"What trains can you make that are the same length as the yellow rod?"
Following Madeleine Goutard's lead, I'm leaning towards - and today I asked for - writing rather than drawing as a way of recording, which I would have gone for more in the past, but I was happy to see the drawing too. The rationale here is that symbols are a quicker and simpler way of recording and so they can allow you to think further.
We talked through using the first letter for the rods:
It was interesting to see the different ways the children demarcated their different trains. We should look together at how they managed that.
Although I'd shown them the + sign before, when on the carpet at first with their whiteboards I asked them to write down a train I showed, that wasn't how children recorded, so we went with a list of letters. One boy did add the +s. He wrote
y+p+w
I suggested that to show p+w was the same as y, he wrote
y=p+w
but this was evidently confusing as he then switched to
y=p=w
Maybe I should have just left it!
Where would you go next with this?
I think they need to do something similar a few more times, look at each other's pages, see how to show what they want to say really clearly.
Any thoughts, suggestions? I'm feeling my way through this...
Here are thoughts that occurred to me as I read your wonderful blog.
ReplyDeleteI love the idea of getting children to use writing instead of drawing to record their trains. This seems like a natural way to engage students in using symbols to represent ideas that they have. Plus it helps them move away from drawings which can be laborious.
In my experience, as in yours, using w, r, g, p, etc. for the rods seems OK with them (except for your student lacking in English). They can physically show a rod for each letter, making the link concrete. I’ve sometimes connected the idea of using letters to the idea of nicknames or codes, which has helped some students. The letters are short cuts that make sense and are easy to remember.
I’ve typically had more difficulty with trying to have children use + and =. With the plus sign, I’ve encountered children not seeing the benefit of inserting them when merely writing the “code” of something like wwg seems to do the trick as well as w+w+g. There really isn’t a payoff, except to follow a social convention, and that’s a hard sell at the beginning. I’ve found it useful to make a set of cards with a different expression on each—e.g., w+w+g, r+g, w+w+w+r—and then use them for matching games of building the train for each. Or to make cards so that the expressions represent different rods and having them sort them. And I reinforce how we “read” trains as “white plus white plus green,” which helps “plus” being used for “putting together.”
But I’ve had much more difficulty with the equal sign, and wrote about this in a blog a while ago: http://marilynburnsmathblog.com/wordpress/the-equal-sign-what-it-rally-means/
I think that this is because the plus sign is an operational symbol that connects to doing something physically—putting rods into a train in this context. There’s some action. It’s not the same with the relational symbol of the equals sign. I’ve found this much more abstract for students.
I’m not sure any of this makes sense. One idea that occurs to me is that it might be interesting to write a codes and ask students to build what they might mean. Kind of a read-my-mind game. E.g., suppose I write ygww. It’s not clear whether I’m thinking of y + g + w + w or y = g + w + w. Using plus and equal symbols can help me communicate.
Not sure this helps, but I appreciate the chance to think about these ideas.
Thank you Marilyn. It's all happening in real time for me with this, so a comment like yours that gets me thinking too is really what I need.
ReplyDeleteYes, symbols. They're conventions. But that doesn't mean we have to say, "Just put a plus between all your letters." It's better if they can see the need right from the word go. Dan Meyer's "what is the headache?"
You can see some of the children wanting, needing, an equals sign in there. They've wanted to include the yellow rod next to the train they've written, as in the first book picture above:
y r w r
We know it's not, but perhaps I could put it to the class that someone looking at the book later might mistake it for that train. What can we do?
I like your idea of a card game. I'm turning that over in my head. I think I'd do it with trains of just two rods, so there's just one plus sign. I think too many will look like spaghetti to the children who are only just on the first steps of reading.
I think hearing the trains read as “white plus white plus green” will help, as will seeing me write that way. But as you say, it is a hard sell without the immediate need.
Another thing: although Gattegno and Goutard propose to teach inequalities right near the start, > and <, I'd not seen the point of this. But now I'm thinking, let's really make equality meaningful... perhaps a lesson or two, perhaps a card game, could focus which train is longer and writing that symbolically. Then equality, that special case between the > and < has another entry point, that might make sense of it in a different way.
It's good to ponder this, and it really helps to have input from someone who has been there and come up against the same challenges!
Perhaps this is also a case where writing numerals creates the need for the plus sign. 1+2 is not the same as 12. There are a handful of children who can't write all the numerals yet. But they can do 1 and 2. We could use cubes and compose 5 with, say, ones and twos, and they would hopefully see the need for the plus sign.
DeleteTeaching children to write is not an easy task. My sister sits every evening with her child to teach him how to write. She has admitted him in one of top reputed Phoenix pre-k and now she quite happy with his performance.
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