Last semester I broke my own rule and switched math curricula. (I can hear the sad trombone even as I type.)
As I’ve thought about why, I’ve come across some ideas that are transforming the way I view math altogether.
One of the very first pieces of homeschool advice I received concerned math: be careful about curriculum hopping. If it ain’t broke, don’t fix it. This makes a lot of sense to me. Math programs are cumulative and each speaks a dialect of its own.
I did my research before we began formal math study, and landed quite happily on Singapore’s Primary Mathematics- supplemented by Miquon, and with Life of Fred for dessert.
Hold up, three things? Yes! and I’m sorry – I always feel like I have to apologize for our extravagant math buffet – you do not need three math programs. I do not need three math programs.
We all have our faults.
I like Singapore because it moves very intentionally from concrete to pictorial to abstract. Each concept is introduced from a variety of angles and addressed using a variety of methods.
As a student, I was always quite strong in math. I could memorize and apply an algorithm like nobody’s business, and I took true delight in the logic of my high school geometry and trigonometry classes. Geometry aside, now I realize that underneath the excellent math grades, my understanding was not only unrooted, but quite fragmented and broken.
Which didn’t affect my ability to ace my classes.
How crazy is that?!
This is why Singapore’s concrete, multi-method approach to problem-solving really appealed to me for my own kids.
It’s sort of like taking a magnifying glass and a pair of pliers to something – once you’ve thoroughly dissected it and examined each piece carefully from all sides, you might begin to understand what you have, how to put it together again, and why it functions as it does.
If Singapore is our main course, Miquon is our mac and cheese.
Miquon is an out-of-the-box little program that stretches the way we look at math. It’s mostly independent, exploratory, and manipulative-based. As gentle as it is, it’s also full of depth. Miquon helps a person see math- its components, how they fit together, and how to manipulate them. I’d love to do a thorough post about it someday, because it really is one of our must-have’s.
Life of Fred
Life of Fred’s elementary series is a piece I could easily cut and don’t even bother to schedule – and yet, my kids would be so disappointed if we ditched this one!
Math as a successful arranged marriage?
For several years, forward we trotted in math.
As my big boys worked through their upper elementary levels, I began to notice something that bothered me. The boys were learning math well, but they sure weren’t taking much joy in it anymore. One liked to get it done ASAP, just to be finished. The other put it off as long as possible and then rushed through it, making careless mistakes.
This made me a little sad, and I felt sad for mathematics itself too, as well as helpless– why must this always be the dreaded subject, even amongst kids who take to it intuitively? Poor math.
Do we need to love everything that must be studied? I suppose not. There’s value in working hard despite how we feel.
BUT. It seemed awfully soon to resign ourselves to that lesson. Can’t exposure, study, practice, and familiarity actually beget love? Yes!! Only, it seemed like we were going backward. The opposite was happening between my boys and math.
I didn’t have a great solution for this small problem – it almost seemed inevitable. Math in our modern education culture feels born to be named in foreboding italics: math.
Then one day, I got a text from a friend. She was considering switching her 3rd grader to a program called Beast Academy. What did I know about it? Well, I’d heard of it. I’d heard vaguely good, non-specific things about it. I knew there were comics. And monsters?
My friend bought some Beast Academy materials and began using them with her son, and soon I was on the receiving end of rhapsodizing texts.
I got curious, and started looking into it – just out of curiosity, you know, not because I might switch. I read odds and ends but the thing that really made me wonder if this might actually change math for my kids was this review at Kate’s Homeschool Math. (Which, on a side note, is a fantastic site and well worth perusing.)
What did we have to lose? I gave my boys the placement tests, and then I ordered materials. At this point we had roughly 9 weeks left in our school year. (I won’t go into details here about which levels I ordered or how we got started, but am happy to answer specific questions if you have them for me.)
Math Lab vs. Math Assignments
And so we did an about-face on math. Instead of specific daily assignments for each kid, we did a daily math lab every morning. I’d be sure the boys knew where they were in their texts and workbooks, settled them at the dining room table, and set the timer on my phone for 40-45 minutes. Off they’d go.
How much they got done each day varied, but they worked with a new interest and a focus that was quite different from the ways they’d approached math before. Spending 40 solid minutes working hard was satisfying, effective, and came entirely without the burden of an unfinished assignment.
Sometimes I’d even catch a boy working math problems at other times of the day. Just because he wanted to finally solve that one challenging problem, or because he liked what he was doing so much that he wanted more.
This was mildly astonishing.
Beast Academy is very very different from anything we’ve done before, and I don’t feel equipped to give it a thorough review until we’ve used it a full school year. (Again, see the above link for more info.)
Anyway, this post isn’t really about Beast Academy; Beast Academy is only a tool, and there are many tools. The tool isn’t the important part. This is about my boys’ shifting relationships with math and the distorted lens through which I’ve been viewing it- even as someone who has always enjoyed it.
Maybe our STEM-frantic culture is missing the main point.
On Arithmetic as an Art
The other day, I read something about arithmetic as understood in terms of the Quadrivium.*
*Complicated not-a-footnote: the Quadrivium being the four liberal arts (arithmetic, geometry, astronomy, and music) that bring us the mathematical tools necessary to pursue the higher ideas of philosophy, metaphysics, and theology….the Trivium refers to the three liberal arts (grammar, dialectic, rhetoric) which are the tools for language; we hear about the Trivium the most, but it is only one piece of a much bigger picture….as are the seven liberal arts as a whole.
I’m not a good ambassador for this stuff! I’m still attempting to grasp the basics. I’ve learned that the liberal arts are a topic you can’t crack without an abundance of ideas flooding the one piddly one you were trying to straighten up.
(Along with a couple of friends, I’m reading and discussing the mind-blowing book The Liberal Arts Tradition: A Philosophy of Christian Classical Education by Kevin Clark and Ravi Scott Jain. I am underlining basically the whole book and filling the margins with notes, and wondering what on earth my own education was about.)
Anyway, this thing I read. In this book. About arithmetic as understood in the first century A.D. This quote is what I’m getting at:
Arithmetic began in, and culminated in, wonder.
This makes my heart sing. Wonder provides a clear lens, free of murk and distortion. Math! Wonderful! We study it to chase God, to chase wonder. The quote continues:
Students who encounter mathematics in wonder are far more likely to commit to the rigor of its work.
Well, that makes heaps of sense. And there’s more. Traditionally, the authors say, arithmetic was not only viewed as a means for wonder, or for practical work, but also as a path to wisdom and worship. A nurturer of human formation.
This changes everything! My burden feels lighter.
Only Joyful Stakes
Doesn’t it feel overwhelming sometimes, to be entrusted with this nurturing of small humans?
My biggest mistake has probably been assuming that the burden is mine at all – that my shoulders are burdened with high stakes, that my decisions about math and grammar and reading material are going to determine whether my children become faithful lovers of God or, you know, egocentric secular reprobates.
This is what I know: the burden is not mine; the work is mine.
And this: a math program, or any other program, will not break (or make) my kids. They’re not parts on a Christian assembly line, they’re persons.
I think that these big ideas about math take it altogether out of the high-stakes game and put it squarely into the joyful-stakes game.
And I land here: isn’t it fun that we get to find this stuff, that we get to educate this way?!