For those of you who have a hard time keeping it straight, left-brained is the orderly, rule-oriented side of the brain, and right-brained is the creative, free-thinking side of the brain.
Conservative people tend to value the school-way to do math. "Do this step. Memorize these facts. Drill these facts like crazy. Follow this step next. No, you can't do it that way! Do it this way instead." When you're dealing with a classroom full of children whose needs must all be met as best as possible, when you have children who annually change from one teacher to the next, it helps to have standardization in the math program.
Some teachers and curriculum-planners have tried to bring reform to that staid, old-fashioned, rule-oriented way to do math. People may have conniption fits over the changes. "It won't work. That's not the way to teach." Both sides have their points. The old way of teaching math leaves most kids without understanding of what's truly going on with their computations. On the other hand, with the newer ways of teaching math, there are problems. There's too much instability as kids change teachers annually. Kids mature at different rates, and teachers become impatient for "results" (that is, good scores on the standardized tests) instead of developing math-brains and math-smarts. Occasionally, teachers will even go so far in wanting kids to "understand the process" that they give equal credence to right and wrong answers. If a teacher doesn't understand math, she's going to have a booger of a time helping kids to understand math. And so, sometimes the best a school can aim for is to give up on math, but to make sure the kids can manipulate their numbers and do their arithmetic.
And, YES, there is a difference between arithmetic and mathematics.
Arithmetic is a tool. Being adept at arithmetic involves not only some understanding of what's going on with the numbers and why they work the way they do, but it also involves memorizing addition tables and multiplication tables and some formulas. Becoming good at arithmetic involves enough practice and drill that processing those numbers becomes simple.
But math? Ahhhh. Math is beautiful. Math is like art. Math is creative. Mathematics explains and explores and delves and marvels.
Amazingly enough, arithmetic is NOT necessary to understanding mathematics. Kids can begin to understand decimals and negative numbers before they've done the grunt-work of learning their addition and multiplication facts. Kids may begin to toy with number theory before they can earn A's and B's on their third-grade math worksheets. Kids know something about fractions before they've learned to count to twenty. Kids can wonder at the concept of infinity before they've learned that 6x5=30.
Good math teachers want their kids to learn (eventually) to do their arithmetic painlessly. Arithmetic is a vital tool for mathematicians. But as Penrose and Marilyn Burns and Sir Cumference will show, mathematics is a treasure over which little hearts can delight ... even prior to having mastered simple arithmetic!
Teaching math is like teaching reading. You can teach a kid his phonics and he may be able to decode words, but the higher priority is to teach him to cherish books and reading. Phonics is merely a tool. Same for math. Teach the left-brained arithmetic (hopefully on a timetable that fits the individual child), but don't let arithmetic sap the child of his wonderment over mathematics.
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Nice.
ReplyDelete- Jane S.
So true. Thank you for the reminder!
ReplyDeleteHanging my head in shame, because I had always thought arithmetic was all there was to math. . .needless to say I've never equated it with fun!
ReplyDelete"Math is like art. Math is creative."
ReplyDeleteI'm an artsy-fartsy graphic designer. I have always believed that math and art are polar opposites. Math is the OPPOSITE of creative. I didn't understand Algebra II or Pre-calc even a little bit in high school. I memorized the steps I had to do to get the right answer. That's it. I wish I could've seen the creativity in it, but it was either never taught that way, or I just didn't see it that way. Not surprisingly, geometry came naturally to me.
Meghan, arithmetic is the opposite of creative. But even with arithmetic, there is some hope somewhere to find the beauty in math, and how it fits together, and how those little rules and procedures are part of something bigger and artistic.
ReplyDeleteWhat I don't understand is what value we (as a society) find in teaching kids to do algebra and calculus if the only way to do it is to memorize the steps, grunt through it, and call it done. What's the point in that? They're not seeing the big picture. They're not learning to do more wondrous things with it, things beyond the schoolwork. They're not likely to use it in real life. So the only point is to do it because the school says you have to do it, and if you want to get into college, you simply have to jump through the hoops.
It would be so awesome (in my dream world) if teachers could give their students a glimpse into why we care about mathematics ...
beyond the utility of being able to balance your checkbook or measure in the workshop/kitchen.
"It would be so awesome (in my dream world) if teachers could give their students a glimpse into why we care about mathematics ..."
ReplyDeleteAssuming I'm not the only homeschool mommy who never learned to care about math, only to fake her way through the minimum requirements, I'd love it if you could share some suggestions to save my kids from my own fate. ;)
Angie, I've been pondering how to answer this without writing a doctoral thesis. The best thing I can come up with for now is to hit up the library for some of those math books by David Schwartz, Marilyn Burns, Theoni Pappas, Cindy Neuschwander, and others.
ReplyDelete