Working on Projects

I keep trying to find projects that are fun, creative and involve problem solving. You may have noticed the 8th iteration Sierpinski Triangle at the back of the room. It is soon to be a 9th iteration fractal which is 4 times larger than the one that has been up for the last week. It will go go from floor to ceiling in the room. What I've liked about this project is that everyone has contributed a small amount of work and several students have gone on to figure out how to make the larger iterations and continue to work on it just becasue they like doing it. This is the ultimate goal, to find things to do that students actually enjoy and are challenging problem solving activities.





Your class has had a tesselation project for the last few days. At first it seems like an easy problem, most of you have done something similar in prior years. What I've tried to do is leave it more open-ended so that there is something to solve rather than give you pre-set tiles. There are an infinite number of solutions and that is where art and math intersect, way out there in infinity. I'm curious about your thoughts about these type of projects. Would you like to try to work on the 10th iteration of the Sierpinski triangle? What other things would be interesting to work on?

"I don't do math!"

I've heard and read some comments about math that sound something like, "I don't do math except in math class". I've even heard teachers say this with an added "We don't do math in this classroom". This usually comes from a language arts teacher and I wonder what the reaction to me would be if I said, "I don't do words!" It's kind of absurd because I couldn't survive without words. The same is true with math, of course. Frequently, I'll hear one of these comments and the speaker then immediately looks at their watch and says or thinks "Oh, I've only 45 minutes to..." or "I just can't afford..." It's kind of ironic. Math is a language that helps us understand the world and everyone uses it whether they realize it or not. The trick to being the master of our own lives is finding the underlying reasons that things happen, which allows us to make predictions and solve problems.

The Rest of the Story

Most of you got to see the video of Robert Lang talking about origami on Friday before the mid-winter break. There were several things about his talk that I found very interesting, even beyond the mere fact of what he is able to create with origami. These relate to our study of math because they address what we call "the process strands". There are 10 standards that the National Council of the Teachers of Mathematics (NCTM) has laid out and that we try to meet in math class; 5 content strands and 5 process strands. You are probably familiar with the content strands which are:

1. Number and Operations


2. Algebra


3. Geometry


4. Measurement


5. Data Analysis and Probability

We are focused mostly on Algebra in our class but touch on all of the others at various times. What I really want to get across is the importance of the other 5 strands, those "process" strands. In many ways these are even more important than content strands because they are the "real life" skills that math is supposed to be all about. They are:

1. Problem Solving


2. Reasoning and Proof


3. Communication


4. Connections


5. Representation

Now what came up in that origami video was that he touched on all 5 of these process strands and I'm wondering if you are able to see how that is?

If you would like to see the video again, here is the link:

http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html

it's only 15 minutes long but I think it deserves more than one look.

Another thing that I found interesting was how Robert Lang simply stated that math was capable of taking things up another notch because it looked at the underlaying principles of origami. This is true of so many things I can't even begin to emphasize the importance of that thought. And lastly, I loved the way he said that we can use the work of dead people to make things easier for ourselves because I've said some similar things about how we are studying solutions to old problems in order to help us find solutions to our problems. There is a saying, "We stand on the shoulders of giants."

The World's Biggest Problems

Last week our class came up with a list of the world's biggest problems.

• global warming


• the economic slow down


• using up limited resources


• providing enough energy for the future


• war

We also agreed that the solutions to all of these problems involved math in some way. There was an assignment to write down some of the ways that math could help in the solution of these problems. It was just before the end of the term and only a few students actually turned in the assignment. I'd like to get every one's input on this so I am reassigning it.

The goal of math is problem solving, so I really want you to think about this. The solutions to the world's problems are your futures.

Please leave a comment. If you already handed in a written version your comment could be that you did give me a written response. Of course, there is always room for more thought.