How I learned algebra
I was in low track math. I remember when I realized it. I was in the front row, on the far right, and did not understand anything going on in algebra class. We had a tiered system in our school. I was in the highest track for most classes, and the lowest track for math. I remember wondering what the school would do with me when they realized that I couldn’t even keep up in dumb-kid math.
Amazingly, after that, I was moved up for geometry, into a higher track, presumably because in a class of 1500 students, I was in the top 10%, but I was in special ed math. Something was wrong.
But something was really wrong in geometry. I was so lost that I still have nightmares about walking into class and having no idea what people are talking about.
I never needed math again until I founded my first start-up. The guy who funded it hired a CFO-type person to show me how to build financial models. Using algebraic thinking. I realized that not only was he assuming I knew how to do math, but he was assuming I knew how to use Excel. So I hired a college student to teach me how to use Excel.
Excel is amazing. It taught me how to think algebraically. And as I got better at Excel, the formulas showed me how to think in terms of possibilities, and the columns and rows taught me how to look for patterns in business models to evaluate feasibility.
I’ve founded three start-ups and each time, my Excel skills have improved because it’s fun for me. I love building financial models, and in my last company I put an investment banker on my advisory board specifically so he could help me get better at using Excel.
So I am starting to believe the people who say that kids learn math when they need to know math. I’m believing the people who tell me that it’s okay that my son can’t do long division. My son has a goat business. It’s time to get the goats pregnant, and he can’t pay to rent a boy goat until he can figure out how much money he needs left over to feed the moms and the babies over the winter. So I know that somehow, he’s going to learn math this fall.
When I was a child, I used to tell my mother that children *knew* stuff already, but that teachers just helped draw it out of us.
That’s not exactly true, of course, but I think humans have an instinctive drive to discover and learn. Nurturing that impulse and feeding it works a whole lot better for us than my playing a pedantic schoolmarm.
Pamela
@redwhiteandgrew
Excel is an amazing tool. I use it for a number of things and yet I know I’m only scratching the surface of it’s capabilities.
The long division that your son is having problems with is not math – it’s calculating. Math and calculating are two very different things entirely. Leave the calculating to the calculators and computers so that you can focus on the math concepts.
Here’s a TED talk given by Conrad Wolfram titled Stop Teaching Calculating;Start Teaching Math –
http://www.computerbasedmath.org/resources/reforming-math-curriculum-with-computers.html
This video and transcript is so spot on that I’ve played the video several times.
i want to watch this when i get home! i’m at work.
when P was talking about goats and money i realized that our ancestors had to learn that way. no sitting in school for it.
I love that TED talk link. It makes so much sense. Thanks for posting it!
After two years of homeschooling, your posts on unschooling and project based learning have given me confidence to give it a try, but I can’t give up my math curriculum. I know that I am not being logical – if unschooling works it should work in all areas – but I can’t do it. I think that I’m hedging my bets in case some unforeseen circumstances result in me having to send my kids back to school. I want them to be able to fit in and keep up if that happens. Hopefully, if i see my sons having success in other areas, it will allow me to take that leap of faith and chuck the workbooks. I am consoling myself with the fact that both my boys enjoy doing it – it is their favorite subject by far, but it still feels like a cop out. Glad to see that I am not the only one with doubts.
I really thought that when we started K/1 that I’d lean heavily on math workbooks, too. But we haven’t. In fact, I wound up really slowing us down to make sure that we master concepts first. But we’re at the beginning of grade school, so that’s different.
As kids mature and get into more advanced work, I think we all learn to *know* when to adapt and change our game plans. If your kids are content with workbooks for math, then it sounds like all is swell and you’ve made the right choices for your kids. And that you’ll make changes if and when they’re right, too!
Karen, the idea of hedging bets by making sure kids keep up in math — that is something I’m doing but maybe unconsciously doing. I don’t think I realized it until you wrote it. I think I’m really at the point of no return when my kids would not be able to go back to school if I needed them to.
Penelope
I am all in-favor of your opinions. I think you know that. And I’m not necessarily criticizing your approach…
Buttttt – When it comes to any subject matter, you can usually tell those people who have a fundamental, “classic” understanding versus those who don’t, especially when it comes to problem solving. To me this applies to anything – music, math, administration, web design.
I’m glad you conquered your own hurtles in algebra. You have applied this logic daily and successfully. But, it is somewhat sad to me, that you do not share an appreciation for math theory, which is actually beautiful when you build a foundation that makes your understanding deeper. This renders you unable to see and appreciate how many of these theories also have deeper, philosophical meanings that resonate within our lives.
I really have been enjoying these lively discussions you are having on your site. It has open the floodgates of my own opinions.
In the spirit of decreasing your state of being “somewhat sad,” I recommend thinking of math the way some people think of any number of other subjects which have deeper, philosophical meanings that resonate within our lives. Things like math and music and literature and history, or even something like cooking, they’re all like ice cream flavors that inexplicably appeal to different people in different ways. Some people will find deep philosophical meaning in math, others in a variety of other fascinating subjects.
We all find meaning in the things that interest us the most.
Penelope, your post reminded me of this Oatmeal comic on what we should have been taught in our senior year of high school. Scroll down to the math section for full effect: Oatmeal comic
hahahahaha I LOVE that comic.
Thanks, Irina.
Penelope
Ditto, great comic.
And I could really relate to the imperial-metric system unit conversions … mundane, boring, and totally off the mark since it was a distraction from learning the science. It was important to know how to do the conversions but not on every problem on every stupid question on a given test.
Penelope, FYI, Free online training for all MS Office products including Excel –
http://office.microsoft.com/en-us/support/training-FX101782702.aspx
Thank you for this great post. My children have been struggling in math and I’ve wondered what the point is in teaching them miscellaneous mathematic concepts that they can’t seem to grasp and that I have never used. I want them to learn real life math and let the rest work itself out. You’ve helped me see that I’m on the right track.