Dan talks about is not that clear to me, but if the kids are still talking about it when they leave the class then I know the activity was a success. What were the attributes that made it a success is what I think about afterwards.




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