>Dear Tracy: >Please, make me a favor: choose a `real-world' problem which >you consider really good and send it to this list, so that we >could discuss it. >I have heard much about this `real-world problems movement' >but had no chance till now to get acqainted with its fruits. >I am sorry that I comment on your message to another person. >Andrei Toom
I'd be interested in hearing your comments on material found in a transcript of a recent program in our Michigan Gateways Series. This is a television series for K-12 math and science teachers. The episode is "Tasks for Learning." The transcript of this program can be found on the WWW at:
The "Gateways Report" and "For Discussion..." segments of this program relate to your request above.
The "Gateways Report" segment begins with a look at a sample problem from the NCTM Professional Standards for Teaching document (a companion to the Standards for Curriculum and Evaluation). As far as I know, this particular NCTM document is not available on the www at this time.
Here is a brief excerpt from the program transcript: ========================= CARTER: What IS a good "Task for Learning"? This Gateways Report begins by comparing two tasks that teachers might use to explore area and perimeter with upper elementary students.
Task One: Find the area and perimeter of each rectangle. [image: two rectangles, with dimensions indicated].
Task Two: Suppose you had 64 meters of fence to build a pen for your large dog, Bones.
What are some different pens you can make if you use all the fencing? What is the pen with the least play space? The most play space? Which would be best for running?
This task comparison is drawn from the NCTM Document, Professional Standards for Teaching Mathematics.
DR. DEBORAH BALL/TEACHER EDUCATION/MICHIGAN STATE UNIVERSITY: I think that in general we're looking for tasks that have layers in them, that is, there are multiple ways you could actually attack the task or engage it and presumably there are even some different things you might learn from doing it.
CARTER: Deborah Ball was a contributing author to the Standards for Teaching. She talked to us about why Task Two is the better task.
BALL: one thing that's different is it has multiple solutions. Instead of the first one you gave where you just find the area and the perimeter of one rectangle and the area and the perimeter of another it's straight calculation, I mean, all you have to do is to remember the formula and calculate it, you're done.
excerpted from Michigan Gateways #305: "Tasks for Learning" first air 3/3/95 copyright 1995 MICHIGAN STATE UNIVERSITY ==========================
I'd be interested in hearing any comments you might have on the full program transcript.
Bill Richards p.s. I've cross-posted to NCTM -L , my apologies to folks subscribed to both.
----------------------------------------------------------- William R. Richards firstname.lastname@example.org Producer/Director BillR@wkar.msu.edu ----------------- MICHIGAN GATEWAYS --------------------- The Television Program for Teachers of Mathematics and Science 212 Communication Arts Bldg - East Lansing, MI 48824-1212 ph: 517 355-2300 ext 422 fx: 517 353-7124 --------- http://www.msu.edu/comptech/gateways ----------