In this next installment in the Common Core implementation series, I continue the interview with Phil Daro and Jason Zimba.
Marc Tucker: Phil, I remember, years ago, we were having a conversation about the materials produced by several of the National Science Foundation-supported programs in mathematics and science. You pointed to the great stack of materials for each of these programs and compared their great volume to the equivalent materials from Japan and Singapore, which were a tiny fraction of the volume of the American materials, very spare and elegant in their presentation. You argued that the standards were obvious and front and center in the materials from Asia. You also argued that the standards were contained in the American materials, but were buried in an avalanche of other stuff, so that they were effectively concealed from all but the most dedicated teachers. What does this say about the American scene? Can’t the purchasers of American materials just tell the American text publishers to emulate the Asian materials?
Phil Daro: You are getting at one of the reasons that we cannot rely on teachers’ homemade materials but cannot rely on the American textbook publishing industry, either. We desperately need the kind of elegant, spare, focused materials that we see in many Asian and European countries. The first thing you should know is that American publishers publish both the American textbooks and their Asian counterparts. The problem is not that American publishers won’t publish the textbooks our teachers need. They do publish them. But not for us. That is because the American purchasers of textbooks won’t buy the spare, elegant, focused textbooks demanded by Asian teachers. The mantra in the United States is “coverage.” So every topic must be treated separately, in detail. Asian teachers work together, collaboratively, to create their own lessons, honing them into excellence systematically. American teachers want the lesson plans spelled out in the teachers’ version of the text. American teachers want workbooks with innumerable versions of the same problem, to give students practice in solving standard problems. Asian teachers work on creating their own assignments for the students, designed to enable them to solve problems in a way that promotes deeper understanding of the mathematics. So the problem is not recalcitrant or greedy publishers. They will produce whatever the market demands. The problem is what the market is demanding.
Jason Zimba: And that’s huge. A decade of very inexpensive testing has in my opinion greatly damaged the curriculum. When I look at texts, I ask three questions: Is the procedural work of high quality? Is there close attention to the development of the underlying concepts? And, how robust are the applications? If you look at a typical chapter test in a book, it’s big problems on all three. So the procedures are usually only a caricature of the mathematical procedures students should understand. Concepts are largely absent. And applications appear at the end of a chapter test reduced to stock word problems. It is not often recognized how weak a position we’re starting from on the curriculum.
MT: The Japanese textbooks are written on the assumption that the teachers have a deep command of the subject they are teaching. Do you think that is true in the United States?
PD: This is a problem about which something has to be done. One of the great contributions of the Common Core is to draw attention to this problem. It is not a problem caused by the Common Core. If the Common Core went away we would still have this problem.
JZ: A mathematician I know who has been working with teachers for forty years said to me that, because of the Common Core, this is the first time teachers have been asking him to teach them more about fractions and other aspects of elementary mathematics. But this is a very deep and difficult problem. It will not be solved by a few workshops. This whole conversation has been haunted by questions of timeframe. Rewriting the textbooks and re-teaching mathematics to our mathematics teachers is an expensive, long-term proposition, even if the market wants it.
MT: Do you actually see key people at the state policy level understanding the depth and breadth of this problem of teacher knowledge of mathematics and do you see them actually starting to address it?
PD: To a degree, in a somewhat confused way, I see more professional development dedicated to math content now. I do see teachers, middle school and below, who are interested in learning more math and talking openly about wanting to learn more math. It’s less clear that’s true at high school level. But workshops are not the way to approach this challenge. The way to do it is the way the Asians have done it. It is called lesson study in Japan, and goes by other names in other countries. It has to do with the way the work of the school is organized. Teachers have much more time than they do in the United States to work together in a very disciplined way to improve their curriculum, build more effective lessons, get more student engagement with those lessons, ask the most telling questions during the lessons in order to figure out, as the lesson is given, who is understanding the materials and who is misunderstanding it, so they can correct course right in the middle of the class. This way of working results, among many other things, in constant learning on the part of the teachers. That, I think, is the only way the United States is going to meet this challenge.
MT: What changes are needed in our teachers colleges?
PD: Two related things need to happen. Elementary teachers need to specialize, so the training they get in the university can provide a deep foundation for the subject they will teach in school. Second, if they are going to be mathematics teachers, they need to take a lot of mathematics courses in college. But those courses should not be the topics ordinarily taught in mathematics in the university. They need to go far deeper into the mathematics of arithmetic and middle school mathematics than anything they have had thus far. Those courses don’t exist in this country. And they’re certainly not part of any program of teacher preparation here. But they do exist in Singapore and that is no small part of the reason that Singapore’s mathematics performance is so much better than ours.
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