Note taking.
Note taking is a key part of math class, right?
What better place than math class to learn that essential life skill: Note-taking
I already know how to solve systems of linear equations, factor trinomials, and calculate surface areas. So what good does it do my students to watch and copy me while I work through endless example problems when we all learn better by doing? If I teach by working out example after example on the whiteboard, I simply get faster and faster at solving the problems, and most of my students get more confused. Then they need try complete homework practice problems by mimicking what I did. Do you remember the feeling? Everything 'made sense' when the teacher was explaining, but when you were on your own, it was just numbers and letters jumbled together!
With this in mind, I have removed note-taking and lecturing from my classroom. I try to get my students doing math the full 50 minutes they are in my room. They are not always doing the math correctly. That is okay... because they are still in the learning process. If they did everything correctly... they are probably in the wrong class. Through making mistakes, comparing solutions with others, debating about which strategies make more sense, adjusting their strategy, making corrections, and all around doing and talking mathematics... the students are learning mathematics! On top of learning mathematics, they are getting a deeper understanding of it. They start to realize there are multiple ways to solve a problem. They also learn to interact with their resources... textbook, peers, teacher, and computer. Learning is no longer a transfer of information from teacher to student... but a learning network.
BUT...
There are still times that I 'lecture' my students. By this I mean, I have them all sitting and listening while I explain something to them. This is pretty much always AFTER they have worked on a problem for a while in groups, and in order to complete the problem, they need some new mathematical strategies. The reason I do this is because there are some algorithms or procedures for which they need to learn a specific method. [Especially in the Grade 10 course, since it has a provincial exam]. I introduce algorithms afterward, so they already have some hands-on experience with the underlying concept, and they can make better connections between the algorithm and the mathematics.
Here is how I 'lecture' in my non-traditional classroom:
1. I tell my students: "Please find a seat somewhere in the room so you can see me and get comfy because I need to talk to you for a while".
2. As I explain a concept or procedure, I either point out or ask them to make a connection to some prior knowledge they have or to a recent task they completed.
3. I write notes on a whiteboard... usually non-linearly.
For example, starting from a diagram in the middle and working out in all directions. I don't really have a reason for this, except that it is usually the way I personally think and problem solve. When I am brainstorming or problem solving, I rarely start work left to right, top to bottom.
4. I try to keep all notes to only 1 whiteboard... or less.
If it is full, it probably means lecture time is up. What? Not boards full of examples and explanations? No. A high school student can focus on a lecture for only about 10 minutes. Or, somewhere between 8 and 20 minutes according to a few random online sights I came across, here's one link: Why Long Lectures are Ineffective. If they can only focus for about 10 minutes... they are going to start phasing out on anything important I have to say after that.
5. The students don't copy down my notes. Just because.
Because... When students copy down notes, the notes are static. They do not hear everything I say. They do not see where I am pointing. They do not see how the labels and arrows are in response to questions. They are usually 'behind'... copying down meaningless equations and diagrams... while I energetically try explain new diagrams to the few students that have their eyes facing the board. When they look back at the notes later, it is usually a confusing mess.
6. Repeat. The students DO NOT copy down my notes.
Because... When I make diagrams and notes, they are dynamic. I am talking. I am pointing. I am drawing. I am labelling. The students are asking questions. I am responding. The diagrams are part of a bigger conversation.
7. I usually do not erase my notes.
After a 10 minute 'lecture' (I prefer to refer to this as a mini lesson), I do not erase my notes. I also take a picture with my iPad, just incase a student wishes to see them again for some reason. Then, I have the students work in their groups on whiteboards to solve a problem. This is another reason I keep notes to 1 whiteboard... the students need to use the other whiteboards. Students can easily refer back to my notes as they work through their problem.
8. Tools to become comfortable with.
I like to think of the mini lessons as a way for me to introduce new tools into the classroom. In any classroom, some students catch on to a new concept really quickly, while others need a little more time. When I give a mini-lesson, I am hoping that some students will immediately understand HOW to use it, and that the rest of the students simply know it exists. Then, as they are working on problem solving tasks, the students will become more comfortable learning the tool. If they don't know how yet, hopefully someone in their group will have the ability to demonstrate the tool. Having random groups every day means that the students comfortable with the tools will always be working with different peers. It also means that students confused about the tool will eventually be grouped with someone who can share their knowledge of the tool.
9. I expect everybody to listen, but I don't expect everybody to 'get it'.
When I teach a mini-lesson, I am keeping it short so they can use it as soon as possible. They are going to fumble and falter. This is good, because we only build our brain by experimenting, making mistakes, making connections, and correcting. They are going to ask good questions. They are going to problem solve. They are going to work in teams to build on their knowledge. They are going to learn how to learn. They will learn how to use their resources. And, when they finally do 'get it', they will probably never 'forget it'!! And those who did 'get it' right away, will 'forget it' right away... except now they have the opportunity to teach their peers and therefore for more chance of gaining and retaining a deeper understanding of the topic.
These two charts are slightly different... but I'm sure you get the idea!
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