I love aha moments. They light up my world and are one of my favorite things about homeschooling, being there for the good ones. We had another one yesterday.
Math, for JediBoy, has been an on-again-off-again enjoyment. He was very interested in learning about math, trying things out, and we played with lots of manipulatives and did lots of talking and exploring when he was 3 and 4. Last year, I decided to try a more formal program with him, because to me the nature of elementary math lends itself well to a linear curriculum. We bought Math-U-See Alpha, and although JediBoy enjoyed the blocks and some of the supplemental topics, he found drilling his addition and subtraction facts pretty boring. We stuck with it (in a flexible, no-pressure kind of way) because I agree with the reasoning that later skills are easier to perform - and learn - when the most basic facts come without a struggle. Eventually they came easily, and we moved on.
We’ve been working on the next level - Beta - for a few weeks now and are in Lesson 13. Today we looked at the topic of Column Addition.
17
59
63
20+
___
Here, we are encouraged to look for groups of ten - the 7 and 3 in the units column become one 10, with 9 units remaining; the 1, 1, 6 and 2 in the tens column become one 100, with 5 tens (50) remaining - so our sum is 159.
JediBoy loved this.
We did dozens and dozens of columns. Last night, he came up to me and asked if we could “go upstairs and do math - not problems from the book but just adding columns, we can take turns making up the problems and doing them.” And of course we did, for about half an hour. He gets such a kick out of this. Finally he sees math the way I do: a series of fun puzzles. Aha!
Another interesting thing, to me, is evidence of his number sense. He’s not just reciting facts, he’s really understanding them. We had a review word problem that went something like, “Ethan found 33 widgets yesterday and 49 widgets today. How many widgets did he find in all?”
I assume the intention was for the student to carefully write
33
49+
___
and then continue with a “multiple digit addition with regrouping” problem.
JediBoy read the problem. Wrote nothing. Didn’t stop to think, but immediately said, “If I take one from the thirty-three, give it to the forty-nine, I have fifty and thirty-two, so my answer is eighty-two widgets.”
That’s good number sense. It’s not a strategy or a trick or a way of thinking that anyone explicitly taught him. It’s what has developed inside him, and his explanation is to me a sign that he is really connecting with the numbers and truly understanding what is going on.
Whatever else I do or don’t help him to learn, to me this number sense is as basic to continued studies of math as the ability to read is to continued studies in the humanities, and having those, he can learn anything he puts his mind to. What a great feeling!
Categories:
