The piece shown above is an example of a needlework technique called crochet. Another form for making lace patterns is tatting. Both were part of the compulsory school curriculum for women in Finland, and as shown in the photo below, the University of Helsinki still has a room dedicated to their collection of student work which I visited in 2008.
It is interesting how much emphasis is placed on instruction in algebra, a thing most students will not use following graduation, even in college unless they're judged deficient and placed in remedial classes.
I'll go out on a limb here to suggest that the value of fine lacework may be of equal or greater value in the construction of a solid mind than balancing algebraic equations, and of equal value to algebra in mathematics through the building of spatial sense. Spatial sense is a factor in mathematics that is useful in all occupations, and even helps in doing algebra.
I have particularly enjoyed descriptive geometry in secondary school (don't know the US equivalent).
ReplyDeleteUseful in (timber) carpentry among others.
I am afraid it isn't taught anymore (in secondary school) with the advent of CAD software.
While a good spatial representation makes descriptive geometry easier to use, having made descriptive geometry helps me understand some woodworking operations which would otherwise be an unjustified recipe.
Doug, I typically agree with you on most things. On this one, I just can’t. But I do suspect that algebra has fallen prey to the tendency to teach things in isolation from the physical and practical representations of real world phenomena.
ReplyDelete(Likewise with calculus. But if algebra is a bridge too far, I won’t pick that fight. Suffice to say it’s been a struggle for me to actually find the connections between math and physics, in a modern educational environment, that I was always promised would be there.)
Maybe not everyone will use algebra daily. Especially now that most jobs are dumb McJobs that go nowhere. But the truth is that algebra, and calculus, were contrived by scientists who almost exclusively had to figure out how to make their experimental equipment with their own two hands. And they had to invent the math to describe the phenomena and realities they were experiencing.
At a certain point, the mind can only hold so many variables, and even when your hands are providing a very visceral feedback, sometimes you just need to lay it all out in a way that gets the logic out of your head, so you can see and work with it, and come to a better understanding of the experiences that your hands are trying to explain.
And that’s the bridge that’s missing. So many students can ‘do algebra.’ But word problems continue to pose a real challenge. It’s that ability to connect the real world experience to the theory in the math that is, I would think, pretty central to the methodology you describe: Start with the concrete, and then use the abstract to make sense of it. Math on its own, for its own sake, is as useless as learning to sharpen tools that you’ll never put to practical use. Using it to make sense of the relationships you can feel…
Why does a hammer with a longer handle pull a nail more easily? What’s the relationship?
If you need to scale the dimensions of a piece that’s being built to fit a specific dimension in a home, or a boat, how would you approach it?
The proverbial 10 foot pole? It’s a diagonal brace that will hold an 8’ pole at a plumb 90 degrees to a 6’ span. That’s trigonometry and algebra.
How do you describe how the different gear ratios work on a bicycle? How do you make sense of block and tackle systems to lift heavy loads? Why do the different diameters of hydraulic pistons result in the multiplication of force applied? If I’m making $xx/ hr, how does that translate into an annual salary? If I’m running a bakery, how do I know if the load of bread I just sold cost me more to make it that I got back from the customer, or if I’m making a profit?
If the state of Kansas cuts taxes, why does that affect their ability to pay teachers?
For that matter, why do so many ‘pro business’ politicians seem to think that you can cut or repeal taxes, and still maintain an educational and infrastructural status quo? Worse: why can they sell this idea to the population?
Those equations don’t balance. And people don’t seem to under that.
I would argue that the separation of mathematical understanding from practical application is just as bad as being finger blind, when it comes to making a world that works.
Math for its own sake? You’re right. It’s silly. To describe the world we can touch and feel? Very useful. To understand the economic necessities of the world?
“Let them eat cake.”
My opinion: any student who has to ask ‘yeah, but when will I use this in the real world,’ hasn’t really got his hands in that real world, and hasn’t had to think about it.
My point about algebra is not that it's not important. It is. But educators try to insist it's developmental, not that it's useful, whereas an activity like crochet can be equally developmental and useful. Algebra should be fun and likely would be for those who've been adequately prepared for it. Crochet, can actually help prepare the mind for algebra, through the development of spatial sense.
ReplyDeleteThat’s fair. I think my point, if I had one, is that the concrete and abstract are both necessary… and that maybe, in neglecting the concrete, schools are diminishing that abstract understanding as well.
DeleteApologies for going on a midnight rant.
No apologies needed. I'm glad you're reading and continue to find interest in what I write. I had a good conversation yesterday at the gym with two younger men. One loved word problems in math. The other hated them. The idea of a word problem is to propose that math is useful, which it is. But that's something you have to "get." And for many students, the launch into the abstract is insufficiently scaffolded by the concrete. The same affects reading. Kids need to know what words mean before we can expect them to take an interest in reading them or spelling them. Bruner's concept scaffolding is a good one and scaffolding is built by encouraging the kids to do real things.
DeleteMathematics requires a good command of the language; not only comprehension but also rigor in the use of words. Learning the grammatical analysis of sentences is fruitful.
DeleteRigor in the use of words is not limited to Mathematics. I had the opportunity to participate in rule making at EU level.
For instance, most people don't take into account that "or" by default means "and/or" and not "either X or Y". It makes a difference in the reading of a rule.
That can be shown with Boole algebra.
To flatten a board, one has to plane in three different directions. Planing in only two directions might result in a "ruled surface" like a paraboloid. See https://en.wikipedia.org/wiki/File:Hyp-paraboloid-ip.svg
ReplyDeleteYou will notice that the paraboloid is generated by straight lines in two directions.
Isn't it nice to be able to justify some practices?