Each of us craves knowledge of our world and our place within it.
We learn because we want to learn, because it’s important to us, because it’s natural, and because it’s impossible to live in the world and not learn.
Then along comes school to mess up a beautiful thing.
~ Peggy Pirro, 101 Reasons Why I'm An Unschooler
MJ helped one of my nieces with her long division homework the other day. Hearing that she had done this got me thinking again about what a waste of time and brain cells it is to learn long division.
#1 - As Pam Sorooshian pointed out in her math talk at Good Vibrations last year, the precision of long division is just not what we need out in the real world. Think about when you use division in real life: calculating the best value at the grocery store, figuring gas mileage, seeing how many of something you can use in a given time period or distribute to each person, and so on. And how do you do it? In your head, using estimates. "258 miles on 7.8 gallons, um, that's a little better than 30 mph." Done. Typically, we don't need to know that it was 33.07692 mph. And if we do...
#2 - Most of us carry calculators with us all day every day. We have calculators on our computers, in our phones, in our PDAs, in our watches, magnetized to our dashboards, clipped to our grocery carts, whatever. With a little practice, we can use these faster than we can estimate in our heads.
So, why are they still teaching long division in schools???? It is but one example of how schools have failed to adapt.
Once upon a time, it was vital for a certain group of people to know that wearing a silk shirt under armor might save your life, since the silk makes it easier to remove an arrow if you get shot. Somebody figured this out, and the word spread, and it became part of the standard warrior curriculum. Back then, knowing this technique was a matter of life and death. Nowadays, it's a quaint little factoid.
I'd rather have my kids learning about that than long division. Long division is a dead end, an exercise in tedium, a compelling bit of evidence that "math is hard" (not to mention unpleasant), or worse, that "I am stupid."
That little silk tidbit, though... Now that's interesting. I don't remember where I learned it—probably in a romance novel—but I looked it up on the Internet. It led me to Mongols and absorbency and sutures and animal rights for worms. And it led me to wonder: Who figured this out and how? Can you imagine the circumstances...? Chloe and I laughed together as we talked about it.
In other words, that little tidbit is fun. It opens doors. It engages my brain and reminds me that the world is full of things to discover.
That is what learning should be. I wonder why our schools haven't figured that out.
12 comments:
LOVE this. Especially since I've recently noticed a trend in our lives - every single time my kids have been "called out" by traditionally schooled kids on what they're supposedly lacking by not attending school, EVERY TIME, the kid will start quizzing my kids on long division to prove the point. It's uncanny to me, it's as though in their minds long division is the beginning and the end of what it means to be educated. Which is something I find alarming.
The last time this happened I wasn't present, but Shane told me about the exchange later on. And my favorite part about the entire thing was that it was my daughter that the kid chose to question. My daughter actually knows long division. She refused to answer him, though, because she has more self respect than to dance just because someone snaps their fingers. This is why we unschool.
@K.
I found this interesting to note since it was during the years of "long division" that school became the rank and file of hellfire and brimstone that still gives me nightmares...
Maybe the phrase means something else, and we just put it on mathematics?
Beautiful. I want to save it forever somewhere in public if you don't mind. In case the blog disappears.
Sure, Sandra. Thanks!
I love your prose but I have to completely disagree with your perception of the need for understanding long division. As a child, I found long division to be a fun puzzle. Each number had it's place and each problem worked out in long, long strands finally came to a conclusion. Only one answer completed the puzzle. It was so much fun that my sister and I often created long division problems for eachother just for the fun of it.
But it's not just for fun. Being able to do long division makes the numbers that you punch into the calculator make sense. It is what gives us the sense that the answer the calculator shows is correct or that we must have punched in the wrong numbers.
I say, rather than eliminating long division, embrace it. Play with it. Have fun with it.
Some people LOVE long division and finding square roots and the volume of solids. No one is saying that shouldn't still be done, for fun. More people would love those things if school didn't maim their curiosity and love of learning.
I love the ideas and trivia around musical transposition, that it's not just straight physics and some keys do sound better or different than others to those with such an acute ear. I love that I figured out myself that if a hymnal has something written with four flats, it can be played (same notes) with three sharps. Five sharps is too hard for me to read, but I can re-read it as though it had two flats. When I told my music teacher, he said I was wrong, that wouldn't work. But it can and it does.
I love gerunds and I love adverbs, but that doesn't mean I think everyone should learn about them or even try to think about them, if they don't discover them in a fun way and pursue the ideas with joy!
I love ideas about having choices and making connections most of all, and have been playing with those ideas for years now; still not tired of it. Some people don't care a bit about that.
What a great post. During the years of exploring with my daughter, it was always the 'silk" that sparked learning. You out it so well. Thanks! Please contribute to the Carnival of Unschooled life.
It's acceptable and expected that people differ in their expectations of what education should provide for students. but it is stupid to blanket label a subject taught in schools "outdated" or "useless". It's true that long division has no immediate practical use in the average person's life - that's not the point. Without formal education in Math people would get along just fine. Like you've said, we have calculators and computers. The point is that long division is a purely algorithmic solution to a problem. Before students can get practice designing their own solutions to problems, it is helpful for them to understand existing solutions - especially those which are similar to more abstract solutions. In fact, long division does have abstract applications in algebra. For some students, there is absolutely no need for long division. but what about those who want to become engineers? chemists? mathematicians? Can you expect students to have made such a decision at a young age? It seems counter-productive to limit their options by being selective about what they should learn.
"It seems counter-productive to limit their options by being selective about what they should learn."
My point exactly.
Let me try to be more clear. I have no issue with long division IF it's something the kid is interested in (both my daughters asked to be shown how do it), and if it's presented in a fun way with no pressure or expectations attached and no lies about how useful it's going to be. Remember, I wrote this post after my daughter's homework session with a niece and it was clear that neither of those prerequisites had been met.
I never want to see another child crying over long division. That is what's stupid.
As for your question about the future engineers among us: People with a natural inclination toward math or writing or climbing trees will do those things, and unschooling parents WILL help their children with those things.
We. Never. Limit. Our. Children.
Why is that so hard for people to understand? When I post about the stupidity of a school approach to something, it does not mean that we have NO approach. It simply means we reject the school one.
-=-It's acceptable and expected that people differ in their expectations of what education should provide for students. but it is stupid to blanket label a subject taught in schools "outdated" or "useless"-=-
WHOA!
"Stupid"? My kids don't use that word. It's rude and vague and it hurts feelings. It's often used wrongly, too.
Some school subjects, especially as they are taught in school, are information created and designed to help people succeed in 1955. For people born in the 1990's and twenty-first century, who will work at jobs you nor I have ever imagined, preparing for 1955 is outdated.
Penmanship should go the way of calligraphy, because very few things are done by hand anymore. If you mail a package at UPS, you enter the information into a computer terminal which prints out the label. Most jobs my kids have applied for involved online forms and tests. Many forms now say "PRINT" rather than "write legibly." Cursive writing might be considered outdated now.
"Long division" is merely one algorithm for a simple numeric manipulation, and not even the most efficient. Does "formal education in math" equate to the public education system's curriculum for teaching math? Is that what you're defending? Really? School, not the real world, is where student access to math is limited and twisted into something meaningless. We don't limit access to knowledge, information, or learning. Your imposition of that assumption into this discussion is erroneous. My rant on "math" in our society begins here.
Personally, I love math, and I love long division. That was not always the case, as I absolutely HATED it in high school, as evidenced by my sterling 1.7 GPA. But as I grew older, I realized that my interests - sports-related statistics, business metrics, and supply chain - required me to learn math in-depth and to use it several times daily. So I did what anyone in a similar situation would do - I learned it. And I learned it because I knew that I needed it in order to pursue my passions. Our kids learn information in the same way - they can gain knowledge if we force them to by making them do math, but knowledge and learning are not the same thing. The ability to truly learn something and applying it is directly proportional to the passion and desire of the learner - not the coercion of a grading system established by a school curriculum. If we want our kids to learn, we cannot force - we can only expose, and partner, and support, and encourage passions.
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