I had read most of Marilyn's books but not this one until yesterday. I think I have to consider it the best I've read so far on why we need to change math education. I kept reading it thinking, I'm so GLAD someone with as much of a voice as she has is saying this. So much of what she expresses is what I've felt myself as I've changed the way we "do" math in our home.
Rather than summarize, let me quote from parts that really resonated with me:
"The main premise of this book is that what was good enough for us in learning mathematics is not good enough for our children. Despite the reality that learning math was a bust for so many of us, we have pressed on with ineffective teaching approaches that clearly don't work. If they did, math phobia wouldn't be rampant today.
Even in the face of widespread failure in learning mathematics, we seem to want to cling to educational methods with a nostalgia for them that has long outlasted their usefulness and has perpetuated failure. The way we've traditionally been taught mathematics has created a recurring cycle of math phobia, generation to generation that has been difficult to break. We start young children with counting and move them along through arithmetic, then on to algebra, geometry, trigonometry, and so on. The 'and so on' depends on whether or not the student sticks with math, which means not falling off the ladder of math progress in school. But an alarming percentage of the people in our country have fallen off the ladder and feel like mathematical failures. And once people fall off the ladder, there seems to be no way for them to get back on.
. . . Children must be helped to learn mathematics in a better way than we were, so that mathematical limits do not shut them out of certain life choices and career options."
Chapter 1 does a better job of describing the true relevance of math in our daily lives than most books I've read. One anecdote that I loved: "A friend of mine is an interior decorator. ' I was never good at math,' she once told me 'I'm so grateful that I have work to do that doesn't rely on doing math.'
I looked at her in amazement. To do her work, she has to measure the dimensions of rooms for floor covering and wallpaper, figure yardage for drapes and upholstery, calculate the cost of the goods, and prepare invoices for clients, figuring in the percentage for her services. I've watched Barbara size up rooms, her eyes darting as she takes in the floor area, the ceiling height, the placement of windows and doors,; suggest the right amount, size and scale of furniture; prepare an estimate that is amazingly close to actual cost. I experienced this firsthand when we remodeled our house. No math? What was she talking about?
I asked her. 'Oh that,' she said, 'That's easy. It's those pages of math problems in the book I never could do.'
That's the problem. People think that doing math in books is what doing math really is. It's not. What we need to do for our children is get math off the textbook and worksheet pages so they can see reasons for doing math and gain experience using math to solve problems."
There is a very interesting portion of this chapter that sizes up the impact of years of pencil and paper arithmetic instruction when we hardly ever use this skill in real life - we usually either estimate in our heads, or use calculators. Kids don't get the point of "estimate first, then get the 'right' answer" because all that seems to count is getting the right answer. But in real life, the estimate is what matters, because so many "calculations" have too many variables to be accurate.
There is much, much more of course. Chapter 6, Calculators - Crutch or Tool? is very interesting to me because I've had a hard time explaining why I've felt there is way too much emphasis on pencil and paper arithmetic, on skills we *don't* hardly, if ever, use in real life.
This is also the book I recommend to rebut those that recognize the problem but suggest more rigor in arithmetic instruction as the solution. I agree with her, it's just throwing more bad after good. She promotes rigor in learning to problem solve and to *think*.
I highly, highly recommend this book even if you are not math phobic yourself but are looking for reason and validation to change from a traditional math approach. Her writing is clear and easy to follow.
> I have a question. I certainly see Marilyn's argument for using calculators more and the paper and pencil less. But in order to understand how to program a computer, the programmer must understand the need to borrow tens, hundreds, thousands, etc. >
Borrowing is a term for an algorithm, a process (when your son said he hated borrowing, that's what he meant, right?) All programmers today use programs that have basic arithmetic operations built into them and they do not in fact need to be able to tell the computer to "borrow."
It is actually quite possible to never "borrow" or "carry." Some of us are "adders". For example, in the book Marilyn points out, if you double 38, how do you do it? Many will double 40 and subtract 4; but other will double 35 and add 6, or double 30 and add 16. Others will perform the borrowing algorithm mentally in their heads. Same thing if I were to subtract 18 from 40 - I think of subtracting 20, then adding back 2. I don't borrow at all.
If a person can manipulate numbers like this in their head, then numbers that become too cumbersome will either be dealt with through a calculator or a computer, with pencil and paper being a last resort if neither is handy. That's just a fact. In 13 years of working in national public accounting firms, I almost never used pencil to paper math, and I was highly successful.
In her chapter on this, she relates a discussion with an engineer who also points out he rarely if ever uses this skill, but he could not shake his belief it was necessary, and she highlights this illogical connection quite well I think.
> What do you think? Isn't there a balance between living math and traditional math? Are we in danger of throwing the baby out with the bath water? >
I think common sense, if allowed to reign, will prevail. It's when we allow ourselves to pendulum swing in fear one way or another that we do this. Taking steps based on ideas that make sense to us, taking in constant
feedback as to the results we get, continuing to be open to making changes wins the day.
Also, some things I feel need to be said strongly to combat such deeply held beliefs such as "doing math" = working pencil and paper problems. There is little danger I really feel that by making changes we will be tempted to completely swing the other way. For one thing, when I'm working *with* my kids, pulling out pencil and paper is the only way I can *show* them how I think. It obviously has a purpose, as writing things down vs. narrating has a purpose.
July 30, 2004