
Re: new tutor here
Posted:
Jun 19, 2013 4:58 AM



On Jun 18, 2013, at 10:43 PM, Joe Niederberger <niederberger@comcast.net> wrote:
> I must say again, I wouldn't use either of your {1] or [2] in school; the original is better, simply: Which is larger..etc. I see little value in trying to mold people in one direction.
Ok, I am not talking about a class of math geeks who have already acquired (or were born with) the ability to reason and now challenge each other to create the most elegant proof. I am talking about teaching the other 90% of the students how to reason mathematically. And molding is a good word but I think I have made my case that whether you use geometry or algebra or both, the underlying theme that makes it mathematics is a reasoned argument of justification which is logical, not visual. That part doesn't change. Your picture requires an understanding of logarithmic relationships, algebra and analytic geometry, and the ability to chain it together, does it not? That is what I am trying to mold. I am not just trying to teach a student to think, but to think as strongly as possible.
If I started with the original problem, my first question to the students is "Why is this a hard problem?" and I would expect that at some point in the discussion it would emerge that there doesn't seem to be any apparent strategy to attack it, other than simply using a calculator. And I would use a calculator to show that these two values are rather close together, which would explain why our sense of number (approximation etc.) is of no help in this case. We are going to need something more exact to resolve this question. We are going to need an analytical approach. At this point we would start discussing alternative representations, like taking the ln() of both sides and if that seems to help or hurt and why? Of course, that assumes that we have done enough "work" with logarithms and exponents up to this point. Somewhere in all that, this visualization might pop up. But not without the analysis and justification before hand.
The last thing I would do, unless my students are far enough along, is to give them this problem and have them discuss it amongst themselves. That is just wasting their hour. I am the expert and I am supposed to be using that to reach them how to be experts. I am supposed to be coaching them.
Bob Hansen

