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31 May 2019

Math as a Window to God's Character

I got asked today about how it is that I came to see math as a window into the character of God. I'm not sure how to show what I've learned, other than to tell how I came to know it.

* * *

I did not enjoy math in school.

The way I was taught, math was arbitrary: a never ending pile of largely unrelated formulas that must be memorized perfectly and then worked flawlessly. Close doesn't count; it's right --or it's wrong. Teachers seldom had an answer for "When are we going to use this?" They assured us that the upper math has value, but never seemed able to articulate what that value was.

I graduated from high school with a huge sigh of relief: the pre-calculus course I'd taken that year had not gone well, and the hit to my grades carried a heavy cost at scholarship time, and I figured that I'd reached the ceiling of what I was capable of in math. Though I briefly flirted with studying astrophysics, in the end the math intimidated me out of the dream, so I went with Japanese, which required no further math at all.

Then we decided to homeschool.

This meant starting over in math, from the beginning. I was intimidated, not considering myself to be very good at the stuff, but I figured that if I had a particularly "mathy" child, we could outsource math classes when I started feeling like I was in over my head.

But elementary math shouldn't be so hard. I headed to the forums to read about various math curricula. In the process, I ended up discovering how it is that people come to love math: math is patterns. And patterns are both beautiful and fascinating. Math is patterns that can be approached in many different ways, taken apart, and played with, and put back together. On occasion, I got so into a problem -a pattern- that I continued to work it even after my son's interest was spent. (This emphasis on patterns is also the core of the "new math" that everybody hates: my experience was far from unique, unfortunately, and the new "constructivist" approach to teaching math is difficult for parents who were taught with the algorithms only method, like I was.)  We started with Miquon math, which in spite of some weaknesses, taught me as much as it did my children, and then when my oldest outgrew it we continued with MEP, first because it's free, but then afterward we stayed with it because it's just excellent at teaching the kids to find the patterns. And we've all learned a lot about how to see the patterns. I find that I'm actually excited to find out what happens as my oldest gets into the "higher" maths: I am looking forward to the chance to try my hand at it again, this time realizing that there is an underlying pattern, a Real Idea, some bit of reality, that is being described by each type of problem.

I should not have been so surprised by the beauty; math is full of Truth about the world around us, and Truth, Beauty, and Goodness fit together, so where you find one, you'll usually find all three. But the idea that math could be beautiful was so different from the grind of algorithms that I'd always experienced. The reality is, algorithms are only a relatively small part of the story, and if you can work the formula, but you can't see the pattern that makes it function, then you don't really get it, and you haven't learned what it has to teach.

01 May 2019

Commonplace Book: April 2019

A sample from my commonplace book, and brief instructions for how to keep one.

A commonplace is a traditional self-education tool: as you read, grab a notebook. Write down things that embody Truth, Goodness, and Beauty. Write down notable quotes, with or without your own thoughts about them. Write down the questions you have as a result of the text you are reading. You will find the book becomes a record of your own growth, and it becomes a touchstone for memory of things you have studied in the past. This is what Mother Culture is all about: self-directed, conscious self-education.

"I need space --thought space."
-Cheryl Swope, The Classical Teacher, Spring 2019, p48

"I remembered a quote I heard a number of years ago from F.W. Boreham. He was speaking of the events during the Napoleonic wars in the early part of the 19th century:
'. . . men were following, with bated breath, the march of Napoleon, and waiting with feverish impatience for the latest news of the wars. And all the while, in their own homes, babies were being born. But who could think about babies? Everybody was thinking about battles. . . .
. . . in one year. . . between Trafalgar and Waterloo, there stole into the world a host of heroes! . . . in 1809. . . Gladstone was born at Liverpool; Alfred Tennyson was born at the Somersby rectory . . . Oliver Wendell Holmes made his first appearance at Massachusetts . . . and Abraham Lincoln drew his first breath at Old Kentucky. Music was enriched by the advent of Frederic Chopin at Warsaw, and of Felix Mendelssohn at Hamburg. . . Elizabeth Barrett Browning [was born] at Durham. . . . But nobody thought of babies. Everybody was thinking of battles. Yet. . . which of the battles of 1809 mattered more than the babies of 1809? . . .We fancy that God can only manage His world by big battalions . . . when all the while He is doing it by beautiful babies. . . . When a wrong wants righting, or a work wants doing, or a truth wants preaching, or a continent wants opening, God sends a baby into the world to do it. That is why, long, long ago, a babe was born at Bethlehem.' (F. W. Boreham, Mountains in the Mist: Some Australian Reveries [1919], 166-67, 170)
"As was the case with the Napoleonic wars, during the years of World War II the news and the eyes of the world were on the battles and not focused on the babies. Yet in 1940, the year many of the western European countries fell and the air over England rained destruction during the Battle of Britain, babies were being born. Three of the babies born that year, you are familiar with. They are, Dieter F. Uchtdorf, Quentin L. Cook, and one who is the commencement speaker today, Jeffrey R. Holland. The eyes of the world were not on these babies in 1940--they were following world events--but the Lord's eyes were on them because He knew they would be called upon to help change the world."
December 17, 2011
Paul V. Johnson
Commissioner, Church Education System



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