College teaching doesn't count. ; ^ )
Just something to keep in the back of your head. There have been a lot of serious problems with the way math education has been approached over many many decades. I think you'd be doing yourself a disservice not to become very familiar with them.
The biggest problem I've seen with educational research in general is that it isn't very honest. A true researcher should go out of their way to try and disprove their own claims and see if they will hold up to rigorous scrutiny. To often they try to force the facts to fit an ideology rather than make the facts drive the conclusion.
There's also a problem with indentifying the practicality of a lot of approaches. I'll give you just a few examples:
First I'll show you my approach, and keep in mind that I had very little experience (2 1/2 years of teaching), yet still had the *highest* test scores and passing rate in the school for my algebra classes.
1) I didn't waste time going over homework. They turned it in, and instead I would have them work on problems on the board that were very similar to the homework problems. This saved a lot of class time as most people just tune out when going over homework. It's better to get them *solving* new problems rather than passively listening to me explain old problems.
2) I didn't have kids write out explanations or write them on the board and explain them to the class. The claim was that this would help them learn.....except that it took too much time. Only 5 kids would actually be able to participate at a time, while 25 kids would watch and do nothing. The explanations were poor and no one could understand them (because they are kids explaining it, not teachers).
3) They would work on problems by themselves. If they didn;t understand, they'd have a partner help. If they still couldn't get it, I'd help them. This all heppens while I take attendence and collect homework. Again, EFFICIENCY!
4) I'd quickly go over the problems and explain how they should have done them, but this won't take much time because the problems were basic and the class had their chance to get my help already.
5) New topic - explanation "This is the pythagorean theorem. Here's how it works. Here's why it works." I don't waste time deriving it because they get nothing out of it at 14.
6) We work through an example together while they watch me on the board.
7) They do an example on their own, get help from partner if needed, or me if needed.
8) I go over the answer. I do another example with the class. I have them do another one on their own. I then give them 10-20 problems to work on.
Remember - *highest* grades in the school!
My adminsitration hated this process. What I was supposed to do is have them work in groups of 4, explain to each other how to do the problems, write answer on the board, and explain them to the class. For learning the Pythagorean theorem, for example, they were supposed to do an activity where they measured the sides of a bunch of triangles, put them into some sort of grid, and see if they can "discover" the relationship between the different sides. In theory this is supposed to be a better method than having me just tell them and then have them work on problems. The problem is, by employing these methods, I burn about 20-30 minutes of class time and end up having to just tell them anyway.
This kind of method works much better in a smaller setting, or possibly with a more advanced group of students, but it is horribly inefficient with teaching a larger group of average to below average students. They require structure, and efficient activities that they can work through.
Much of modern math ed. programs focus on trying to make math class not seem like math class. The bottom line is, they actually have to work through the problems. there just isnt any way around that! As an old physics grad told me, "you learn physics (or math) with your arm, not your eyes."
My 2 cents.....I can rant on. ; ^ )
-----------------------------Baron Von Speedypants
-----------------------------RunTraining articles here:
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