2. Together, the group met regularly to discuss their plans for teaching differently, a Japanese version of TKOT; at the end of a discussion, they’d usually invite each other to their classrooms to study the results. In retrospect this was the most important lesson Matsuyama taught Akihiko; not how to teach a lesson, but how to study teaching, using the cycle of jugyokenkyu to put his work under a microscope and improve it.''
3. ... choosing 13-9 as the perfect subtraction problem because it forces the learner to use one of two methods; either the subtraction subtraction method or the subtraction addition method. “Knowing two methods would come in handy when students encountered new problems that worked better with one or the other. And, in general, seeing two paths to a solution helped students understand just how subtraction worked.
4. Reform’s next frontier, they wrote was teaching - the way students and teachers worked together in school. Standards set the course, and assessments provide the benchmarks, but it is teaching that must be improved to push us along the path to success.
5. We have this idea that if you discover something quantitatively in a research study, and then you tell everybody about it, that’ll improve teaching, Stigler says. The truth is, with teaching 10 percent of it is the technology or the idea of the innovation. Ninety percent of it is figuring out how to actually make it work to achieve our goals for students.
6. The takeaway message was not that conceptual understanding is more important than memorization; it was that the two are inextricably enmeshed. Any supposed dichotomy between them was false. Magdalene summarized the lesson in a single phrase. children, she said, were “sense makers.” …. Educators who imagined otherwise - assuming, for instance, that memorization took place outside the context of concepts and principles, or that repeated rewards and punishments were enough to help a person learn - did so at their own peril. Children would try to make sense of rules, even rules that made no sense.
7. Because the definitions were not all the same, neither was the teaching they argued for. In math, for instance, the “You, Y’all, We” lesson pattern popularized in Japan (as well as in Magdalene and Deborah’s math classrooms) made sense for structuring investigations of big ideas, like the meaning of fractions or negative numbers. In English, meanwhile, where students needed to learn specific reading and writing strategies - how to figure out the meaning of an unfamiliar word, for example, or how to build ideas for an essay - the “I, We, You” pattern of modeling followed by guided practices was more appropriate. And within each subject, different topics could call for different structures.
8. They taught by helping students see the world differently, pushing their intuitive knowledge closer to the bank of understandings and rules of operation that mathematicians (and scientists, historians, literary theorists, and so on) have arrived at over centuries. Teaching, in this view, began with listening. “Part of interacting with kids, “ Magdalene says “is assessing where they are and thinking about what experiences you can give them that will challenge their way of seeing the world.”
9. If teaching really was the most important of all the educational interventions, then the only logical conclusion was that American educators ought to build a coherent infrastructure - clear goals, accurate tests, trained instructors - to teach teaching.
10. We have a moment when we could do something different, “Deborah said one day, sitting in a coffee shop in Ann Arbor. “But if everybody does it their own way, forget it. It’s going to be the same thing again.”