Daniel Stamm, a retired physics teacher in the US, discusses below the strengths of various math curricula. Posted below with Daniel’s kind permission, is his perspective on what works and what’s great about the J-math (public school) curriculum.
There were certain things I tried to do in my teaching, such as illustrating ideas as concretely as possible and sequencing topics correctly or breaking complex topics into simpler ones and mastering each of those in sequence; things that should’ve worked, but never did seem to be that effective. Well, I found two translated Japanese lessons. One is the third grade lesson on weight in the article, “What We Can Learn from Japanese Teachers Manuals”, and the other one a chapter on area, which was sent to me by someone in charge of translating that article, Shin-Ying Lee.
These lessons to me are absolutely amazing. You can see how they meticulously developed the ideas, and they have specific connections with things that were taught in earlier grades. They actually seem to be teaching kids to think. It’s a subjective but very strong impression that the principles I mentioned above were carried out very carefully and thoroughly. So it seemed that when I tried to do it, it was simply about 10 years too late.
One of the main findings in the book the Teaching Gap, which are summarized in the paper, “Teaching is a Cultural Activity” , was that in the U.S., almost all emphasis is placed on teaching procedures – very little on developing concepts or understanding This is also why the things I tried to do didn’t work. The kids just didn’t care about concepts. They didn’t care about understanding. They just wanted the points, i.e., the grade. (I had a sign on my wall that said ”Get the point-the points will come.”)
Also, the idea of mastering things in sequence implies the essential nature of a foundation, and Japanese teachers develop such a solid one in primary school that it affects the entire remainder of students’ academic careers. It’s SO good and SO thorough, in developing the basic concepts and an understanding of them, that it could account for almost all of Japan’s superior performance on the TIMSS tests (at least in 4th and 8th grades). A foundation is more than a metaphor. It affects everything that comes later. I know juku must have an effect, but the foundation even for juku is developed in the early grades, isn’t it? The TIMSS problems are nothing compared to your high school entrance examination problems, and the variability of Japan’s scores is the lowest in the world, which means that the basics are being taught well to everyone, not just kids going to juku..
You mentioned Singapore Math. I actually bought the first four grades of that series, after getting all six grades of Tokyo Shosheki’s series (which was just translated and published here). So far I’ve only read the first grade of Shoseki and looked at Singapore math for comparison. I think the Shoseki is even better than S.M. (the first grade), but that may be only the American version of it. In Shoseki you can see exactly what they’re doing and why, most of the time; for S.M. they have a set of DVD’s costing about $500 explaining their system.
I also tried to develop a sense of quantities in measurement and of the units used to represent them. But this never worked either because of the stage at which I was teaching . I once had a student that I had asked to convert two grams into kilograms. He was so wrought up in his procedure, which was to move the decimal point three places in some direction, that he ended up saying that two grams equaled 2000 kg! This is a junior in high school in a class of advanced students. He wasn’t stupid, but the American system literally teaches kids to do stupid things. Or you could say that they’re simply never asked to think He was saying that something that should be the weight of four paper clips actually weighed 2 metric tons. He simply never thought about it with any understanding They simply never had the sense of the quantities and units developed the way it’s done in the Japanese system, which is in the second grade or third grade.
Believe it or not the same problem exists among American adults. In the book Knowing and Teaching Elementary Mathematics by Liping Ma, she discovered that (here just in regard to mathematical knowledge) Chinese ninth graders knew more math and understood it better than some American teachers with masters degrees!
[I’ve included several more articles sent in other e-mails: a summary of the Li Ping Ma’s book, and the two translations of the Japanese lessons].
Also, on one occasion, when she was observing a college professor and classroom teacher supervising a student teacher, conducting a lesson on measurement in a fourth grade class, a student was asked to measure the length of one side of the room with a yardstick. He came up with 7 yards, and so many inches and did some work on his calculator and told them that equaled 85 inches. The teacher duly wrote this on the board and Liping Ma noticed that that was an incredible error. But none of the three other teachers ever noticed it. Even during the their discussion of the lesson after the kids had gone. She was flabbergasted, but didn’t say anything. Even they had never had a sense of quantities and units developed, the way Japanese elementary school teachers do it with their kids.
There’s actually a simple explanation of how this unbelievable, depressing and mortifying situation came about. It has to do with the different roles of American teachers and Japanese teachers, which started developing as early as the turn of the last century. At that time, American teachers were completely excluded from doing any research. They actually had been involved in it with John Dewey at the University of Chicago. Then somebody decided that they needed “experts” with Ph.D.’s to conduct the research, and teachers were turned into almost an occupational caste. This is all explained in the TG.
In Japan there’s actually a long history of involving teachers in research to improve instruction. In America, we have a long history of so-called researchers (education professors) outside the classroom, out of touch with reality, who have developed innumerable crackpot ideas, which never work and which are forced on teachers from the top. In Japan, in contrast, teachers do research lessons in the classroom, involving the content that is to be taught (American “improvements” in education almost never have anything to do with content. They involve “brain based” education, “learning styles”, “learning modalities”—anything but content, because American education professors don’t know the content as well as many classroom teachers do.) And in Japan, teachers publish more than university researchers.
Another problem are the textbooks in America. They have evolved into gigantic collections of paper and ink, covering far too many topics, often in a very poorly integrated and poorly sequenced manner. They’re really designed to appeal to textbook selection committees, which are made up of bureaucrats who usually know nothing about teaching. One other article I sent you is “Coherent Curriculum” has some interesting photos of American and Asian textbooks.
Curricula suffer the same fate. They have a ridiculous number of topics even in the early grades, simply to impress some ignorant bureaucrat.
Everything in American education seems to be done for adults, rather than for children. Textbook publishers making money and “academics” and bureaucrats accumulating power (and making money).
As I said before, it’s unbelievable, depressing and mortifying. And your education system, despite its problems, is like a breath of fresh air, especially your elementary schools.
– Daniel Stamm
P.S. The Learning Gap and The Teaching Gap are cross national studies on attitudes toward educational achievement and teaching practices