Wednesday, October 23, 2013

Abstract Addition


Well, you could have knocked me over with a feather today.  In the photo above Kal-El is completing dynamic addition equations with addends in the millions.  

This week he started short multiplication on the large bead frame.  Long multiplication with two- and three-digit multipliers is just around the corner so I was reading the presentation instructions.  When I got to the part about adding the partial products I thought, "Wait a minute, when was I supposed to teach him dynamic addition purely on paper?"  

I have been dutifully guiding the boys through the primary math albums for years and appreciating all the preparation for abstract borrowing and carrying throughout multiple works but still expected a "Now you're done with manipulatives.  Do this work purely on paper." presentation to appear.  When I ran out of primary album I wasn't alarmed because I thought "must be in the elementary album."  But then it occurred to me yesterday, there aren't any addition and subtraction presentations in the elementary albums.  And, here we are, only a couple presentations into the first big work needing that skill.  Did I miss it?


What followed was over an hour skimming six different Montessori math albums trying to figure out where I missed a step.  That was followed by a cry for help to my mentor, Jessica.  She talked me off the ledge, assured me I'm not blind, and assured me it's not in there.  Apparently in a traditional Montessori classroom the child either discovers this on his own, is clued in to it by another child, or if all else fails is clued in by an adult.  So, theoretically, if I just point out to him that the bead frame can be "in his head" and show him how to notate the carried numbers into the next category he will be able to do this.  

As always, I didn't believe her.  I never believe her.  

She's been proven right quite a few times by this point so I thought we would take a stab at it today.  Last night I wrote out 10 equations on some graph paper and gave them to him this morning. He said, "should I get my bead frame?"  I said, "let's try having the bead frame be only in your mind."  He attacked the first equation without any help from me until hit his first exchange in the 100,000 position and asked, "how do I do the exchange?"  I showed him how I track the exchange by adding a superscript number at the top of the column and he was off and running.  He completed in the whole page in just a few minutes, declared it "fun and easy," and needed no further help from me.  Well.  I feel downright unnecessary!  DOESN'T HE KNOW HOW HARD IT WAS FOR ME TO LEARN THAT WHEN I WAS IN SCHOOL! This was supposed to be a big production!

He asked me if he has "mastered addition now." I told him that I would give him more equations tomorrow done without colored pencils.  Then Kal-El said, "And the next day give them to me without colored pencils and also not on graph paper. THEN I will have it mastered."

All right then :) 



11 comments:

  1. Kal El's response is so funny. I think he has you figured out :)

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    1. Ha! My husband just said, "No, if he really had you figured out he would have had you laminate it and get out the label gun."

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  2. My children have done things like that before, surprising me with things they knew that I didn't show them - and EVERY time I am shocked at what they knew that I didn't show them and didn't realize they knew. But - without trying to sound like I'm given to too much flattery - I am not surprised at all that Kal-El knows that - you are a *very* good teacher :)

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    1. Aww...thanks Amy! I DO have those moments a lot. The other day at a pack meeting the leader asked the group of 60 1st-4th graders "what is a synonym" and NO ONE raised their hand except Kal-El. I shuddered because everyone knows he's "the homeschooled kid" and I was pretty sure I couldn't remember talking to him about synonyms. He said, "a word that means pretty much the same as another word." My husband asked him in the car how he knew that and Kal-El said, "Mom told me." Huh.

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  3. Wow Kal El!!!!! There you go!!!! So proud of you!!!!!..... Between us MBT, It was sooo hard for me too at school!!!LOL That{s one of lots of reasons I LOVE MONTESSORI!!!! hugs!!!

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    1. Karen you are just sunlight in the form of typeface! Thank you! I'm glad I wasn't the only one who struggled with that. I remember it being a BIG DEAL.

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  4. That is great!!!! I shared this post with Legoboy and he said, "I don't even remember learning how to do that - I just did it." (I honestly can't remember when he started either - did I show him, did he figure it out, did he see someone else??? I kind of wish I knew these little accomplishments...)

    :)

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    1. Did you remember to put another tickmark in the "Jessica" column on your Andrea's right/Jessica's right chart on your refrigerator?

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    2. haha ;) It's all on one big paper entitled "We're all on a journey together!" ;)

      See - you've got more tickmarks anyway - because you're actually recording these great moments of realization - and I missed so many with Legoboy, I'm sad about it. I didn't even write the date he read from the Bible itself for the first time - though I do remember the moment, where we were sitting in our living room, and how long I cried in joy and pride! But what season was it even?

      ;)

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  5. I'm right there with you on trying to figure out where I missed things. I know why they have so much training for "real" Montessori Guides. The manuals are great to have but they can also be such a source of frustration. I have sadly, chosen a set that seems even harder. There are so many different manuals with R&D and I dont have them all. Im sure everything is there, but its all over the place so I miss things and wonder where.
    It is so great that he found it fun and easy. I hope it goes that well when we get there. I honestly, do not remember learning this in school, but then I've chosen to forget much of my school years.
    I love your comment about synonyms as well. It always shocks me when my son knows something I dont remember teaching him. They pick up on so much! For us my son is asking questions constantly. I often will answer him with only half thinking about it. If it is a simple question, I will give him a simple answer but he will store it for later.

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