Tuesday, May 15, 2012

Math Tweaks

Thank you to everyone who left me advice last week in response to my questions about the stamp game.  It was much needed and appreciated.  As suggested, Kal-El worked on addition for about three days last week and we probably could have covered it in two.  Yesterday he insisted on beginning subtraction.

We spent a ridiculous amount of time on the golden beads (Mommy may have had issues moving on) so he is super well-prepared for this.  Also, once I told him the same rule of order applies to the stamp game as the golden beads he has consistently begun with the UNITS.

As you can see, we changed mats.  The stamps stuck to the felt map and wouldn't slide well.  You absolutely don't need a mat for this work, but as it so happens the mat is Kal-El's favorite part of the work.  Although that is really splitting hairs.  Everyday he waxes poetic about how much he loves the stamp game.  As he is working his mouth never stops running.  I don't know how he concentrates on the math while he is talking like this, but he does.  His hands are sliding stamps a mile a minute and his mouth goes just as fast, "Mommy?  Did you know this is the perfect game?  Just look at how many  materials I have at once.  I love my stamps.  I love my tray.  This is the perfect tray.  I love my mat.  I love my stamp game book.  I really like using this ruler.  This is so much fun.  This is the perfect game..."

Consequently, I don't think I'll be able to switch out our homemade version for the real thing.  He is emotionally attached at this point.  I made the new mat (poster board) bigger so he would have room to build his equations with his extra large stamps.  I itemized a few minor problems we are having with our homemade stamp game in my previous post.  I can add two more now that we've spent even more time with it.  Firstly, now that the mat is big enough to accomodate his equations you can tell that the felt mat, as designed, was the perfect size because he could reach everything while sitting in his chair.  The top of this mat is out of arms reach and it seems awkward and uncomfortable.  Secondly, because the stamps are jumbo-sized it is really hard for me to fit ten stamps into my hand when I slide them in for exchange, much more so for Kal-El.  But, he does not want me to change a thing.

Well, maybe sometimes he wants me to change something.  He says the only thing that could make the stamp game better is if you could snuggle while doing it.  As a result, he asked me to show him how to keep track of his exchange when he does the problems in this stamp game book without using the stamps.  I showed him how to "carry the one" (or two, or three, etc., as the case may be) and he completed quite a few pages snuggled up on the couch with just his book and a pencil.

He really freaks my husband out when he does that.  It is because of the way he counts on his fingers.   Let us say you were adding seven and five.  Most people would put up their fingers one at a time and count "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12."  When they run out of fingers on their two hands the drop all of the fingers and continue with "11, 12" starting over with the original hand as if it were a third hand.  Alternatively they might count "1, 2, 3, 4, 5, 6, 7" and "1, 2, 3, 4, 5" but using the the same finger pattern as previously described.  Kal-El does neither of these.  He puts up the first seven fingers all at once and says "seven."  Then, without moving any fingers his says "five" and stares at it for a couple seconds.  Just about when my husband is expecting mathematical disaster, Kal-El blurts out the right answer.  What this is, is a side effect of learning the bead bars and the snake game.  He is picturing a seven-bar and puts up all seven fingers at once.  Then, he pictures a five bar but puts up NO fingers.  What he is doing is using the "down" fingers and comparing them to a five bar to determine how many are left on the five after he exchanges the ten.  His actual fingers become like a ten-bar and the two "imaginary" fingers are like the black beads in the snake game.  I didn't tell him to do this, and he hasn't explained it to me.  But, after sitting next to him watching him complete dozens of equations I'm almost 100% certain this is what he's doing.

I have a feeling that last paragraph might make a lot of sense to people who have worked with Montessori kids and absolutely no sense to anyone else.  To put it more simply, my husband expects him to add the numbers as if he is using golden unit beads, but he actually does it like he is building a golden snake.

Don't worry, it is not "all stamp game, all the time" here.  As someone gently pointed out in the comments, several areas of math are to be running in parallel.  We are also still working on squaring and cubing chains.  We are also working through the memorization sequence.  Yesterday we moved on from the snake game to the addition strip board.

However, I have to admit, since we finished the constructive triangles we have completely been ignoring geometry and I have absolutely no motivation to start it up again right now.  I feel like I'm up to my ears in math as it is.

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  1. My kiddos are younger than yours and not ready for any of this, but I really enjoy your posts. Your kids don't necessarily seem to be the most advanced in the blogosphere, but they seem to perhaps be the most engaged and interested in their work and are really developing a deep understanding of it. You must be doing something right! :)

  2. I love this post!

    The patterning on the fingers: I did that all through childhood (still do it!) and I didn't have Montessori as a child. It's like filling in a puzzle :)

    Snuggle Time: My son is totally the same way - if everything could include snuggle time, he'd be in heaven ;)

    He also talks NON-STOP through his most favorite activities. Go figure.

    You'll get back around to geometry when the time is right :)

  3. Kylie,

    Thanks, I think :) LOL! Actually I know totally what you mean. Your comment made my day!

  4. Jessica,

    Thank you, I love it when you stop by and comment.

    I have a feeling the time will be right to straighten out geometry right about the time I want to introduce the detective adjective game. Otherwise, we are going to get stuck.

  5. I love how you figured out what your son was doing in his head to work out the sums. Little-N did something similar and when I asked him how he works out sums he explained how he visualized beads.

    I'm sorry I didn't reply to your comment on my blog earlier. I just saw it! I usually introduce the equation slips while the child is working on the addition charts. When working on chart A they do not need to complete all the strips. I observe the child closely to see if the begin to remember the answers to equations. Once the child begins to recall the answers I introduce them to addition chart B and for this they will have to use all the equation strips to fill in the chart. I hope this helps in some way.

    Your son is doing some amazing work and it's very inspiring to read your posts. Thank you so much for sharing your experiences.