The National Council of Teachers of Mathematics has come out with a new set of recommendations for the teaching of math. Headlines on the subject have said things like “Back to the Basics” and “No More Fuzzy Math,” but that is just the irritating way headlines fail to jibe with reality. In fact, the new recommendations merely suggest focal points for each grade. They continue to encourage problem-solving and algebraic thinking at every grade level, and continue to mandate basic skills in calculation and so on, but they are saying “If you can only get a few things across, let it be this group.” And “this” is the usual counting in kindergarten, adding in first grade, subtraction in second grade, multiplication in third, and division in fourth, along with the math topics (that’s stuff like measurement) as usual. The NCTM is, I think, responding not so much to the possible overdoing of the discovery method as to the test-driven panic over long lists of things like having kindergartners say “rhombus” and practicing all possible varieties of graphs each year in case one shows up on the test.

Education is very fashion-driven, and it is usual to behave as though every new thing were New! and Exciting! when it’s really just the hemlines going up and down.

Then Knitsteel was saying that geometry was the most important thing. If you are only going to teach your kids a little math, she said, let it be geometry.

The combination of these two discussions have made think about what little bit of math would really be the most important.

I have to say that I don’t ever favor knowing just a little bit. We live for a long time nowadays, and we ought surely to be learning every day, so we have time to learn a lot of things.

But if you were only going to have a little knowledge of math, for the sake of argument, what would you pick?

Now that Blessing (That Man’s new assistant) is on the force at work, there are accounting conversations going on. When That Man and I have conversations, they tend to be about music, politics, where mislaid items might be, and things like last week’s “Did you throw away the giraffe’s bottom, by any chance?”

He and Blessing say things like “So they overpaid #42763, but underpaid on the 9th, so they have a credit of 12 cents, reflected in the $10,724 on the second page.” I say, “What’s 12 cents between friends?” and they look at me uncomprehendingly.

Perhaps knowing about money would be handy. The accountants always use calculators, of course, but the way they throw around the names of all those numbers shows that they could do without them if they had to. Faced with piles of papers and people overpaying and underpaying, I would probably just cry. Is this a specialized skill, or something we all could benefit from?

Music involves math, of course. Our director once announced that it was “just math,” as thought that would make it easer for the choir to get the syncopation accurately. Our director loves syncopation, and works diligently toward crisp rhythms. And knitting is all math, in exactly the same way that music is all math. In both cases, it is probably mostly ratios and measurement of various kinds.

So we need to be able to calculate, estimate, measure, and comprehend ratios.

You need fractions for cooking. Sometimes for knitting, too. In fact, fractions and decimals are required for most calculations in the real world. Things are rarely so tidy that you can just go with whole numbers. And we have to be able to tell time and to work with time a little for cooking and for scheduling.

It seems to me that percentages are key for understanding the news, determining whether the latest Huge Sale is actually all that, and estimating sales tax accurately enough that you won’t be startled by your totals when shopping. They are also handy for reading in the social sciences.

For reading in the natural and physical sciences, you sometimes need quite complicated math, but that may be optional for daily life. Those who need to be able to do the calculations involved in reading about advanced chemistry probably have studied math more thoroughly than the rest of us anyway.

So, let’s see, we need basic operations, the math topics, some geometry, a bit of algebra… Pretty much the usual elementary and middle school math syllabus.

Not that all of us in Hamburger-a-go-go-land leave middle school knowing all these things. But that is another subject entirely.

Those of us doing the HGP will, this week, clean our bedrooms thoroughly. We will put a meal and a batch of “goodies” in the freezer. We will begin spending an hour a day working on homemade presents, and buy 1/8 of our store-bought presents. We also check our towels and table linens. I had planned on making some for my SewRetro project this month, though I notice that the month is slipping away without my having done so. Maybe this is the week.

Hqwanda has a countdown that involves buying massive quantities of luau foods. Sounds a bit jollier than the HGP.

Wonderful post…. thank you. I would add only that the widespread ignorance about basic statistics is what makes it possible for us to be so easily swayed by every passing “we now know…” and “research has shown….” I bitterly resent the fact that I was never properly taught statistics.

I should preface this comment with the note that I was a math major in college. I would vote for combinatorics. It’s the lovely field of math where you figure out how many ways there are to to group or divide things up. For example, if you have 5 children’s Easter baskets, 17 chocolate eggs, 4 rabbits, 52 jelly beans, and 11 Easter eggs how many possible ways are there to divy these up? Okay, so the mathematics behind putting together Easter baskets is probably not what people do in real life. (It’s also useful in games like Yahtzee.) But it was so much fun to learn about!

well in the computer world (which it will be for quite some time) Algorithms is where I would be focusing my energy…

i think you make and excellent point about what kinds of math we use in the real world. that said, i struggled mightily with math (sadly, most kinds) and never developed an affinity for any of it. well, except for percentages off on sales and such….i think it’s amusing that every generation has “new math.” i remember my parents thinking the math i was learning in grade school was so different from what they learned, and now i find my middle son is learning to do long division in a way that i still don’t completely grasp. well, i guess i grasp it, i just don’t see the benefit to teaching it that particular way. in my experience with my children they have focused so much on problem solving they’ve neglected basic multiplication and division. #2 boy, who is 11, still has trouble with his nines times tables.

Interesting that addition/subtraction and multiplication/division are apparently taught separately in the US. We started addition and subtraction when we started school (they are both taught in the same year) and we were taught simple multiplication and subtraction from second year on. For the first 3 years of school (5yrs, 6yrs, 7yrs) our homework consisted of learning spelling lists (we would be tested each day on a list of 10 spelling words) and learning multiplication tables from our second year (starting with 2X table, 5X table, 10Xtable) to the third or fourth year (11X table and 12X table). In Standard 1 (3rd year) they started teaching long multiplication and long division. In the final year or 2 of primary school (9yrs, 10yrs) I have vague recollections of Venn diagrams and we may have started geometry then as well – not sure ‘cos I hated geometry. At Intermediate it was very simple algebra (getting used to the idea that letters could stand in for numbers), basic stats, timetrialled arithmetic, and geometry. First Year of high school (12 or 13 yrs) algebra and geometry, second year of high school, pre-calculus, third year, differentiation and a little bit of integration, fourth year integration and I suspect they went into matrix arithmetic in fifth year – by that time I’d had enough of school and had left. We were working from the British public school system at the time which seemed to put a high value on the basic 3Rs.