Tuesday, February 14, 2012
Happy Valentine's Day! :)
Started by talking about the video we watched, Using Dynamic Geometry.
- Was that a public school? In both cases yes, just different ones.
- What would happen if we only had half as many computers? Two people per computer. One person might get more experience than the other person. Can create conflict because the two people want to explore different things, but the person with the mouse is pretty much in control. The same thing happens in group projects in general, not just on the computer.
- Research has been done. Some has shown that when you have to share you're more cooperative, but other research has shown that students don't like it. If you're going to use computers with your students you need to make sure you have enough for what you want to do.
- In here were all using different computers, which can be a problem if you're looking at commands, or things that are specific to the computer.
- You can chose how you want students to use the computer. You can have meaningful learning experiences even if you don't have a computer for every student. Don't use that as an excuse to not use the computer.
- Female teacher talking to students about tessellations, it seemed like she was telling them what to do and what to see.
- Male teacher had a very open ended task. You find something and explain/ prove it to me.
- Convince yourself, convince a friend, then convince me.
- You have to be able to prove your conjecture.
- Don't just convince, but ask why. Asking why is looking at it from a different perspective than just proving it
- Proof doesn't always play the roles we wish it would. The proofs need to be talked about, not just done.
- different types of proofs/ reasons to prove: establishing something for the mathematical community, convince yourself, understand why.
- Why do a proof?: You notice something. Then you try to understand the underlying phenomenon, then when they understand what seems to be true, then try to prove it.
- How would you prove that the angles of a triangle add up to 180.
- what do you know about triangles? examples.
- draw parallel lines to get congruent angles.
- Technology can be precise. Of course we could draw, but it takes so long, and you can loose site of the math that you're trying to see. First teacher points this out.
- Female teacher seems to talk a lot, which takes away chances students have to understand something.
- although she seems to be talking a lot, the students are still talking a lot about the math, which is good. They are engaged in the mathematics.
- Male teacher was good with just having the students do the proofs.
- His question to the students was very open ended. Some students got more out of the exploration than others because some students stuck with the easy shapes, and some went to harder shapes.
- think about that when designing tasks.
- give them a reason to do more, once they've had a chance to explore direct them to certain shapes and have them prove them.
- Be prepared for possibilities, if no one is doing what you noticed before hand then ask the class to do it.
- What is it about doing this on a computer that makes this different than doing it on paper?
- don't want to draw and erase
- can communicate properties
- potential problems:
- no one was taking notes
- Students seemed to keep the figure static. they didn't vary the sizes of the circles or shapes, just looked at the one set of circles. don't make good use of the dynamic aspect of the geometry
- programs take training which takes time out of the mathematical learning
- Student could go up to SMART board and draw the shapes he found and show his proof.
- Is it worth all the fancy, expensive gadgets if we only use the projector or i clicker functions.
- if you're going to spend the time and money to get the technology, then spend the time and money to learn how to use it.
- You're not going to use a part of the technology if you don't know about it
- you go through stages. Get it, play with it, learn more about it, realize why it's cool (or not)
- We've made this assumption that if we really did put the time in to learn about it, would it really make a difference? is it really worth it?
- so far teacher doesn't think so, but he might have thought that about using a computer in the classroom, and now he wouldn't teach without the computer.
- SMART board is designed to do what we do on a white board, and then the work can be saved and it's available to everybody.