While copy, practice, repeat is not always (ever?) fun, it has a place. What I heard in Dan’s original post is that both skill practice and conceptual understanding are essential, and neither should be sacrificed on the altar of the other.

Even Michael Jordan and Tiger Woods spent countless boring, repetitive, hours practicing their skills so that we can/could enjoy the beauty and wonder of their performances.

Boy, I can imagine arguments for it. They may not be very good ones, and they may not be “ideological,” but I can certainly think of them.

What if the stepped-out water tank problem comes after a more open-ended introductory problem like the one you created? How about before? Still bad? Does the textbook specify that thou shalt only give students the problems written in the textbook?

If you think about the ways that our brains learn and remember things, there are different ways to make something become a long-term memory. The first is through repetition, assuming you are practicing correctly, and assuming you are disciplined enough to practice it repeatedly, you can create a neural pathway (like wagon ruts in a grassy field) for that piece of knowledge. Another way is if there is a significant emotion attached to it – like how we remember everything about where we were when a loved one died, etc. The more modalities you use to learn something (listening, writing, seeing, thinking, touching, moving, etc) the more likely you are to have it go to long-term memory.

Copy, practice, repeat is probably the least efficient and most boring way to learn something, although it can work. It’s a great way to kill motivation and take all the beauty, wonder and fun out of what should be a fascinating subject. Some kids still need this, while some kids, we know, absolutely do not and we are holding them back from reaching their full potential if we force it on them.

Teachers, in a perfect world, would have small classes and plenty of planning time to be able to meet the individual learning needs of all their students.

This is not to say that there is anything wrong with being a math teacher like they are. There are a lot of kids who do really well with that kind of teaching, some who move on to do great things in math or math heavy fields. But those are not all kids and teaching like that leaves too many of us behind. There is an assumption that because a kid like I was doesn’t hack it in a classroom like theirs, we are just not capable of learning it.

Nothing could be further from the truth.

The biggest problem I had as a math student wasn’t getting the right answer – for lower level math I rarely had any trouble getting the right answer. I just had serious problems with following the proper road map to the correct solution. Moreover, I really didn’t understand why those roadmaps were so very important. I just knew that I could sit there, rumble the numbers around in my head and generally from a completely backwards method get the correct answers.

When I would try to challenge my middle school pre-algebra instructor to explain why the proper roadmap was so important, I was seen as interfering with his instructional time. Because he had already written me off as someone who was ever going to succeed in math or math heavy fields, he really wasn’t interested in wasting his time on me. What he failed to understand about me, was that I have neurological issues that make it very difficult for me to apply myself to things I don’t understand. Being told that I need to do something a certain way because that is the way it needs to be done, when I can get the right solution my way, is not going to get anywhere.

What really bothers me about this experience, is that I ended up going into contracting and quite often had to do rather complicated math – mostly geometry – on a near daily basis. And for the most part I had to do it in my head. While I did have the benefit of only having to estimate most of the time, I still had to make sure my figures were extremely close. We always hated having to return materials and even worse was disrupting a job to compensate for insufficient supplies.

And now, eighteen years after dropping out of high school, I am studying neuropsychology and linguistics. While I still have a great deal of trouble with math – still have a lot to pick up on, I am finding that when things are explained reasonably I really get it. Reasonable in this context means taking a very similar approach to what you describe in your TED talk. I am not deficient, nor am I incapable (though I sometimes complain that algebra just isn’t logical) – I just don’t learn the way kids who can pick it up from standard practices and retain it do. I need to see the problem.

Two semesters ago I had to deal with some math for statistical analysis that I was completely unfamiliar with. The problems were laid out in the context of a particular study – it explained what we were looking for from the data and it provided the raw data set. Now I will grant that what I picked up in last semester’s algebra class taught me a much easier way to solve that very problem, I was actually able to figure it out. Yes, it took me several hours more than it would have, had I attempted to take that class after my algebra class. But I worked it out.

This si really just my long winded way of saying that while your critics at KTM are certainly teaching many kids the way those kids should be taught, they are also leaving a lot of kids behind. And I am more than a little bitter about my own experience with teachers like that. I cannot begin to express how refreshing it is to run across teachers like you.

This videos shows the “fishbowl” process you describe: http://www.edutopia.org/math-social-activity-sel-video.

Thanks for all you are doing.