Tuesday, October 18, 2005

Where is Tom Lehrer when you need him?

I spent a good part of the afternoon today talking with folks from various WebCT campuses and all seem quite antsy about the proposed merger. Me, I’ve got other headaches. I get back to my hotel room after have Dinner and a few drinks with buddies from Frye, and there is a message waiting for me from my wife, all stressed out, because she can’t do my kid’s math homework. He is in 6th grade and they are doing something new.

The question at hand: under what conditions can you take four lengths and make them into a quadrilateral? Hmmm. I had an idea and tried to explain it to my wife on the phone. That was a total disaster. So I wrote up the following

https://netfiles.uiuc.edu/l-arvan/Capture1.jpg

But I’m scratching my head asking, can 6th graders articulate this? I couldn’t explain it to my wife, how could my kid explain it to his teacher? I’m all for giving conceptual problems to kids at an early age but if they are really to come up with a general solution to this in a pre-algebra class --- that is asking a lot.

I do think using a Tablet for writing up stuff like this is really cool. If they were cheaper I’d buy one for my kids for Christmas.

2 comments:

Juliette White said...

I think it's partly a question of what sort of answer you expect - I think a bright child that age might be able to work out what the rules are but not produce a formal proof of the sort you're envisaging.

It also depends on whether this is something students are expected to be able to do or something to stretch the brighter students and make them think. There's a massive difference between the two.

I suppose I think much more of school-level mathematics should be about concepts, solving puzzles and justifying yourself carefully rather than just learning different techniques, which is what it tends to be a lot of the time because that's easier to teach and assess.

Lanny Arvan said...

Juliette - Thanks and good point about what they are expecting in return from the students - a competency or something to stretech the mind, as you say. I don't know. At home we're clearly reacting as if it is supposed to be a competency, indeed as if everything the school assigns is to build a competency.

This piece by Jerry Uhl from the math department here, though about college math, seems insightful to me and could apply to what my kid is learning.

http://mathforum.org/technology/papers/papers/uhl.html

The assignment my kid had started off with these combination of sides for them to build quarilaterals.

6, 10, 15, 15
8, 8, 10, 10
3, 5, 10, 20
12, 20, 6, 9

It seems to me it would have been more illustrative to have examples where 3 of the sides are held fixed and the length of the fourth side varies. That would produce an experiment of sorts from which the kids could draw a conclusion.