The usual, plus O Sapientia. (Yes, it’s for Vespers. I know.) Talked about it, prayed it, followed along in Latin with the recording on Fr. Z’s page.
Very brief rabbit-hold discussion of the meaning of “prudence.”
Let me pause for a moment and give you an example that shows why I’ve become such a fan of the Art of Problem Solving.
I’m not a math person, I’m not mathy, but neither did I ever hate math (except for Geometry, but that’s another story.) I grasped most of it (never went higher than what we called “Advanced Math” in the day – no calculus for me!) and can compute well in my head. That particular skill was helped along by the fact that the summer and Christmas I worked at K-Mart – even though this was in 1979 and surely the registers computed change – my recollection is that they did not, so I had to work it out myself. Perhaps they were broken for while? I don’t know. I just remember developing that skill during that time.
(We also were paid in cash. Isn’t that odd? A store that’s part of a major corporation paying in cash in 1979? Really? I always wondered about that.)
So anyway. AOPS is – well, you’d have to go check out the website to understand – an approach to math that emphasizes creativity and understanding, really, basic arithmetic principles as a key to solving problems. The Pre-Algebra is traditional in structure and subject matter, but as a non-math person who made A’s, but never really understood the substructure or the reasoning – it’s illuminating. Let me give you what is probably a silly example, and one that might end up revealing more about my own inattentiveness forty years ago than anything else.
Consider operations with fractions. We all know how to add and subtract fractions: find the common denominator, blah, blah, blah. Multiplying is easy. Go straight across, top and bottom. Hurray. But then we get to division, which is unlike any of the others. What you have to do here is (for some reason) multiply by the reciprocal of the divisor. Okay, kind of tricky, but I guess I can remember that.
Now, let’s learn this the AOPS way. It starts way back in chapter one, when you’re learning about arithmetic operations. This is what addition is. Easy. This is what subtraction is: adding the negation of a number. Huh. That’s strange, but we’ll go with it. This is what multiplication is. Got it. Now, time to define division: it’s multiplying by the reciprocal of a number. (6 divided by 2 is 6 times 1/2. And so on.)
So. Jump back to fractions. Now, why do we do this crazy thing when we divide by a fraction? Why do we up and decide to multiply by the reciprocal?
Simply because that’s what division is.
*lightbulb in my brain*
Similarly, having the definition of subtraction – adding the negation of a number – in your head – makes it a lot easier to deal with signs when you start doing equations. It makes it crystal clear why when you see 3-(-2) you can render that as 3 + 2 : because subtracting -2 is just adding the negation of -2, which is 2.
Today’s subject was increasing and decreasing percentages, and the lesson – centered around this video and the next – were equally illuminating and just made so much sense.
My 12-year old understands math so much more deeply than I did at his age, I’m sure. He understands it more deeply than I did last year, I’m thinking. Thanks, AOPS!
3. Then….finish Across Five Aprils. Do some brainstorming on some writing related to that which will hopefully happen tomorrow.
5. Art time:
…which also included a bit of science as we talked about why the oil pastels resist the water.
While they worked, I became truly insufferable and crammed in some Messiah. They listened to a recording, I jabbered about Handel and oratorios, I chirped, “Oh, this is from Isaiah, remember reading this last week?” They nodded and colored with their pastels and were probably just counting the minutes until….