kitchen table math, the sequel: Puzzle

Thursday, September 6, 2007

Puzzle

Question. What do the following have in common:

Youth Service
Ballooning
Ladder Safety
Deserts
Buying a Computer
Fundraising
Politics
Communication
Wages
Billiards

Answer. They are the "Applications Highlights" from a chapter in a math textbook; the chapter title is Linear Equations and Functions.

Catherine is right; it's always worse than you think.

(This came up on a list about converting math textbooks to braille. I don't have the book title. It's published by McDougalLittell.)


triplets homework
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16 comments:

Catherine Johnson said...

lolll....

I am sitting here in front of an extremely grumpy email I've just written to the assistant superintendent re: the extremely expensive spanking-new Glencoe aligned-to-state-standards New York Algebra books our math department has seen fit to purchase.

I'm debating whether to press send.

September 6, 2007 at 4:58 PM
Catherine Johnson said...

OK, debate over for the time being.

I stashed it in "Drafts."

YOU WOULD NOT BELIEVE HOW MANY UNSENT EMAILS-TO-THE-POWERS-THAT-BE I HAVE STACKED UP IN MY ENTOURAGE DRAFTS FOLDER.

September 6, 2007 at 4:59 PM
Catherine Johnson said...

More than you can shake a stick at.

September 6, 2007 at 4:59 PM
Catherine Johnson said...

As my friend the philosophy professor once said, "More than you can shake a stick at is a lot."

September 6, 2007 at 5:00 PM
Catherine Johnson said...

This is one of those pick your battles days.

The Mathematically Correct review says Glencoe algebra will support student learning at moderate levels, but not at advanced levels.

We're going to be lucky to get to moderate levels given the situation around here.

So I guess I'm not going to march on the administrative bungalows demanding that my kid be given a crack at Foerster or Dolciani.

September 6, 2007 at 5:03 PM
Catherine Johnson said...

grrrrr

September 6, 2007 at 5:03 PM
Catherine Johnson said...

reviews:

http://mathematicallycorrect.com/algebra.htm

September 6, 2007 at 5:03 PM
Catherine Johnson said...

otoh, things are looking up.

C. and I have completed Place Value in Primary Mathematics 3A and have begun Addition and Subtraction.

September 6, 2007 at 5:06 PM
Catherine Johnson said...

Ladder safety is important.

September 6, 2007 at 5:39 PM
Catherine Johnson said...

Also politics.

Politics are important.

Important and linear, too.

September 6, 2007 at 5:40 PM
Catherine Johnson said...

Looking at this list....is it likely any of these phenomenon could be represented by a linear function?

hmmm...

September 6, 2007 at 5:41 PM
Anonymous said...

Wages. Hours worked * hourly rate = pay.

Well, until you start dealing with Medicare deductions, Social Security deductions, (graduated) income tax deductions, etc.

At which point it's getting into CPA territory, not elementary-school math.

Likewise, a lot of the others might be approximated by linear equations, but most, if not all, of them will have discrete steps rather than smooth, much less linear, functions with lots of contributing factors.

Even billiards - there are LOTS of videos out there (Google/YouTube) of people doing trick shots where the balls don't go in straight lines.
- Andy Lange

September 6, 2007 at 7:22 PM
Catherine Johnson said...

Hi, Andy!

Good to hear from you!

September 6, 2007 at 7:59 PM
Catherine Johnson said...

Likewise, a lot of the others might be approximated by linear equations, but most, if not all, of them will have discrete steps rather than smooth, much less linear, functions with lots of contributing factors.

Thanks for leaving this.

I'm nearing the end of Saxon Algebra 2, which I think in reality isn't precisely algebra 2. Saxon's high school "trilogy" is integrated, so I assume that algebra 2 carries on through the 3rd book, too. (Don't know -- haven't opened the 3rd books, which are still wrapped in cellophane.)

So I don't know a lot about nonlinear functions at this point.

But, thinking about it, I didn't really see where these things made a lot of obvious sense as linear functions.

September 6, 2007 at 8:01 PM
le radical galoisien said...

"YOU WOULD NOT BELIEVE HOW MANY UNSENT EMAILS-TO-THE-POWERS-THAT-BE I HAVE STACKED UP IN MY ENTOURAGE DRAFTS FOLDER."

Hey, I can empathise!

Only they are to my country's national newspaper (which tends to be more like a selective state propaganda magazine, although occasionally opposition letters do get through), rather than to education policymakers.

September 9, 2007 at 3:55 PM
le radical galoisien said...

Also, the major thing about linear functions is not about its applications.

I am sort of a student tutor (though not as full fledged as this guy), and the biggest trouble is in trying to get students to realise what the essence of a line is.

Like, given a slope and a point, realising there you have narrowed the line to such an extent there can only be one equation to describe the line.

That given slope only without a point, there's no way to find the equation of a line because it could be 1 million miles away from the origin.

Low-level applications are not what they need. They need imagination and an abstract conception, or they'll get lost when they go to quadratics and then get to calculus with its concept of instantaneous slope and tangent lines.

My teachers often groan if I mention things like non-Euclidean geometry where given a slope and a point, you might not necessarily isolate it down to one line, or where lines of the same slope on different coordinates might not necessarily never intersect.

But to me, these things spur the imagination, and give kids an idea what to look forward to, and that lines are not just about boring calculations of how many hours you have to work to get X dollars. Those problems *I* groan about.

If you're going to use "practical" examples, use them constantly and consistently.

For example, in Algebra I, you use a linear equation to work out how many hours you need to work to get $X.

In Algebra II, you use a quadratic equation to work out how many hours you need to work to get $X -- only now your salary is increasing by a fixed amount every so often.

In Pre-cal (or rudimentary calculus), you use a linear equation to represent a rising salary, and you use "count the area under the curve" integration to find out how much time is needed to earn a certain amount.

It's sort of like spiralling isn't it? You keep on coming back to the same idea, but on a new level each time. You don't need graphing calculators at the early levels. That only undermines the "feel" for the math -- the intuitive instinct.
Rather, start the idea of integration/differentiation early (as Singapore does). My classmates in Singapore did "count the area under the curve" integration exercises months before they ever learnt what the formal definition of a derivative was.

I'm not saying it's constructive to talk too much about non-Euclidean geometry (I simply like to mention it in passing, to make people realise there's more to math), but I've always abhorred telling lies to children.

My teacher groans about that little lie they told to children in elementary school: you can't subtract something from a number if that something is more than a number. This really makes it hard to teach negative numbers later on, and you'd be surprised about how many freshmen get tripped up about that. You have to spend so much time and class hours dispelling the myth.

If you don't feel like concentrating on the possibilities, that's fine. Like in talking about parallel lines you may not want to concentrate too much about how Earth's latitudinal lines are parallel but form a triangle that adds up to more than 180 degrees. But don't limit their imagination! Leave it open!

September 9, 2007 at 4:22 PM

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