by Steph W.
One of my biggest challenges as a home schooling parent has been casting out my own assumptions about learning. These assumptions, which grew throughout my own years in public school, are sometimes unconscious. They surround me - thick, sticky, and sometimes invisible - like cobwebs.
I was taught that the path to learning follows a predictable pattern and must be followed step by step. Then I became a mom. At times, my kids' development unfolded in a predictable sequence but, just as often, it didn't. A child who confidently toddled across the room one day crawled the next. My older daughter, as a preschooler, seemed to have a primitive understanding of DNA and heredity one day; the next day she asked, "How did God put on our noses -- tape?" My ideas about the linear nature of development began to dissolve, and I learned to revel in the twists, turns, and spirals in the path we traveled.
Then I became a home schooler. During the past four years, I have been slowly learning what -- to seasoned home schoolers -- is as natural as breathing: that there are myriad paths to learning, each one as individual as the learner. I have also come to understand that learning styles -- being an auditory, visual, or kinesthetic learner, for example, or being "right brained," "left brained," or "whole brained" -- are not niches we can slip learners into. These models are helpful in understanding how people solve problems and gain knowledge. But they don't categorize people. Each person's way of learning and understanding the world is multi-faceted and unique.
My first challenge as a home educating parent was discarding everything I'd been taught about learning math. I remember being told that it is a clear, linear process. Certain steps must be followed precisely in order, and -- by all means -- SHOW YOUR WORK. There is nothing wrong with this approach, I suppose, except that is doesn't fit either any of my children.
My older daughter is a creative, verbal learner. Her thinking often does not follow a straight, step by step pattern. However, she has a mild learning disability that causes her to struggle with visual spatial and mathematical concepts. Because she has NVLD, she doesn't easily grasp math intuitively (often thought of as a right brained process) . However, she is not really a "left brained" learner either. She doesn't learn best by rote or by learning scraps of information in a way that isn't meaningful. She needs to see the "big picture" to learn, yet the "big picture" is often hard to hard to glimpse.
Sarah had spent four years in public school, taught by smart, dedicated teachers straight-jacketed by the increasing demands of government mandated standards and testing. She had received intensive help with math, thanks to her IEP, and had achieved "proficiency" on the all important state SOL test. But she didn't "get it." She'd look at a problem that traditionally requires "regrouping," for example --
55
+89
She'd try to "carry" the from the "ones" column to the "tens" column, and she'd make an error. She couldn't correct her mistake. When asked to explain her thinking, she'd insist, on the verge of frustrated tears, "that's just the way you DO it" or "that's what my teacher TAUGHT me." She didn't really grasp the concept of place value. She was grappling with a concept that's fairly abstract and complex, if you think about it, with no tools except some poorly learned rote skills. (I've since learned, with the help of Marilyn Burns, that this is a common problem with schooled students).
For most kids, hands-on activities would be the key to understanding. However, Sarah was not a particularly "hands on" child. She lived in the world of ideas, and like a "right brained learner," she needs to glimpse the broader meaning of what she's learning. However, she had difficulty with mathematical and visual-spatial ideas. It was a conundrum.
Our best chance was to introduce math concepts through verbal ideas. After all, this is her strength. She did many verbal logic puzzles. There are plenty of interesting books that gently present mathematical ideas. The Living Math site offers a treasure trove of suggestions.
I also discovered that word problems help. Conventional wisdom -- based on those old assumptions I was taught in public school -- dictates that word problems are "harder" that straightforward math and rote problem-solving. In school, children are taught a math problem through "drill and kill" before they are introduced to story problems using that concept. For example, after several pages of practice with problems like 38 x 14, the child is allowed to grapple with "If you earned $38 dollars a day for two weeks, how much money would you have?"
The problem is that the "story" is what gave the problem meaning in the first place. Without meaning, some kids don't really learn. When presented with 38 x 14, Sarah would shut down. If we talked about 14 shelves with 38 books on each one, perhaps discussing titles of some of her favorite books, the lights came on. Since she doesn't learn by rote, and she doesn't relate intuitively to math concepts -- well -- the story's the thing.
We created elaborate story problems. We talked about the math concepts that arose in novels. We focused on "real life" math, such as keeping track of her allowances in a bank book and shopping. We also used some conventional curricula. We made progress. Sometimes understanding would logically follow. Sometimes it would happen months later, after the concept had been set aside and just given time to germinate. She mastered factorization months after I finally gave up trying to teach it to her. The seeds were there, waiting to sprout. She just needed time and space; when the time was right, the connections happened.
My son James, on the other hand, seems like a classic right brained learner. He turned all my assumptions about early literacy on their head when, after years of making little progress with phonics games and easy readers, he taught himself to read, curled up -- cat-like -- by the heating vent, with a well worn "Calvin and Hobbes" collection. But that's another story. He is quick, imaginative, impatient with step by step processes, and full of pure, manic energy.
James refuses to solve problems on paper. I might present him with 38 x 14, laying a 38 x 14 rectangle of blocks in front of him. He refuses to write the problem, and he won't look at the rectangle. What? A visual, hands-on kind of learner who won't use manipulatives? Nope -- he won't look at the blocks. He covers his eyes. "Wait! I'm straining my brain!" He calls out. He shifts the numbers around in his mind, seeking the answer.
A year ago, I realized he wanted nothing to do with regrouping. In school I was taught that "carrying" and "borrowing" was the only key to solving these problems. There's is nothing wrong with that approach, of course, except that it just doesn't "click" with James. So we just kept practicing these skills in a hands-on way, through games, until he was ready to jump in and just DO it, devising his own methods. His way of learning is not step by step, or through learning a set of rules and techniques, but through intuitive leaps.
I find the way he approaches math problems quite interesting. For example, I once broke down and showed him the “traditional” way to subtract with regrouping. It is hard to exorcise many years of public schooling, after all. The conversation went something like this:
65
-38
Me: O.K. … look at this column (on the right). 5-8. You can’t subtract 8 from 5 so … (I was about to show him how you “borrow” from the 10’s column)
James: Yes, you can subtract 8 from 5.
Me: You can?
James: Of course. It’s negative 3. (Obviously, he’s completely right. Saying things like “you can’t subtract 8 from 5″ is a lie we adults tell to simplify things. But James, who has a strong internal picture of a number line - for lack of a better way to put it - understands the concept of negative numbers very well.)
Me: Huh. You’re absolutely right. Five minus eight is negative three.
Soon, James worked out his own method of solving this problem. 65 -38 He thinks: 60 - 30 = 30 and 5 - 8 = -3 ... 30 + (-3) (or 30-3) = 27. There you have it! No need to go “borrowing from your neighbor.” I thought it was pretty cool. What do you suppose are the odds that he would be allowed to work through this process, honoring the way his brain works, in a public school classroom?
Sometimes James surges ahead in math. When he reaches a point where he can't do the calculations mentally, he refuses to turn to the traditional pencil-and-paper methods I use. He stops. When this happens, I have learned to take a break from scope and sequence-type math, often waiting months before returning to a concept. Meanwhile, we play games. Sometimes we cook together. Recently, he has been teaching himself to play chess using an Usborne book, reveling in the chance to try out new moves.
Much about growing and learning has turned out to be different from what I expected. This included subjects, such as math, that I once thought were simple and predictable. The road to learning and development that I once envisioned traveling with my kids, step by step, has turned out to be more of a labyrinth, twisting and turning, often in unexpected directions. And here's another thing I didn't expect: this has turned out to be one of the most exciting parts of the journey.
Stephanie W. lives with her family in the beautiful Shenandoah Valley of Virginia. She has been learning at home full time with her three wonderfully creative, feisty and quirky children -- Sarah (13), James (9) & Patricia Elizabeth (4) since 2003. Her other interests include literature, writing, editing, and the internet.
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