Is Algebra Necessary?

[ManicMechanic]

We provide "crutches" for the lack of algebra, when knowing it would save paper and money. Tax booklets have 40+ pages of tables with each income level in $50 increments printed with the corresponding tax. If the average American could do the simple piecewise function calculation:

T(x) = 0.15x for x<= 40,000 (or whatever the cutoff income is for the 15% rate)
or = 6000 + 0.28(x - 40000) for x > 40,000 (assuming 28% tax on excess earnings

it would take only an inch of paper on one page, not 40+ pages.

Lack of knowledge of compound interest is a great contributor to the mortgage crisis. A friend from China (an English major) told me "Most of us have our apartments (the equivalent of houses) fully paid off because we know the effects of the formula A = Pe^rt." We can blame our legislators and bankers, but each person is responsible for managing his/her own finances and making informed/prudent choices is something that people in many other countries seem do better than we do. In the county where I live, over 1/3 of homes owned in 2006 have foreclosed, and over 50% of the remaining currently owned homes are "underwater" (with less equity than debt). I can't help thinking that while a knowledge of algebra might not be "necessary", it could potentially save a lot of grief.

Originally Posted by JVN

Building along the same line that Karthik started: I recommend everyone read "A Mathematician's Lament" by Paul Lockhart (sometimes just referred to as Lockhart's Lament).

http://www.maa.org/devlin/LockhartsLament.pdf

-John

As a jr. college math instructor, I have to admit that I'm not crazy about the appeal to math as an art, with self-discovery as a necessity.

In robotics, not many students can invent the (mecanum) wheel, but many more are capable of copying and using the designs of others. Strict copying (similar to memorization and application of formulas) allows students to practice until understanding kicks in, and allows them to reach much higher levels (and generate more enthusiasm) than self-discovery would in the same timeframe. Shortly after the Vex platform was released, I watched students spend months building robots less functional than the Squarebot. That's where self-discovery without copying gets you (especially if you have solid but not stellar talents), and I would never want to return to that.

Exceptionally talented people seem to pick up the concepts and use them for their own purpose, no matter how badly a subject is taught. They're also the ones who see patterns and beauty in discovery. However, I have a child who struggles with math, and for her, "drill and kill" math has been very effective. Like washing dishes, she may find it boring, but with hard work, she can do it,and there's pleasure in doing something well, even if you didn't discover it yourself.

Motivating students to do the boring work helps, and connecting math to previously discovered concrete examples (rather than to what they can imagine/discover) seems to work well with my lower level students. For example, whenever students ask "Why do we have to know about singularities?", the Tacoma-Narrows Bridge, coupled with a discussion of resonance caused by undefined frequencies gets their attention. I don't expect them to discover the formulas on their own. And I don't see being on a time-table to teach a broad-based curriculum as necessarily bad.

[Ian Curtis]

Originally Posted by ManicMechanic

Motivating students to do the boring work helps, and connecting math to previously discovered concrete examples (rather than to what they can imagine/discover) seems to work well with my lower level students. For example, whenever students ask "Why do we have to know about singularities?", the Tacoma-Narrows Bridge, coupled with a discussion of resonance caused by undefined frequencies gets their attention.

In that case, you should definitely talk to them about flutter. 747 Wind Tunnel Flutter Test

It's been really interesting reading everyone's responses. I went to a magnet school, and for us Calculus AB was a graduation requirement. I thought that was pretty awesome, even my friends who said they were "bad at math" still got mostly 4s and above on the AP.

Originally Posted by JVN

It is my hope that natural curiosity would drive people to seek out this understanding. Algebra is of course (imho) a big part of this understanding.

Spot on! I think Linear Algebra was probably the coolest class I took even if I liked it the least. I always get excited when something I thought was unrelated pops up in a new place, and Linear Algebra has this tendency to show up just about everywhere. But that sort of natural curiosity means that I would be okay with really any class so long as it wasn't pointless.*

*I can't think of a pointless class I took with a good teacher...

[Taylor]

Student: This has no application. I don't get it. How can I use this? I don't understand it. It has no meaning to life.

Teacher: Well, this is how it's used every day. And here. And here.

Student: But those are story problems. I don't like story problems.

... and so the cycle continues.

[Ankit S.]

One thing that I don't think was brought up earlier is what happens if Algebra is no longer made mandatory in school. Many of my peers are lazy and would cut corners in any way possible. If given the option to take a moderate-workload Algebra class or to take the relatively homework free class Art 1, many would choose Art 1.

As a result, they would not even try to take Algebra. And who knows? Maybe some of them really will not benefit from Algebra and skipping it was a great choice, but for others who do no know what they want to study later on, the skipped Algebra course also narrows their options further along the road(either not do something related to math, or confront Algebra years later).

In summary: many people are lazy, if given the option to skip Algebra for an easier course they probably will. This skipping will narrow their study options later on.

[Tom Ore]

One of my favorite quotes that applies to some of the discussion here:

"Culture is what's left over after you've forgotten the details of what you've been taught."

EDIT: Another quote applies also: "The purpose of computation is insight, not numbers."