Cookies

Several people have observed that they would love to have audio of the conversations I report under the heading Talking Math with Your Kids. I agree that this would be helpful. But here’s the rub. These conversations are a natural part of our day, and they have to be natural.

My kids have no interest in being show ponies. Oh, they’ll show off for the recording device, but it won’t be natural. Observe Griffin as a young lad in this video, for instance.

He’s totally making faces for the camera and watching himself in the monitor. (You may also note that the spinach is washed; and please forgive the praise style—I know better now!) This mugging behavior has only gotten worse with time.

I do have some ideas for getting good audio, but these will require funds (Do you have a couple thousand dollars for a good cause? Tweet me! We’ll talk!) So in the meantime, we’ll continue the transcribed conversations.

Today’s conversation is a brief one, but I want to make a comparison. The discussion in the following video is not a natural one. (Tip o’ the hat to David Wees for the find.)

Here’s what I mean. The woman discusses cookies because she thinks they will interest the child in question, not because cookies are already under consideration. The question of multiplication (or repeated addition—I have no interest in that distinction here) doesn’t arise naturally either. It arises in the context of putting four chocolate chips on each of three cookies.

To be clear, I have no problem with any of this. But it’s different from the kinds of conversations I am hoping to encourage. The ones I hope to encourage go more like this…

Tabitha (5 years old) and her mother made cookies from one of those frozen-cookie-dough-school-fundraiser things over Thanksgiving weekend. These cookies were stored (unwisely) in a transparent Pyrex container on an open shelf. This led to a desire on Tabitha’s part for a cookie before dinner.

Tabitha: How many cookies can I have? One or two?

Me: Zero. You can have zero cookies.

T: A half?

Me: No. I said zero.

T: Zero whole ones and a half cookie?

Me: Zero halves.

T: And a quarter?

This is a natural conversation about cookies. The opportunity to turn it into a mathematical one was Tabitha asking, How many can I have? I could have played the role of rule enforcer and replied, We don’t eat cookies before dinner; you may have one for dessert. Responding with zero in answer to her question gave her some mathematical wiggle room to play with. And we are far enough along in this talking math adventure that she’s going to play with it nearly every time.

For the record, Tabitha and I have spoken about zero before. And several times, we have had conversations about fractions.

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2 responses to “Cookies

  1. No disagreement here about the need to make more of our conversations around math more natural. This is obviously easy for you as a mathematician (as it is for me) but I wonder if an unnatural conversation from a parent (or teacher) who is less comfortable with math is better than no conversation at all. Perhaps we can use unnatural conversations as a stepping stone into more natural conversations?

    I chose the video in question for my blog post describing some different multiplication algorithms/models because it was easy to see what strategy was being used (and I didn’t have to search ages for the “right” video, but that’s another story around how much time we have to search for resources), not so much because I would like teachers to duplicate the way she speaks verbatim. I will definitely have to talk to my colleagues about the need for more natural conversations though, and see if they can nurture them in other areas of discussion that come up.

  2. Rats. I worried I might come across wrong here. My intention in using the example was to illustrate what I am trying to do by contrasting it with something else. Not with something bad, but with something different.

    Over the last couple of years, I have been exploring what I might have to offer to parents who are concerned with their children’s mathematical development, but who don’t know what to do about that.

    One of the questions on my mind is precisely the one you allude to here, David:

    No disagreement here about the need to make more of our conversations around math more natural. This is obviously easy for you as a mathematician (as it is for me)[.]

    The implicit question is What does a parent need to know in order to have a natural conversation about math with his child?

    I don’t think a parent needs to know a tremendous amount of mathematics, nor a ton about child psychology, nor much of anything about teaching. A parent does need, I think, a few principles and a ton of examples. And a parent needs reassurance from someone who does know all of these things that natural, casual conversations can support children’s mathematical development.

    So in critiquing the video above, I am doing it from the perspective of trying to make clear what I hope to contribute, and how that might be different from the work of others.

    I offered that video of Griffy and the train cars in the same spirit. That was a staged conversation, not a natural one. I have—through practice—gotten much better at talking math with my kids than I was then.

    I don’t know how much of this transfers to principles of teaching. A classroom is an inherently unnatural environment (first of all, for its being compulsory). I understand that there are classrooms in which the questions being explored are nearly always natural outgrowths of students’ natural activity. But I’m not advocating for that here. I’m closer to Dan Meyer’s compromise on this: I would love for classrooms tasks to be as close as possible to what children might naturally wonder about, but I am also willing to choose today’s topic, and the context in which we will study it.

    But home life is different. There are many opportunities to turn natural activities into mathematical conversations. If parents can develop a habit of mind for noticing and then following up on these opportunities, they’ll see a pay off.

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