I am working on a ton of interesting projects right now. Not least of these is my classroom teaching at the community college. My fingertips are sore from typing.
And yet there is always more to say. More to think about. More conversations to have. Here is a peek into one that is ongoing.
Malke Rosenfeld and I have been going back and forth about math, dance, Papert and learning for a few months now. I am learning a lot from the conversation. She asked some questions this morning.
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Malke: A thought just entered my head — why are you offering TDI? Is it based on a question you are unsure of and want to see what others think? Or are you seeing a deficit in math teachers’ thinking that you want to shore up?
Me: When ranting on Twitter, I could see that some of my assumptions about baseline teacher knowledge about fraction/decimal relationships as they pertain to developing children’s thinking were unfounded. That is, I was assuming teachers knew a lot more than they seemed to. Which has implications for my Khan Academy critiques, and lots of other writing on my blog. Yet people were also curious. So I wanted to say more in a way that would draw from and build on a larger collective knowledge, so it’s not just my spouting off.
Malke: Is there a reason you offered it specifically as a course, and not a moderated discussion (which it sort of seems like right now)?
Me: When you view learning as a social process, you tend to think of courses AS moderated discussions. I mean this quite seriously. I know that it goes against the grain of online (and face-to-face) course design. But that’s not because I think of online instruction differently from others; it’s because I have a particular view of learning that runs much deeper than that. If I tell and quiz, you’re not learning very much. If I propose a set of ideas, listen to what you have to say, encourage you to interact with others and move the conversation in directions that seem useful based on those interactions, you’re probably going to learn a lot.
As long as I can keep you engaged in that process. Which is a different challenge online than in the classroom.
Malke: Is there a place you specifically want your students to get to by the end of the seven weeks? Or are you just curious to see what develops?
Me: I am curious to learn what I can about teaching at every opportunity. I want to produce “students” who can articulate important questions (see? learning as having new questions to ask?) about curricular approaches to decimals. Ideally, I would help them to develop a critical voice that speaks to/through them when they work with individual students, when they plan lessons and when they talk with their colleagues in a variety of settings. In short, I want to change the way teachers view the territory of decimals, fractions and children’s minds. Strange mix of lofty and specific there, huh?
); I do have some critical questions about whether money is a strong foundation for building generalized decimal concepts.
feet, although I know that I could. Likewise I don’t think of 1 hour and 5 minutes as 
hours, although I know this to be correct.
dollars?
of a dollar, does money support the repeated repartitioning that is essential to decimals? E.g. Find a number between 0.04 and 0.05. Does thinking about money support a student in getting to 0.041?
Overthinking my teaching 