Tuesday, March 21, 2006

Innumeracy

Did I only imagine it, or did I really just see a high school college-prep geometry student multiply 4 times 25 longhand on paper? Did I also imagine her asking me what 10 times 10 is?

*sigh*

And really, even if every college-prep high school student could mentally multiply 4 times 25 or 10 times 10, would that really bring us closer to reducing the alarming innumeracy rate in America? Not by much.

Taken from a random website:

Functional illiteracy refers to the inability of an individual to use reading, speaking, writing and computational skills in everyday life situations. For example, a functionally illiterate adult is unable to fill out an employment application, follow written instructions, or read a newspaper. In short, when confronted with printed materials, adults without basic literacy skills cannot function effectively.

Tweaking a bit:

Functional innumeracy refers to the inability of an individual to use mathematical applications, mathematical terms, ciphering, and computational skills in everyday life situations. For example, a functionally innumerate adult is unable to do simple mental arithmetic, solve a simple word problem, or apply mathematics to real-life situations. In short, when confronted with numbers, adults without basic numeracy skills cannot function effectively.

I think innumeracy is a real problem in our nation, and sadly unrecognized as such by most. Numeracy is not the same thing as plugging-and-chugging one's way through the typical public school mathematics course. Mathematics is about problem-solving, not just rotely repeating steps, just as reading is not just about sounding out syllables. Reading begins with phonics (which is sorely missing from today's classrooms, mind you), but should move on to incorporate synthesizing, reasoning, and applying. The same goes for mathematics, and unfortunately what is disguised as mathematics in our nation is barely the phonics of mathematics.

Our high school math textbooks are still teaching Dick and Jane, and most students will never get the opportunity to read Jane Austen, George Elliot, Charles Dickens, or C.S. Lewis. I would hate reading too if I was still reading Dick and Jane, so it's no wonder mathematics is so vehemently hated by so many. Convincing most students that math is fun is like trying to convince someone that cherries taste good, if all the person has ever had is cherry cough syrup. It's a bitter imitation!

As a high school math tutor, I submit that what most high school students need is not a regular math tutor to reteach them what they were not able to learn or refused to learn from their teacher. What they need is not so much to learn how to solve by factoring, or how to graph an ellipse, or how to calculate the probability of drawing a green marble from a given bag. They need to learn how to learn.

Give a man a fish, and you feed him for a day; teach a man to fish, and you feed him for life. I would add, show a man the beauty of fishing, and you've hooked him for a lifetime.

14 comments:

Adrian C. Keister said...

You sound like you've been reading John Allen Paulos.

You wrote "...so it's a wonder mathematics is so vehemently hated by so many..." Did you mean "...so it's no wonder mathematics is vehemently hated by so many..."?

Learning how to learn: that's what classical Christian education is all about.

Great stuff!

In Christ.

Ashley said...

I hated math until my parents switched me to Saxon. Doing 30 problems of repetitive long division was not my cup of tea! My mom tried everything to get me to do my math, but I was stubborn. I would sit at the table for hours doodling and listening to all the things I was forfeiting by not finishing the lesson... Haha no wonder I became an art major. ;-)

Ben Garrison said...

As smart as the people I work with are, the three times that we've encountered anything at all to do with math in a meeting, our collective math has gone horribly and amusingly wrong until I pointed out that it was way off and they got a calculator.

And yet my coworkers still continue to function. =)

I suppose being functionally illiterate wouldn't be as much of a problem if you could buy a $5 computer that could read and write everything for you. =P

Susan said...

Adrian,

Actually, I've never read Paulos' book Innumeracy, though we do have it. Mother Dear read it and liked it for the most part, minus his slams against the ark, etc. I was staring at the title while I was typing my post, but my post was inspired by tutoring experiences, not his book :).

"Junior Editor" strikes again :(. Technically I could claim my sentence was meant as sarcasm, and thus not a typo, but I did mean to say "it's no wonder. . ." :)

Learning how to learn - yes, that's precisely why I like classical education :).

Ashley,

Yes, we've had "Saxon discussions" before, methinks. *shudder* I'm happy it worked for you, but really I think the curriculum is horrid. I've tutored high school Saxon, and didn't relish it. Saxon is huge in the home schooling community.

It's not repetitive, but it's also not very deep in some areas. I really don't like their geometry content (or lack thereof). Geometry is my favorite mathematics discipline, and it was just watered down and butchered by Saxon, stuffed into an Advanced Mathematics book. It's sad :(.

Boy,

Your coworkers may function, but do they soar :-D? There's a huge difference.

I'm not denying that calculators have their uses, but they shouldn't become a crutch. Calculators are actually a huge waste of time often, and they can be deceptive. Nothing can quite substitute for a real-life person. I can mentally multiply two and three digit numbers (with the distributive property :-D) way quicker than it takes my students to plug them into a calculator. Although now that I showed my geometry students how to do it, they can too :). Similarly fractions can often be reduced quicker mentally than with a calculator.

It's kind of like the age-old question of whether a math student should memorize a formula or theorem or not. I'm tutoring students in pre-calc and adv alg and trig right now, and we're doing identities. Now, sure they have access to the identities on the homework and if they ever needed them in "real life" they'd also have access to them, but the students who complete the problems way quicker are those who at least have the basic identities like sin^2 + cos^2 = 1 committed to memory. That way when they are working through proving something, a situation with that identity jumps off the paper at them, but without that already mentally committed, they're going to be pouring over their list of identities and floundering quite a bit. They have to recognize an identity in order to apply it.

I think there is a fine balance to be had, but let's face it. We carry our brains with us everywhere, but most of us don't have our calculators (especially graphing calculators) with us at all times. My purse holds everything except a graphing calculator and the kitchen sink ;). (For years I did carry around a protractor/compass/straight edge set in there, but I digress ;)). It sure is helpful to be able to mentally figure out a 15% tip or a 40% discount, and those are situations that often occur on-the-spot calculations, sans calculator.

Well, even if I could buy a $5 computer that could read and write everything for me, I don't think I'd promote its general use. It wouldn't be a substitute for a human being, and it would suck the joy right out of reading and writing, two of my passions that are right up there with mathematics :).

Mrs.B. said...

Susan, I have a technical blogging question for you. A friend of mine said that she noticed that my side bar had dropped way down and that it might be because I have quite a few posts. So I set it up to only display a week's worth. Is there a different way to fix the problem because I'd really like to archive my posts monthly instead of weekly.

Also, on my computer the side bar doesn't drop so I can't tell, does it look that way to you?

Thanks for any help you have to offer. (o:

Susan said...

Mrs. B,

Your sidebar looks normal to me! Hmmm.

Jessica (Everything Domestic) and Lydia (Renewed Day by Day) have both had that problem, though I think Jessica may have fixed hers. Maybe she can help?

I have very limited blogging skills, taught me by my friend Ashley (Ashley Design). I'll ask her if she knows what could be wrong. I hope you can get it fixed!

Mrs.B. said...

My friend said that it was fixed but I changed the setting to show only 7 posts at a time instead of 7 days worth...I'd rather do 7 days worth but I don't know what else to do.

If you don't mind, go ahead and ask your friend because I'd appreciate any insight that they can give.

Thanks! (o:

Anonymous said...

http://www.cbs.com/primetime/numb3rs/ti/activities.shtml

CBS drama Numb3rs, you’ll be excited to learn that the math utilized in each episode comes from actual FBI cases. The website has a page of free “We All Use Math Every Day” activities to demonstrate these concepts. Not that the math is reason alone to watch the show, but it's nice to ingest a little learning while you're "tuning out".

mayanne

Anonymous said...

http://www.cbs.com/primetime/
numb3rs/ti/activities.shtml

oops sorry

Susan said...

Thanks for the link, Mayanne. I had a friend recommend NUMB3RS to me a few months ago, and I've been meaning to watch it sometime. I don't watch TV much, so I keep forgetting.

The activities look fun. If I taught with a 5-day-a-week program, I'd try to work those into relevant topics. As it is, 90-120 minutes a week is barely time to get in the lecture and quizzes :(.

NUMB3RS sounds like a much more sophisticated version of Square One's old Mathnet section (right, Ashley ;)). Ah, Square One; those were the good old days. I wish they would release those on DVD.

amy said...

I spent most of my school years struggling with math and believing I just couldn't do it. The reality was that my early math classes had moved a little to quickly for me so I wasn't very solid on the basics. After graduating from high school I wanted to take nursing but my math grade wasn't good enough. So, I took grade eleven math by correspondence. Once I was able to work at my own pace it all fell into place. I got a B+! The strange thing is that I was using exactly the same textbook that was used in my high school classes.

My little sister was an honours student as well throughout school, but she graduated without being able to understand basic math concepts such as adding fractions (and thus, couldn't even understand a simple recipe). She also can't explain what a verb, noun, adjective etc are.

These are part of the reasons why we chose not to put our children in the public school system here.........

Ashley said...

I like Numb3rs but I don't know how well you would like it. My dad says the math is silly, and I've heard that from other math-y people too. But of course being the non-math person that I am, it all sounds very deep and intelligent to me. ;-)

zan said...

This has absolutely nothing to do with math.

Had mt baby last Sunday morning. Can't write the details right now but if you go to Carrie's blog (you can get to it through Crystal's) and scroll down to her "eating for two" blog.
I wrote about my experience there.

I am typing with my left hand now and really am unable to write a nice narrative abot the birthing experience.

Susan said...

Thanks so much for letting me know, Zan! I figured you must have had your baby since you had been offline for a while :). I'm glad your labor was so quick, but sorry it was more painful than before. That is great that Harry took to nursing right off. Rest well and enjoy your baby :)!