Math Goals with your bits & pieces

June 06, 2020

Can’t stop long… there’s the garden and a million things to do. Including finish the draft of my book!

But good comments about math in the last post. I will probably put my own math thoughts directly into the book. The main point will be that teaching children math is not as complicated as you think. As always, I try to give you criteria and an overview of the goals rather than minutiae, which I think are readily available elsewhere.

Numbers

The goal for the young child (before about 6th grade) is to arrive at full facility with operations.

To get there, he needs to know numbers.

This knowledge begins intuitively and can be conveyed (and elicited) by conversations and shared observations. “You give me those two and I will give you these three.” “You have ten; why don’t you give half to your brother.” “This flower has four petals; this one has five.” “Let’s fold this tissue paper so it has twelve points.”

Threeness and eightness and elevenness must be encountered and internalized. It seems to be built into human nature to “get” the numbers between one and five (interestingly, not zero). After that, things become a bit hazy.

We adults take this grasp of number for granted, but it does take time. Intuition needs a boost from outside, especially as the child goes beyond the number five. Seeing larger numbers in groups made up of one, two, three, four, and five helps. Your child needs to relate to numbers on a visceral level before he can tackle operations.

A child needs to learn numbers and their operations the way he learns to ride a bike — without thinking about it. He just must. If you are having trouble with your 7th grader, it’s because he doesn’t ride the math bike, he wobbles and is afraid of falling. There is no remedy but to stop everything and get those facts down.

But I need to tell you something: There are a lot of ways to skin this cat. One way is drills. Another is games. To this day, I divide a pot of tomato seedlings or count the up to seven eggs I get from my hens the way I divided jacks as a fifth grader, when I was crouching out on the school porch with my best friends (our school had wide wooden porches where we could play on a rainy or hot day). That is, in groups of three and four, or what have you. (Did you play jacks? It’s a game that has it all for internalizing number groups that add to ten, while developing fine motor skills and hand-eye coordination.)

Operations

If your third grader plays Parcheesi all day (a deadly boring game, come to find out as an adult; it’s really just good for facility with numbers up to twelve, so get another child to play with him), then you’re good. Done and done. And of course there is a veritable panoply of creative and enchanting math games out there. A simple online search will yield a surfeit.

I once overcame one child’s subtraction resistance by assigning an older child to play blackjack with him for a week in lieu of his usual math lesson (but not hers, poor thing). Problem solved. Truly — he went from answering the question of what 12 – 8 equals with “zero” — so vexing! why must they torture us this way — to complete facility with addition and subtraction. Assigning a card game seemed preferable to tossing him out a handy window.

There is no reason to shed any tears over this process; but the process must be undergone. If your child is “hating” math and you are dragging him kicking and screaming every day, stop everything and just give him games to play that require him to add and subtract, and later to multiply and divide. TRUST ME. It’s all about knowing. the. facts. Who cares how you get there. If calculating batting averages teaches your son how to find the average, why spend a lot of money on a curriculum for that purpose?

Algebra

The older child, having mastered the facts and operations (which lead up to short division aka fractions, which enables him to work easily with converting units later in algebra, especially in chemistry), must do algebra.

This brings up the eternal Saxon question. Saxon was developed for a specific purpose: To help children not lose skills ahead of the SAT. By rotating through the skills as they build incrementally, this is achieved, not necessarily in the most elegant way. (Saxon is not good for the earlier, pre-6th-grade stage, which demands repetition, not rotation. Once you can subtract, you can subtract. I really advise you to use an older “lesson and drill” type text as the foundation of your curriculum.) Without a dedicated math teacher for algebra, Saxon will work. It’s not the greatest, but it will do, especially if you take it lightly and add Kahn Academy.

Algebra is the logic of mathematics, akin to expressing thoughts in language. (If you do the two subjects together, language grammar including sentence diagramming and algebra, your child’s mind will be patterned to think about things systematically instead of only intuitively.)

The older, more traditional textbooks are better, though. When I was a girl, you did the “odds” and often skipped the A and B sections of the problem set entirely (maybe a few at the end to be sure), going straight to the C, if you were able to do the examples and warm-ups perfectly. The answers were in the back of the book and you just plowed ahead if you could. The tests were the proof that you learned the lesson. Many teachers only collected tests, but went through the lessons the day after they were done.

Geometry

The final piece of math education in secondary school is geometry. If possible, the child should be introduced to Euclid. Yes, working through his Propositions would be ideal. However, Jacobs will do. Something along these lines is essential, and the Saxon method of throwing occasional geometry problems in the mix cannot substitute for a concentrated year spent delving into axioms, propositions, and proofs.

Everyone says they want their children to do what they call “Critical Thinking,” but they start at the wrong end. I cringe when I hear it. They let children meander all over in elementary school and then expect them to get a crash course as a senior.

It’s fashionable in such curricula to offer some current opinion and then have the students work through it critically, but how are they supposed to do that? You need a foundation, especially in knowing when you have or have not proven something. And for that you need Euclid. Which means you need everything that came before… like I said.

Geometry is visual algebra, algebra requires math facts. See how it builds up?

Calculus is a language for science. It’s not a sort of “bigger abstract mental hurdle” for someone who has gotten through the other subjects, to be done apart from its object, which is science (physics). I encourage you to read Arthur Robinson to understand this if you don’t get it.

The main point, though, is that your job as a homeschooler is to guide your child through math facts to algebra and geometry. The rest he can do later if he needs it for the science he is interested in.

It’s doable, so don’t worry

Somewhere John Taylor Gatto says that the student can learn a particular skill he needs in six weeks. If you were paying attention in school, you will remember that the first 6 weeks of every year were spent in review, and the last 6 weeks were spent making sure everyone was up to speed. We never got to the end of any textbook!

If your child suddenly realizes he needs to go to engineering school, he can find out their requirements and remedy any gaps or lacks — and he’ll have the motivation to do it, unlike when he’s moping around in your kitchen not getting why you force him to do math. So don’t worry.

Really: I have one child who told me in 8th grade that he didn’t want to do any more math (having completed his second algebra year). I agreed. Subsequently, he learned calculus in a high school physics class. Another son vowed never to take another math class after high school; naturally he studied calculus in college. It’s not all up to you! Just give them the tools to learn and they will do the rest.

bits & pieces

Read more John Taylor Gatto.

I don’t know if I’ve ever shared this article before. It concerns the philosophy behind David Clayton’s establishment of The Way of Beauty at Thomas More College. His ideas will be fruitful for anyone contemplating a life of learning. The article begins on p. 16 of the PDF.

David Warren on the misguided tendency to appease. What he says expresses my attitude exactly. Here on the blog I am focused on helping you establish your peaceful corner of life and love. Some are surprised and shocked even when they check in with me elsewhere (Facebook and Twitter) and find that I, as Warren recommends, pull no punches. I just want to say that there is a way to live that is both committed to beauty and uncompromising in opposition to evil. Softness in one’s positive life does not require softness in one’s dealings with aggressors. That is my apologia in a nutshell: that I am attempting it.

If you have never read Vaclav Havel’s speech The Power of the Powerless, please, I beg you, read it now. It’s not long. Please invite your friends over (you can sit on the deck) and read it with them and discuss it. And then you will understand, at least, why I don’t put on a happy face when confronted with ideology and why I won’t post a black square or a gay rainbow, not even to be nice, not even to show how much I love my fellow man.

I talked about family life with some friendly folks at Great & Main: have a listen! The topic was the heroic meaning of parenthood.

2,000-year-old rooms found by Western Wall

Pentecost is a glorious season — are you looking for a lovely and contemplative activity for your children? Our friends at Liturgy of the Home have made another liturgical calendar. Do check it out.

My friend Peter Kwasniewski writes about St. Paul’s prescription in the first letter to the Corinthians for liturgical renewal.

I am looking forward to seeing what Sally Thomas does with her new blog, Abandon Hopefully. (Make sure you read all the way down to the explanation of the name!) Years ago I wanted to post her essay on Swallows and Amazons, Not Duffers, Won’t Drown, here, but it was behind a paywall at that time. I even wrote to First Things to point out to them the benefits to their publication for allowing access through this blog, to no avail! But later I was able to do it. Just my kind of thing.