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Schmidt, of the University of Michigan. At the time, Dr. We had the opportunity to interview Dr. Schmidt had to say in the early years of the research. I hope it does the same for yours.
Can you give an example of a model lesson from one of the top achieving countries, either Germany or Japan, which are the focus of the videos? Some of them are very didactic, lecture-oriented classes. Some of them are like the kind that you see in the Japanese tapes. If teachers know their mathematics well, they can be just as engaging through a lecture format, as they can teaching as the Japanese do.
Instead, the more analysis that I do, the more I believe that there are some principles involved here that just might go across countries. What is the common thread? I think the common thread that makes for the top-achieving countries is pure, honest-to-goodness mathematical substance.
If the teachers really know and understand the mathematics, then they bring that to the students, through whatever means they know best. Also, a large part of this idea is to develop this stuff conceptually and not just algorithmically.
I think many people misunderstand the Japanese videos. It is not so much the methodology, as it is the mathematics.
You watch those lessons and the instructor really understands the mathematics, engaging those students in more ways than we do in this country.
So, if a teacher were to do a dog-n-pony show lecture with drill-n-kill practice, and do it well, would it work? The dog-n-pony show lecture, yes; the drill-n-kill, no.
I think the common element is a clear understanding of the subject matter and then going through it much more conceptually than algorithmically.
Can you give us a model to how to teach math conceptually rather than algorithmically? For instance, there is the example in the videos of a guy teaching geometry. Then they realize that if they put a line anywhere its going to cut it into two parts.
How is a strong conceptual understanding of the mathematics developed among teachers? It comes from two sources. In some countries, they must major in these fields.
But look at what they already know before going to the university. They are already ahead. In regard to the things that our readership is looking at, active learning, projects, manipulatives, do you have any models from these other countries, or that you think could be done here?
They seem to be uniquely American inventions, especially the cooperative learning. We are too much into the methodology in this country, and we miss the substance.
We start talking about small groups and manipulatives and it just becomes process.A Universe of Learning. Whatever you teach, whatever your students want to explore, BrainPOP is a launchpad for curiosity.
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