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 :)