sharris wrote: SpinnerMan wrote:
assateague wrote:No she's not.
If they were able to explain their reason, but they got the answer wrong, we are more focused on the how and moving to the explanation, sure we will correct them, but the emphasis is on the explanation. That's a paraphrase of what she said. The focus is not on getting the right answer.
She said she wanted her students to compute correctly, but to go beyond that and know why they were computing correctly and be able to explain it. I have no problems with that. I can easily see the value of teaching concepts first (and expecting the kids to explain them to show that they are really understood) and then focusing on the end product, especially in early math education.
What did she say they were putting the emphasis on? "We want our students to compute correctly, but the emphasis is really moving to the explanation and the how and the why and can I really talk through the procedures"
That is a direct quote to the best of my ability.
The EMPHASIS should be on one and only one thing, computing correctly. The how and the why and talking through the procedures has only one purpose, so the kid computes correctly
They want that, but that is NOT the emphasis, so what are they going to get?
I want many things, but if it is not something that I have emphasized in my life, I am for the most part left wanting those things to this day. Why?
If you are not consistently getting the right answer, you did NOT learn the concept. They go hand in hand. They are not separable. You cannot emphasize the concept and not emphasize getting the desired result. I don't care if it is playing the piano or learning your multiplication tables, the emphasis has got to be on demonstrating mastery at the appropriate level which allows you to work to mastery of the next level. It is not being able to articulate the concept while being unable to demonstrate a mastery of it. Maybe the goal is entire generations of teachers: the can't really do it, but they sound good describing it, so they teach.
The emphasis has got to be on the results. In math class that is mastery of math skill and not the ability to articulate them. That is a different class and a different, granted valuable, skill.
What I really think is happening is the classic case where whatever you personally do well, you over emphasize the value of that skill.
Generations ago, when someone with exceptional math and science skills didn't have near the opportunities that exist today, they were much more likely to teach. Same with many other skills. Today and for some generations now, what are the odds that someone with the aptitude to be an M.D. or get into a top engineering school or a top law school or ... was going to choose to be a school teacher? The reason people choose to be school teachers in my personal experience has been that it is the family tradition, it was the best they could get into in college, they flunked out of engineering, they wanted to pretend like they were important people, it's a good job for a woman that wants to raise kids and have summers off with them, and the most highly motivated and talented people do other things, while generations ago, very talented and capable people were teachers. I had some very old teachers that were very smart, but I've seen very few young teachers that are not pretty dumb and none that I would consider exceptionally intelligent.
So what are the skills of the mediocre? Well all through school, being right was not what they excelled at. It was explaining why they were wrong
A politician thinks of the next election; a statesman of the next generation. A politician looks for the success of his party; a statesman for that of the country. The statesman wished to steer, while the politician was satisfied to drift.