Monday, August 23, 2010

Top 10 Technology Advances of All Time

Kate, over at f(t) inspired (pun intended) me to write a little about technology after reviewing a TI seminar she attended.

So without further ado...
The 10 Most Important Technological Advances in Math Education (chronologically):
1.     Writing utensil (to write on cave walls)
2.     Paper (because cave walls are hard to take with you)
3.     Ruler (and, in general, the concept of measuring devices)
4.     Abacus (yeah for being able to do large arithmetic problems quickly)
5.     Printing press (makin’ a copy)
6.     Slide Rule (yeah for being able to do large arithmetic problems quicklier)
7.     The industrial revolution (education for the masses…errr…where we learn to sit still and follow directions)
8.     Sputnik (not directly used in math ed, but this played a huge role in shaping our current curriculum)
9.     Computers (beginning with its mad arithmetic skills, case checking skills and evolving into its use for modeling)
10. The internet (for resources, networking, social media learning, etc)
And as a bonus…
11. The TI n’spire

Initially, I put #11 on here in jest but I’m beginning to consider the actual importance of this technology (and not in a good way).  Specifically, I believe that the n’spire and it’s predecessors have played a significant role in shaping standardized testing and that this standardized testing has shaped recent curriculum as much, if not more, than sputnik or the industrial revolution.

Without much thinking, my first criticism of this list is that it is pretty 20th century-centric.  Anyway, something to ponder.  Anything you would add? 

Thursday, August 12, 2010

My Blog Post about Math For Love's Blog Post about Math Mamma's Blog Post about...

Math for Love just wrote a post that I really enjoyed about play.  Go there and check it out and then come back here for the post-game analysis.  I was originally just going to comment over there, but this got too long.  Anyway, I found that it was a really well articulated process of how I want students to work with math problems.  Since you're good at following directions you've already read this but let's recap.
  1. Play (Expansion)
  2. Ask questions (Reflection)
  3. Choose a question that you really want to explore (Contraction)
  4. Try to answer the question with what you already know
  5. If that fails (i.e., if your question is deep enough), start exploring other ways to approach the question, with your own ideas and by looking at what others have done. A teacher or expert can be very useful here (“Oh, you want to figure out how far apart those two dots are? Have you ever heard of the Pythagorean Theorem? It works like this…”)
  6. Refine your question
  7. Repeat Steps 4-6 until you solve your question
  8. Explain your work to people
  9. Realize that you can’t really explain it, and refine your solution until you can actually write down an explanation.
  10. If in a class or group, share your work with the group, or have the group come to an agreement on how things really are.
  11. Satisfaction.

I would stop at #11 (and although this is hard, I would also aim to have students feel #11 after every step).

12. Tweak the original "rules" in some way and return to #1.

In terms of addressing the floundering that can occur in progressive models, I think the key (not that this is easy) is teaching kids how to do #1 through #11 (well, imho the cycle of  #1 through #12).  Even "playing" can be taught. Consider the development kids go through when playing boardgames.  They start with games like Chutes & Ladders which has absolutely no strategy and children simply enjoy the unknown of what you're going to roll next and where you'll end up.  This eventually evolves into greater sophisticated game play where students have to make decisions (whether or not to buy that property in Monopoly, for example).  This evolves into more sophisticated strategies such as thinking ahead (Chess), thinking about your opponent's thinking (Settlers of Catan), making inferences based on past play (Poker), etc.

I believe the game metaphor can be extended to math problems, even traditional ones.  Just as an example, consider how the "rules" of subtraction evolve throughout elementary school:
1. Single digit whole #'s with the first being larger than the second
2. Multiple digit whole #'s with the first being larger than the second
3. Multiple digit whole #'s with the first being larger than the second, but requiring borrowing
4. Whole #'s with the second being larger than the first
5. Fractions
6. Subtraction of integers
7. Subtraction of rationals

We change (usually relaxing) the rules as we progress through the curriculum.  It's nice that this also mirrors what mathematicians often do, relaxing or restricting conditions and exploring the ramifications.

Videotaping my classroom

It's been a while as I've been camping/out of town/packing/moving/unpacking.  That's all (well, mostly) finished now, so I'm going to try and squeeze in some more detailed responses about the challenges of minimally defined problems before school starts up again. Before I do that, though, I need some help. Hopefully there's still one or two people out there reading this. 

So because I will be conducting research and just for my own good, I'm planning on doing some serious videotaping of my classroom this year (not too much, though, as too much data can be just as useless as too little data).  Here's what I would ideally want. 

1. A camera permanently installed above every table (4 desks per table) where, with a quick click at the computer I can turn on one or all of these cameras and record video/audio.  It doesn't need to be HD or 3D, but it definitely needs to be audible and it would be really helpful if it were readable (meaning you can read what the students are writing). 

Of course I should have known that this wouldn't be as easy as just buying 4 webcams, a USB hub, some long cables, and some sort of brace to hold these in place.  I haven't actually tried this, but it seems from some reading on the interweb that this doesn't work because the software has trouble/is unable to detect multiple cameras at once.  Grrr...any advice?  Any advice that doesn't include me also buying 4 computers?  

So...I yield to the tech-guru-blog writers/readers out there for suggestions.  The prize?  I'll write up a detailed description of what I end up getting to work and, barring issues with release forms, some videos of students doing math.  Dan Meyer has no problem creating clones of himself, so this should be a piece of cake.

...which brings me to my second request.

2. Anyone have some suggestions on the easiest way to make student vidoes anonymous so that I can share work without compromising student privacy?  What I really want is for someone to write a program that will take a live action video as its input and output a cartoon version. I'd even pay for the premium version that creates corresponding cartoon voices too.  Sean Cornally created his own grading tool for standards based grading.  Can this be his next project?  Please?  Worst case, I can always blur out faces in Adobe Creative Suite, but ideally I'd like something more automated.  I guess the other option is somehow getting parents' permission to post videos of their sixth grade child on the open web.  In the end, the cartoon idea might be my best bet.