Honestly, when I decided to give myself a break from the guilt of not doing daily sit-down school and call it “unschooling,” I never expected the kinds of results that I’m seeing on a daily basis.
Recently I was feeling a little guilty again for only “strewing” (an unschooling term – meaning to help direct learning avenues by leaving stuff around or suggesting) language, science and religion but sorely lacking in math. Even though I must say I’ve been quite impressed with how naturally Soren has been taking to counting, addition and subtraction, even multiplication with low numbers (though he doesn’t know it as such) with literally NO schooly input at all.
Anyway, it just so happened that Jireh brought me a completed phonics workbook that I’d bought for her 4th birthday and asked me if I could get her a similar one for math. We immediately went “shopping” on amazon.com and ordered some 1st, 2nd and 3rd grade math practice workbooks.
Oh, there’s just something about shiny new blank workbooks and newly sharpened pencils that warms even an unschooler’s heart. It’s a great time of year! 🙂 So Jireh and Miriam wasted no time in digging into the books. They are simple affairs, consisting of pictures to allow counting two groups of numbers and write the sum, type of thing… and then some other pages doing similar things with subtraction. There was no grand scheme type instruction or overarching “this is the principle we convey with these problems” as one would find in a more comprehensive homeschool text – only sums and differences.
I say this to illustrate how I was not expecting anything major from the use of these products. I was merely giving them something “mathy” to do and give them more exposure to numbers. We have done a bit of Math U See, but because the manipulatives are so expensive I will not let them do it without me, which severely limits the spontaneity of such a transaction. Anyway, what struck me as quite amazing was that in one day of doing silly “7 plus 1 equals 8” type things, Jireh has discovered for herself and exclaimed to me about the following principles of mathematics:
The commutative principle (a + b = b + a)
the principle of adding or subtracting zero (n + 0 = n; n – 0 = n)
the fact that the sum of the subtrahend and the difference equals the minuend (i forgot what this property is called)
If you think about it, it’s actually very very basic algebra…
It’s continually amazing to me what the little minds can do on their own with just some raw materials to work with. I can only imagine how frustrating it could have been had I sat at the table trying to ram these principles into their heads and hearing “Mom, I don’t get it.” This way is much easier. It didn’t occur to me, but should have, that the same extrapolation of phonics, spelling and syntax rules (which are really complicated in English, having more exceptions than rules) from practice with reading books, could be reasoned out in mathematics as well (which is really much more systematic and predictable). All this is very encouraging.