Is Algebra Necessary?

[ultrafilter]

@Boyo_Jim

This is my understanding. Historically, it seems that many CS programs developed within an already existing mathematics program, and so the requirements for the degree were very similar to those for a math degree. And once on this track it’s very hard to get off without offending the “old guard” – and since CS is so relatively new, there’s probably some of the old guard left to offend.

I think it’s more likely a holdover from computer science departments tending to be in engineering schools, which are big believers in calculus and differential equations. But I don’t know that for certain.

That said, it’s not like continuous mathematics is completely useless for a computer scientist. Even discounting numerical programming, there’s a lot of continuous mathematics in learning theory and algorithm analysis.

Edit: There’s probably an interesting debate in whether we should continue teaching calculus as the gateway to higher mathematics, or move to create a set of alternatives. But that’s a bit more of a specialized question than whether everyone should take algebra.

[BwanaBob]

Since some of you are insistent on contributing anecdotes I’ll throw mine in as well.
I have been programming since 1976 and been a professional since 1983. Every mediocre programmer I have met over the years had one thing in common: they sucked at math, especially anything that had a hint of algebra. End of anecdote.

[Ruminator]

@The_Second_Stone

Basic algebra and geometry teach students to think critically.

This is often repeated but I’ve never seen proof of this anywhere.

As a math geek, I want your statement to be true but observations of the real world shows that it is not.

Basic arithmetic of addition & subtraction – yes, it’s necessary.

Formal algebra (solving for x, complete the square, quadratic, etc) and geometry (proofs) – no, not necessary for most people. The folks that really do need these subjects will self-select themselves and learn their true value. (Real value beyond the typical school math curriculum that makes chimpanzees regurgitate formulas to pass a test.)

First, Inner, Outer, Last… FOIL. FOIL!!! Got that memorized?! Good! You are are now bestowed the title of “critical thinker.”

[ultrafilter]

I’d really like to see some work on what sort of cognitive changes are produced by studying math. But in the meantime, the Chronicle of Higher Education has a very nice interactive graphic showing off median earnings by college major, and it’s pretty clear that quantitative degrees tend to lead to better median salaries than non-quantitative ones. So even if the abstract benefits are yet to be established, the concrete benefits are very real.

[Bosstone]

@Ruminator

First, Inner, Outer, Last… FOIL. FOIL!!! Got that memorized?! Good! You are are now bestowed the title of “critical thinker.”

You passed right over the critical thinking part: ‘solving for x’. In other words: “I want to know something. I have this related data. How do I manipulate this data to get the thing I want to know?”

FOIL is a rule that gets drilled into kids’ heads, but the important thing is knowing when and why to use it, not what it is itself. I’m not always convinced that gets taught properly, though.

[Voyager]

@ultrafilter

I think it’s more likely a holdover from computer science departments tending to be in engineering schools, which are big believers in calculus and differential equations. But I don’t know that for certain.

That said, it’s not like continuous mathematics is completely useless for a computer scientist. Even discounting numerical programming, there’s a lot of continuous mathematics in learning theory and algorithm analysis.

Edit: There’s probably an interesting debate in whether we should continue teaching calculus as the gateway to higher mathematics, or move to create a set of alternatives. But that’s a bit more of a specialized question than whether everyone should take algebra.

When I was an undergrad there was no such thing as computer engineering. CS at MIT was an option in the EE department. (Everyone at MIT had to take two terms of calculus, even philosophy majors.)
When I was in grad school a large number of CS professors were also part of the math or EE departments, and a lot of CS courses had Math and EE numbers - and the department had been in existence a long time then.

[Ruminator]

@Bosstone

, but the important thing is knowing when and why to use it, not what it is itself.

But that foundational aspect is not what schools “teach” and let’s not kid ourselves that they do teach it or further delude ourselves that it can be taught. I can bring all my enthusiasm for mathematics to bear when tutoring someone on math but I’ve become convinced that there must be some seed of a desire to know the “when & where” that you’re emphasizing. Otherwise, it’s just the same old “plug n chug”

The folks that find value in math will self-select themselves to seek out the underlying “when & where.” Unfortunately, the math enthusiasts that do see the “beauty and truth” in mathematics think they can impart this “critical thinking” to others so that they can see the epiphany beyond regurgitating “FOIL.” It sounds great in theory but it doesn’t actually work.

I had a work colleague that got good grades in university math (Calculus III, Differential Equations). I was working with him on creating math models for computer failure rates and capacity analysis. This coworker could not determine which numbers in our mountain of data would be the dependent and independent variables. Why? Because the problems in the real world didn’t match the standard textbook examples such as decay of radioactivity or Lotka–Volterra predator-prey he’s seen before. I don’t blame the schools at all. They are very good at creating curriculums and tests that properly trained monkeys can pass. He went to good college and he himself admitted he got good grades because he was adept at plug-n-chug. He didn’t have that true inner curiosity to solve problems of which mathematics simply becomes a “tool” instead of an endpoint to get a good grade. I don’t expect schools to teach that curiosity. Can it be taught? Where’s the proof that it can?

@ultrafilter

, and it’s pretty clear that quantitative degrees tend to lead to better median salaries than non-quantitative ones. So even if the abstract benefits are yet to be established, the concrete benefits are very real.

I’m not convinced. That cite just mixes up correlation and causation.

Let’s pretend we have an alternative universe where all mathematics beyond basic arithmetic (addition,subtraction,multiply,divide,fractions) is an elective. Algebra becomes an optional. I would expect the salaries graph to look the same. The folks that want to get into those quantitative fields would work backwards from that goal and take the electives of Algebra, Trig, Calculus, etc so they can participate in those careers.

[GIGObuster]

@Ruminator

First, Inner, Outer, Last… FOIL. FOIL!!! Got that memorized?! Good! You are are now bestowed the title of “critical thinker.”

Warning:

FOIL-ing binomials & multiplying vertically: Explained!

FOIL tends to be taught as “the” way to multiply all polynomials, which is clearly not true. (As soon as either one of the polynomials has more than a “first” and “last” term in its parentheses, you’re hosed if you try to use FOIL, because those terms won’t “fit”.) When multiplying larger polynomials, just about everybody switches to vertical multiplication, because it’s just so much easier to use.

If you want to use FOIL, that’s fine, but (warning!) keep its restriction in mind: you can ONLY use it for the special case of multiplying two binomials. You can NOT use it at ANY other time!

[TriPolar]

@Ruminator

Let’s pretend we have an alternative universe where all mathematics beyond basic arithmetic (addition,subtraction,multiply,divide,fractions) is an elective. Algebra becomes an optional. I would expect the salaries graph to look the same. The folks that want to get into those quantitative fields would work backwards from that goal and take the electives of Algebra, Trig, Calculus, etc so they can participate in those careers.

This sounds right. In high school students should get an introduction to algebra, other areas of math, and other areas of science. But beyond an understanding of how science works, including the various sub-fields, learning the detailed knowledge is a waste of time for those who will never use it. I don’t know where that line is, but at the high school level, hitting the line dead on isn’t that important. Those who will need the detailed knowledge will continue on in school and have plenty of time to pick that up then. A high school student interested in studying math, engineering, and many other fields will want to take more math courses in high school. But even in some scientific fields such as biology the more advanced math studies can wait until college. High schools could certainly use a break from the drumbeat of increasing requirements, and good teachers in technical fields would be more attracted to an environment where they are teaching students who are motivated to make use of the opportunity.

[Paranoid_Randroid]

@Voyager

When I was an undergrad there was no such thing as computer engineering. CS at MIT was an option in the EE department. (Everyone at MIT had to take two terms of calculus, even philosophy majors.)
When I was in grad school a large number of CS professors were also part of the math or EE departments, and a lot of CS courses had Math and EE numbers - and the department had been in existence a long time then.

FWIW: where I studied mathematics (with a CS minor), the computer science department remains to this day under the college of engineering. A CS degree required the same basic math curriculum as any other engineering program, three semesters of calculus, although there was some grumbling about that.

As late as the early nineties, I’m told, it was within Arts & Sciences instead; and maybe it reveals my biases but I suspect it really belongs there.

Edit: This thread amuses me greatly at this point.

[The_Second_Stone]

@Bosstone

You passed right over the critical thinking part: ‘solving for x’. In other words: “I want to know something. I have this related data. How do I manipulate this data to get the thing I want to know?”

FOIL is a rule that gets drilled into kids’ heads, but the important thing is knowing when and why to use it, not what it is itself. I’m not always convinced that gets taught properly, though.

I laughed at the FOIL thing, because that is what I remember of algebra most. It is a mnemonic for a detail. FOIL isn’t critical thinking. That you can solve for two variables (about as far as I got and might barely remember how) is damn important to know. If you run into such a problem, you wouldn’t throw up your hands and say it’s impossible, you’d know it could be done. You’d have a method (or look it up) to deal with it. That is what geometry taught me about logic. I found geometry with its pictures and diagrams and postulates and theorems wonderfully simple, and they taught me the basics of logic (snide pittings belong in the pit). But I never thought of it as abstract. Algebra for me was very abstract and difficult without word problems. With word problems I knew the answer, but I didn’t know how I got the answer. Algebra with just the symbols was supposed to teach me how I got the answer, and for the simple stuff it made sense.

I remember when I was in sixth grade, we were given some sort of word problem that involved the time and distance between two points, and traveling both ways, and what the time would take. We weren’t given speed. This wasn’t a problem we were supposed to be able to get the answer to with our math training at this point. However, I had spent countless hours on family vacations in the family vehicle figuring out in my head precisely this problem and looking at the speedometer and hypothetically figuring out what all would change if we were going 10 mph faster or slower, always knowing the start time and planned distance. (I still do this today on all road trips.) But I digress. I wrote down the answer to the question for the impossible for us word problem. The teacher was puzzled that I got the right answer. But I had shown none of the work. He correctly pointed out that the you’ve got to show the work to prove you know it. I simply couldn’t. I had in my head recalculated for different speeds until I got one that worked. That wasn’t solving for x. I was doing the math equivalent of a pony trick. I’d always be served well with that trick for time, distance and speed (car speeds) for that exact problem, but it would be useless for all other applications. Algebra knowledge means I can apply it to anything.

[Indistinguishable]

@Ruminator

First, Inner, Outer, Last… FOIL. FOIL!!! Got that memorized?! Good! You are are now bestowed the title of “critical thinker.”

What? No! You can’t do First, Inner, Outer, Last. The rule from on high clearly says First, Outer, Inner, Last. I don’t want to hear another word of this blasphemy.

[Ruminator]

@Indistinguishable

What? No! You can’t do First, Inner, Outer, Last. The rule from on high clearly says First, Outer, Inner, Last. I don’t want to hear another word of this blasphemy.

I use wolframalpha.com to multiply polynomials.

However, to multiply large numbers, I refer to my John Napier autographed book of logarithm tables. One can only trust computerized calculations up to a point.

I used my “critical thinking” skills to find the right page in the logarithms book. Others just blindly keypunch the numbers into calculators. Fools!

[antonio107]

@Indistinguishable

Well, if you’re up for it, we could help you out, perhaps. What sort of thing are you interested in learning about and what sort of background do you have?

Thanks!

Mathwise I was an A student up until the 8th grade, then it went 70, 65, and 60 in grade 11. I’m quite convinced my grade 11 math teacher was a moron; she was fresh out of teacher’s college and couldn’t solve problems without an answer key. The only thing I remember about calculus was that she kept writing ‘Asimtoto’ for a week, and she sent me in the hall for trying to correct her spelling. Serious.

Is calculus a good place to start? Something I could whittle at in small chunks in my spare time?

ETA: Also, I found it quite disconcerting that in trigonometry–something I was quite good at for a while, IIRC–we never did it without the calculator. Telling me to press the “TAN” button without explaining to me what it was (even just once as a cursory “this is what it represents”) seems like a shitty way to teach math.

[Ruminator]

@antonio107

Is calculus a good place to start? Something I could whittle at in small chunks in my spare time?

Have you seen the free Khan Academy math videos?

I just saw a TED presentation on it.

(Don’t mean to detract from the help you can get from the SDMB math experts. The online videos (such as Khan) will show visuals which can be more helpful than reading paragraphs of text.)

Telling me to press the “TAN” button without explaining to me what it was (even just once as a cursory “this is what it represents”) seems like a shitty way to teach math.

Instead of saying “shitty”, I’d just call it “cheap.” It’s an inexpensive way to teach math if you must take into consideration that the class has a mixture of motivated kids and plug-n-chug kids that just want to get it over with and move on with their lives.

What’s “shitty” is labeling these teachings as “critical thinking” skills.

[Indistinguishable]

Eh, if they never even explained what TAN represents, I’d call it shitty.

I agree most students have no need to ever calculate TAN by hand, but I don’t think most students are ever drilled to, or even told how to, calculate TAN by hand either, so that works out. (At least in the U.S.; I’m not sure how math curricula standardly run elsewhere, such as antonio107’s country of upbringing, which I suppose is probably Italy, given the “asi[m/n]toto” thing)

[Paranoid_Randroid]

@Indistinguishable

FOIL is what you get when you try to teach algebra to kids who don’t care, and settle for an unthinking mnemonic rather than actually understanding the nature and use of distributivity

I’ve never seen that sentiment put in those exact terms, but I couldn’t possibly agree more — FOIL has always seemed to me the archetypal form of so-easy-to-prove-that-memorization-is-unnecessary. How much extra effort does it really take to internalize the fact that multiplication distributes over addition?

[ultrafilter]

I was taught how to use a table of logarithms and trigonometric functions, but my precalculus teacher was a very old man.

[Indistinguishable]

@ultrafilter

I was taught how to use a table of logarithms and trigonometric functions, but my precalculus teacher was a very old man.

Huh. The only difference between that and a calculator is inconvenience, isn’t it? [And some fussing around to get your input values in the right range for the table, I suppose]

[Sam_Stone]

So, the rule is that if something doesn’t have a concrete, universal real-world application, it doesn’t need to be taught in high school?

In that case, we should drop sentence diagramming. And art classes. And chemistry, and biology. There are very few high school diploma level jobs that require you to tell a genus from a species, or which require you to draw a benzene ring.

While we’re at it, might as well drop literature. You don’t need to know Shakespeare to fill out a government form or write up an invoice. No one other than a biologist needs to know the inner workings of a frog, and no one other than a chemist or physical scientists needs to understand the relationships between elements in the periodic table.

My child’s curriculum is full of subjects that I would drop before I would even go near any math subjects. The amount of filler and useless dreck being taught in schools now is astounding. I agree that kids should get more basic numeracy and statistics, but I wouldn’t teach that at the expense of algebra. I’d teach it at the expense of perhaps her class in ‘community’, or by removing one of the many environment units or native studies units she’s had to go through.

A high school diploma is supposed to guarantee that you are a well rounded individual with at least a basic understanding of a wide range of subjects. If I hire a person with a high school diploma, I expect to be able to say, “We’ve got 27 boxes of material coming in. Here’s a list of dimensions for the boxes in the shipment. Go figure out where we have the floor space for them.” And I expect that person to be able to use math to solve that problem.

Math is important even if you want to go into a trade. Plumbing education is full of math, including fairly difficult algebra questions. My brother is a mechanical insulator, and his coursework had questions like, “You are given a contract to insulate a system of intake and outlet pipes for a factory. Here is the diagram. Calculate how much aluminum you will need to order to wrap all the pipes.” And that diagram will have pipes with their diameters listed, the radius of the bends in the pipes, etc. You need algebra and geometry to solve that problem.

I would go further and say that any kid graduating high school with a desire to go to college should also be exposed to calculus, because calculus is critical in being able to truly understand rates of change, and that becomes critical in numerous sciences and technological programs. Heck, it’s important as a citizen just to understand issues that involve exponential growth, such as population dynamics and climate change.

Let’s be honest about what’s going on here: The schools are having a hard time teaching algebra because they’re done a lousy job teaching math in the first place, so their answer is not to fix the quality of the education, but to drop the harder subjects.

The result of this trend is a devaluation of a high school diploma, which is no longer even a guarantee that the student can read or write with any sort of proficiency. The basic entry criterion for careers is slowly shifting towards a college degree, and even those are becoming so watered down that many jobs that used to require a bachelor’s degree are now demanding a Masters.