


Keynote Part IIConclusions Let me wrap up now with four conclusions: One point I hope I didn't overdo but did emphasize enough to make an impression is that the content knowledge needed for teaching is different from that which is needed for other mathematically or scientifically intensive professions  like engineering or medicine. It is mathematically and scientifically intensive work, but it requires a different kind of mathematical and scientific knowledge than that required for other forms of work. The second point I tried to emphasize is that content knowledge has to be usable for the work that teachers do. Simply increasing teachers' content requirements or the time spent on subject matter in professional development without its connection to use isn't likely to produce very helpful results. The third point that we spent quite a lot of time on was a claim that mathematics teaching involves specialized mathematical problem solving that we have less experience at seeing, noticing and designing opportunities to support. I hope we can talk more about what the analogies and correspondences are  as well as what may be some of the differences as we consider the teaching of science. And finally, learning content for teaching can be better grounded in practice by designing opportunities for teachers to solve the contentrelated problems that arise recurrently in their practice. This is what we did at the end  we looked at some examples of how one could design such problems. We still need to talk more about how one could use such problems to help teachers learn content for teaching.


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