This one has been bugging me and I really wish I had more readers because I think there is a valuable discussion here: The perplexing question here is essentially the same. This guy talks a lot about the quickness with which we move to abstraction. I'm wondering if maybe that applies here. I like the abstract because, in terms of creating a unit with a nice resolution, it easily comes full circle. I'm not sure you can say the same about the coastline. So…"what's the difference?!?"
6 Comments
Yeah, provocative pairing here, Bryan. Let me suggest that both of these are images are "concrete," at least in the sense I intend it. The abstraction happens as problem solvers decide "What information, tools, and resources do I need to answer my question?" So for the Koch triangle, they'll need to know the length of the original segment and how many iterations it underwent. For the coastline, they'll need to know the scale of that map. They'll need to know that the city names and the colors are irrelevant.
Reply
2/13/2012 04:38:47 am
I think the thing that interests me most about this is engagement. Essentially, the perplexity here comes from the same place: the infinite fractal nature of each image creates a paradox about finite measurement. I wonder if students will respond more positively to one versus the other even though the questions are, in essence, the exact same? I think there is a lot more to discuss here but I'm sure you get the general idea.
Reply
A few things come to mind re: "what's the difference?" here. The main issue that springs to mind is the background knowledge needed to approach both pictures. Is the idea to show this to students who already know about Koch's snowflake? I think most students would recognize the coastline of CA, not so many the snowflake. You can make some good comparisons between measurable/infinite, how do you measure something accurately, levels of precision that are necessary to do ___________. Lots of cool stuff.
Reply
blaw0013
2/14/2012 11:57:30 am
Thought of this post when seeing this TED Talk http://bit.ly/yP1pXN
Reply
> "what's the difference"
Reply
Angela
8/7/2012 01:43:56 am
I teach an online HS Geometry course. My students start the fractals unit by doing this activity with this applet : http://polymer.bu.edu/java/java/coastline/ . They do this before they learn about finding the perimeter of the Koch snowflake. This post has me thinking about it again...
Reply
Leave a Reply. |
Bryan Meyer…helping students DO mathematics @doingmath
Archives
September 2016
Categories
All
|