Tuesday, November 4, 2008

'Odds'n'Evens' Week of 11-4-08 Catching Up...

Haven't had one of these overviews for awhile now...

1. Have you had a chance to work on our MathAnagram for Oct-Nov-Dec?

Look here for details.
2. I am still interested in your thoughts on methods of teaching addition and subtraction of mixed numerals. The original post is here and reader comments were fascinating. Perhaps a poll or survey to collect even more input?
3. As some of you know I ran a series of brief calculus videos about a year ago. They are viewed quite often and I'm considering a few more. I did a search of online calculus tutorials/videos and came away with the feeling that there is a need for more. Some of the best tutorials come from the Visual Calculus series developed at University of Tennessee at Knoxville (utk), but these are not videos. Here is a sample of one of their best lessons (on implicit differentiation). I do not mean to slight the other excellent tutorials I found but I don't have time here to review them in depth. At various sites I viewed flash tutorials, one or two videos, lots of text but if you felt my video (even with the one error I made about an "isosceles" right triangle!), was helpful, let me know by emailing me or commenting on this post. I've been thinking about the Chain Rule, Implicit Differentiation and Related Rate applied problems. These are all connected so I might do a series of videos to demonstrate the underlying ideas and applications. Again, I would appreciate your input to encourage this effort since it is labor-intensive.
4. Any more thoughts about the recent post I published enumerating the topics tested on the recently released items from the Achieve/ADP Algebra 2 End of Course Exam? People are reading it but not commenting, a fairly common phenomenon!
5. No more thoughts about the Right Triangle in the Square Investigation? TC suggested a possible generalization but I'm wondering if anyone tried this in the classroom...
6. Perhaps not worthy of a full post but here's a mini-logic problem that reinforces both algebraic reasoning and the issue of demonstrating that an if-then statement is false:
If y2 > x2, then y > x.
Of course there are many variations on this and one could also use this to demonstrate the converse error, but sometimes it's nice to include proof in our algebra classes too.


IBY said...

I guess it has to do with the fact that the square root of a number has a negative and positive answers, right?

Dave Marain said...

To disprove an 'if-then' statement (aka, an implication), students need to find JUST ONE EXAMPLE (aka, a 'counterexample'), in which the hypothesis is true and the conclusion is false. For the given statement, we can choose y = -3 and x = -2 for example.

Yes, the algebraic error is related to the issue of taking square roots of both sides of an equation or inequality but my other focus here was the logic of conditional statements. If P, then Q is equivalent, in symbolic logic form, to ~(P ^ ~Q). This used to be taught in some curricula (and may still be around!). It seems sophisticated but it really does make sense that the truth of P --> Q is equivalent to saying that it is not possible for P to be true and Q to be false! Does anyone still teach this?