Something has been happening here the last few months.
Our 13 year old has her sights set on a certain job, so we've been working out what skills she can learn now to help on that journey, and gathering some resources.
She also feels the need to be "learning more", so to that end I've revisited some things I did with her older brothers around the same age. We're doing dictation - Charlotte Mason style: I dictate a piece of literature and she quickly writes it down as fast as she can. She laughed when we first started, and said "I remember you doing this with the big boys! You sound exactly the same as you did then." That's comforting ...
After she's quickly written the piece of literature she types it up with corrections, and punctuation - a new line for each speaker, quotation marks etc etc. Then I check it against the original.
No surprise, she was very good at it all even though it was the first time we'd done any "official" work like this. She was quite encouraged.
The other thing we're doing is going through the old "Teacher's Manual" of Intermediate Math-U-See. She decided she's not keen on learning about division right now, but is very interested in fractions. I've decided not to buy a new workbook for her. I remembered how to do them from when I learned alongside our older boys, and we whizzed off several pages of questions enjoyably.*
When our 8 year old saw her doing this he said he wanted a maths book, because if he is going to be a pilot then maths will be important. This particular child causes me some ... puzzlement shall we say, sometimes. One of his personal challenges is "Emotional Dysregulation" - a co-morbid condition of Autism Spectrum Disorder (not everyone with ASD has ED). Whenever he's asked to do maths in the past he gets frustrated and angry - I wondered perhaps was I starting too far ahead, or even too far back, how much did he know already? But even getting him to show me what he knew caused stress no matter how gently or briefly, or whatever-ly I tried to do it!
So I dutifully got a maths exercise book from our stock of lovely stationery items. He took the book from me and said "I'll do the questions." "Ok" I said, wondering how that would go. A second later he was frustrated. "I don't know how to do maths questions." He was on the verge of getting angry. I offered to write three questions. He was happy with that. Walking on egg shells I wrote three addition problems.
He was cross that they were so easy, but instead of giving up this time he said "I'll write some now." When I came back to see what he was doing I was REALLY PUZZLED. He'd written questions like 156 - 20 = 136, and 94 + 18 = 112. I said "How did you know the answers to these?" (this child hasn't been TAUGHT addition and subtraction, he doesn't know about "carrying over"). He said "I just knew it." (he didn't have a calculator, and doesn't really know how to use one, so that wasn't it!).
I showed the book to his big sister and said "How can he just know it?" "That's natural learning." All matter of fact she told me what I should have known.
So then, just a couple of days after that I came across this article wherein the author refers to a 25 page article by Paul Lockhart (downloadable link on the article).
From the article:
Before I close, here are a few more of Lockhart’s gems:
We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math…Of course it can be done, but I think it ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in.
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
How can schools guarantee that their students will all have the same basic knowledge? How will we accurately measure their relative worth? They can’t, and we won’t. Just like in real life.
Please take the time to look at the article above, and skim, or devour the 25 page article that Paul Lockhart has written entitled "A Mathematician's Lament."
Just because WE were taught maths a certain way doesn't make that way right.
And if you had a "regular" education like me then the was I was taught was ANYTHING but right.
* As I was doing the fraction questions with our daughter (she wanted me to sit with her and do them together) I started out reading the teacher's book, then thinking out loud and then I saw a pattern and was excited, and showed her and she understood. There are some people who say that a child should see the patterns themselves and not be shown - however in the case of our daughter she ASKED me to show her. She also asked me later if I could perhaps work it out first and not be so excited about figuring it out. She wants me to give the impression that I know everything, and am kindly sharing little snippets with her. That revelation surprised me!! I'm blessed that we can communicate about these things.