Should Algebra Be Required At Community Colleges?

[swampwiz]

This is an interesting topic. I think the main reason that so many community college students fail math is that passing math requires that there be a certain minimum value of the product of raw quantitative intelligence and personal grit. Someone with a high level in one of these does not need much of the latter to succeed in "liberal arts math". However, to succeed in advanced calculus (i.e., "proof" calculus, or introductory analysis), one needs BOTH! Obviously there are a lot of folks for whom "math is hard", and they just don't want to work at it.

And the political situation is that everyone thinks that everyone should be able to succeed equally- which if course is baloney, since life is a nasty & brutish struggle to outcompete one another. Community colleges are designed to be available for *anyone* that holds a high school diploma, which itself is something that folks think that everyone should have as a minimum, even folks who are of borderline normal intelligence (i.e., not mentally handicapped, or "special ed"). but even those folks are guided though to get the diploma. However, since the notion of a college education for everyone is thankfully not normalized, a certain weeding out of folks who cannot do proper rational thought has to be implemented - and 2 of the 3 R's, writing and 'rithmatic, at a certain higher level, become the filter.

 

[vela]

If you'd like to suggest alternatives I'm all ears, and we can debate their merits relative to algebra. I'll stipulate that there are other methods for learning critical thinking skills. IMO, the best possible one is math, so that's the one I support being used to achieve the goal of instilling that skill set in students. If you disagree let's hear your proposal on this subject.

Again, you're misrepresenting the topic of the thread, which isn't saying to eliminate math completely from the curriculum. The suggestion is to replace the intermediate algebra requirement with something else.

You just said that math isn't necessary for critical thinking, now you're saying there's other ways to learn math. Admittedly, I'm lumping "algebra" and "math" together here. So I return to my previous point: instead of just saying the current system is bad, what is your proposal for making sure students develop critical thinking skills grounded in reality?

You're doing more than lumping algebra and math together. You're saying "$\text{intermediate algebra} \Leftrightarrow \text{math}$."

I don't know what would be a good replacement for Math 108. From personal experience, I learned a lot of math on my own because I decided in eighth grade to learn APL. In trying to figure out, what all the symbols on the keyboard meant, I learned about logarithms, matrix multiplication, matrix inverses, trig, Boolean algebra, combinatorics, etc. When I took Algebra II in high school, a lot of it ended up being review to me.

Consider students who wants to go into video game development. There's a lot of basic math they'd have to learn just to understand how to place an object on the screen and to move it in a certain way, questions they're actually interested in, as opposed to learning how to graph the equation y=-3x+2, which may strike them as abstract and pointless because they don't yet realize what it's good for.

So basically, what you're saying is that if math is difficult it's better to just not do it?

No, what I'm saying is it's arrogant to think that what worked for you will work for everybody else. The implication is that if it doesn't work for them, it's because they're deficient in some way.

That's been the prevailing attitude for a while in this country, and it's the primary reason our students fare so poorly compared to other countries:

http://www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/

This study is very recent. Here's another report that might be worth reading:

https://www.usatoday.com/story/news...y-half-hs-seniors-graduate-average/485787001/

Simply dumbing down the curriculum to get more students through with higher grades might be wonderful for self-esteem, but it's hurting us on a global scale, and economies are only going to become more globally integrated going forward. Maybe our students feel better about themselves, but their skillsets are lower.

To quote Jim Jefferies (admittedly not exactly a scholastic reference), "So, you're creating stupid confident people. They're the worst employees in the world!"

The attitude in the US toward math is a big part of the problem, but colleges and universities can't do much to change that except on a case-by-case basis. They have to deal with the students they get. Some students come into classes with a debilitating fear of math. You don't hear the same thing about, say, English classes.

I doubt there's a magic bullet that will solve a college's problem when it comes to math requirements. I do agree with some here that many students don't belong in college, but I don't think getting rid of them would solve the problem completely.

 

[russ_watters]

Because the topic of the thread is essentially, "Is there a problem with the way math is currently taught?"

If the OP had stopped there, we would have responded with "please give us your opinion as a starting point for the discussion." But he didn't, he provided at least part of his opinion: eliminate algebra. And I do mean just "eliminate": the idea of replacing it with something more useful came later after it was pointed out that just eliminating something de-values the degree. And I'm still waiting to hear what we should replace it with that would be more valuable.

Intermediate algebra is what's called a gatekeeper course. If students can't get past it, they're shut out of tons of opportunities.

So is calculus. So is chemistry. So is biology. So is basically every first step in a new subject. Anyway, I'm not sure what your point is in pointing that out.

The fact that a considerable fraction of students currently have a great deal of trouble passing the course suggests there's something gravely wrong with the status quo. It's a major problem recognized by colleges.

Agreed. And I've fully developed what I think that problem is, and am still waiting for the other side - that initiated the conversation - to develop that side.

There's the justification for questioning whether the intermediate algebra requirement, as it's presently constituted, is the right one.

Certainly. And I'm all ears, waiting for someone to develop their argument that it should be replaced with something else. If that is your position, by all means, please lay out your plan.

Sure, these are some of the course objectives of intermediate algebra, but intermediate algebra is not the only way to achieve those goals.

You need to open your mind to the possibility that there's more than one way to learn math.

As pointed out above, you're arguing two different things here: that we shouldn't teach algebra/math and that we should teach it differently. And since this argument has never been about changing how we teach algebra, you have no way of knowing whether I'd be open to changing it (freebie: I am).

A point that seems to be lost on a lot of people posting here is that they're not like the typical student in many important respects when it comes to learning math. Math probably came fairly easily to them, and they found it interesting enough so when they got stuck, they'd stick to it and figure out the problem. Most people aren't like that. When a student struggles with algebra...

Of course everyone is different. Some people are good at math, some good at writing, some good at everything and some good at nothing. This again is arguing that because it is hard we shouldn't teach it.

...it's easy to write it off as the student being lazy, unmotivated, or not hard-working enough. That's simplistic at best.

Agreed, which is why no one has done that here. And I'll be explicit: I think there is roughly equal blame to be put on the students and teachers/schools. Caveat: there is a pretty rough implication of what you are saying: you are implying that a large fraction of students just aren't smart enough to be worthy attempting to educate them past middle school. And that's something I vehemently disagree with. I have a much higher opinion of the potential of my fellow humans.

 

[russ_watters]

Again, you're misrepresenting the topic of the thread, which isn't saying to eliminate math completely from the curriculum. The suggestion is to replace the intermediate algebra requirement with something else.

Again: please specify what you would replace algebra with!

Caveat: you are misrepresenting the OP, which did indeed just suggest eliminating it, not replacing it. The idea of replacing it with something else came later, but since it hasn't been specified we can't even discuss it.

I don't know what would be a good replacement for Math 108.

So then what do you propose? Should we just eliminate it and decide later what to replace it with, in the meantime just reducing the education provided?

Counselor to Little Johnny: "Johnny, you aren't smart enough to handle algebra, so we're not going to teach it to you. You might be capable of learning something else, and if we ever figure out what that is, we'll let you know."

 

[russ_watters]

Caveat; the thread was first about eliminating algebra, then replacing it with something unspecified (and now acknowledged, undetermined).

I think my opinions on the stated problem(s) has been answered as completely as I can, but what about the new question of whether math education can be improved? I think it certainly can. Here's an interesting article on why American students are bad at math:
https://www.scientificamerican.com/article/why-math-education-in-the-u-s-doesn- t-add-up/

What it says is that in the US, most students learn math via rote memorization rather than by learning and applying concepts. This is a cause-effect circle in that it both prevents kids from learning math well and keeps them from getting out of it what they most need; to learn how to think.

As I said before, I think the problem is partly the students/parents and partly on the teachers/education system. The above addresses briefly how the education system is deficient in it methods.

 

[vela]

Caveat:

you are misrepresenting the OP, which did indeed just suggest eliminating it, not replacing it. The idea of replacing it with something else came later, but since it hasn't been specified we can't even discuss it.

That's total BS and you know it. Reread the original post, and PhotonSSBM says what he thinks the intermediate algebra requirement should be replaced by.

 

[russ_watters]

That's total BS and you know it. Reread the original post, and FallenApple says what he thinks the intermediate algebra requirement should be replaced by.

[rereads] Nope. Not seeing it in there. Please quote what the OP says it should be replaced with.
For your part, I don't see why that upsets you, since you just stated that you don't know what you would replace it with!

 

[PhotonSSBM]

[rereads] Nope. Not in there. Please quote what the OP says it should be replaced with.
For your part, I don't see why that upsets you, since you just stated that you don't know what you would replace it with!

Wat? Uh, I said it on page 1 dude:

1. We should maintain algebra up to the level of college algebra (basic equations, plotting lines, factoring)
2. Incorporate basic statistics into arithmetic and college algebra.
3. Incorporate spreadsheet uses and basic programming as a mandatory gen ed.
4. Reduce effective number of required math classes to 2 instead of 3 (Arithmetic and College Algebra)
5. Encourage students to take math courses specific to their fields. (i.e. what our nursing program does) As opposed to just intermediate algebra.

I believe this would be better suited to a person seeking a general education in mathematics. Would you do things differently? I'd genuinely like to hear yours and others' opinions.

 

[russ_watters]

Wat? Uh, I said it on page 1 dude:

Not the OP, but fair enough: I wasn't clear on that that you were calling out the spreadsheet/programming as separate or part of the consolidation of math classes. It seems to me like numerical integration at least should already be taught with spreadsheets, as part of math classes -- but I don't know if it is or isn't.
[edit] It looks like from post #35 that you did indeed intend those to be part of the consolidated math classes. So did I read you wrong or are we still 1 class short, consolidating from 3 to 2?

 

[PhotonSSBM]

Not the OP, but fair enough: I wasn't clear on that that you were calling out the spreadsheet/programming as separate or part of the consolidation of math classes. It seems to me like numerical integration at least should already be taught with spreadsheets, as part of math classes -- but I don't know if it is or isn't.
[edit] It looks like from post #35 that you did indeed intend those to be part of the consolidated math classes. So did I read you wrong or are we still 1 class short, consolidating from 3 to 2?

Ah, ok. I saw OP and assumed thread OP. My b.

 

[gmax137]

A point that seems to be lost on a lot of people posting here is that they're not like the typical student in many important respects when it comes to learning math. Math probably came fairly easily to them, and they found it interesting enough so when they got stuck, they'd stick to it and figure out the problem. Most people aren't like that. When a student struggles with algebra, it's easy to write it off as the student being lazy, unmotivated, or not hard-working enough. That's simplistic at best.

I think the difference between "training" and "education" is precisely this: education shows you that you can learn anything if you want to and keep at it.

 

[XZ923]

I think the difference between "training" and "education" is precisely this: education shows you that you can learn anything if you want to and keep at it.

You're kidding right? No one "can learn anything". Everyone has different aptitudes. Ask Stephen Hawking to compose a symphony or Mozart to do quantum physics (if he wasn't dead and all...)

 

[XZ923]

The attitude in the US toward math is a big part of the problem, but colleges and universities can't do much to change that except on a case-by-case basis. They have to deal with the students they get. Some students come into classes with a debilitating fear of math. You don't hear the same thing about, say, English classes.

I'm sorry, but this is ridiculous. This sort of "let the inmates run the asylum" attitude is what is resulting in college administrators kowtowing to students who have no respect for authority. As for a "debilitating fear of math", even if I stipulate to that, it's well established that desensitization through exposure is an excellent way to overcome a fear.

In regard to English classes, if you read the Pew study I cited, you'll see that while our students are indeed doing better in reading scores than math, we're still middle of the pack. So even in your cherry-picked example, our students are still only mediocre when compared to others around the world.

 

[PhotonSSBM]

I feel like some healthy conversation is happening here, but let me highlight something some in the discussion seem to not understand: CC's are not meant to be like universities, or high school, or anything else. They are their own thing with similar but different goals about educating.

Many of the students who come into CC do not have high school diplomas. They often have GEDs. And even those who did go through high school probably, as many have pointed out, been left behind by the system and thrown into society without any real education. Many more CC students have been so far removed from education for years and simply don't have the same time to pursue an education in a traditional way. I tutored one woman who was 30, had a child, and worked as a Nurse's Aide while she was learning. These people, often impoverished, are the customers of these schools. I understand that there are those here who believe people like her shouldn't pursue an education in anything but a full on traditional way, but those of you who do should realize that people in her situation are the reason CC's exist in the first place.

So what is the goal of a typical CC (other than making money)? It's to educate those people nobody else will take, and give them a gateway to a better life by teaching them skills that will, hopefully, get them employed with a higher salary than McDonald's. What California has decided, and many others across the country have been thinking for a long time is that Intermediate Algebra does not further that goal in many cases, and is an additional hurdle that many students in these living situations find impossible. So, naturally, the questions are raised: Should we require it to graduate? Does it add more value to our degrees than a simple class in programming or something else? Is it wise to mandate it when it's presence forces most of our students who are here on taxpayer money out of their education? Why aren't two courses in math adequate as opposed to three?

This are questions I came here to hear opinions on. There's a lot of good talk here on how students can learn math, the value of the class in question (especially Dr. Courtney), and other cool points. But as vela pointed out, a lot of you seem to be missing the bulk of these questions, which just so happen to be the questions that drove California to this decision. Russ has been the only one with a decisive opinion on this.

So why don't we take a breath and address these questions more directly?

 

[gmax137]

You're kidding right? No one "can learn anything". Everyone has different aptitudes. Ask Stephen Hawking to compose a symphony or Mozart to do quantum physics (if he wasn't dead and all...)

So, you think college algebra is somewhere between a Mozart symphony and Hawking's quantum mechanics?

I did think your point about subjective reality was good.

 

[Vanadium 50]

So what is the goal of a typical CC (other than making money)? It's to educate those people nobody else will take

I don't think I agree. California (the system in question) crows about how wonderful its community college to CSU/UCal transfer program is.

I also don't see how a student can get a GED and still be deficient in arithmetic. Didn't they just pass a test on it?

 

[symbolipoint]

Dr. Courtney's analogy with weight training is great:

Why does an athlete need to lift weights if he does not compete in the weight lifting sports? Because strong muscles are better than weak muscles for lots of sports other than weight lifting.

The math class is the weight room for the mind. A strong mind is better than a weak mind for lots of thinking that does not directly use algebra. Higher education is about training the mind to think.

Every profession has some combination of three fa...

Just so great.

 

[symbolipoint]

I don't think I agree. California (the system in question) crows about how wonderful its community college to CSU/UCal transfer program is.

I also don't see how a student can get a GED and still be deficient in arithmetic. Didn't they just pass a test on it?

Your estimation about the GED test does not work well. GED does not require two years of college prep math of the high school level. It does not even require a full 1-year course on beginners' algebra. The Math portion of the GED tests DOES include some algebra, along with basic topics of common measures, geometry, and reading graphs, and basic arithmetic. Once the persons finish and pass the GED tests, their Math knowledge slowly goes away - unless they choose to refresh it. There are the rare people who do actually take a full year of beginning algebra as part of preparation for GED testing. THEY may do better with their Algebra, and may keep their skills longer. Most just want to avoid any Math as much as possible.

 

[vela]

[rereads] Nope. Not seeing it in there. Please quote what the OP says it should be replaced with.

I propose this, condensing the requirements down for general degrees to one general education style class that covers arithmetic for basic accounting, reading and following plots (not creating them), how those plots can be abused to manipulate statistics, and incorporate how to use all of this in a spreadsheet to manage finances. I honestly believe these are the core things we should be teaching everyone in math, and going beyond this should be an option, not a mandate.

 

[Vanadium 50]

Your estimation about the GED test does not work well.

Your message was about algebra. I can understand how a student can squeak through a GED deficient in algebra. I don't understand how they can squeak through deficient in arithmetic.

 

[XZ923]

So, you think college algebra is somewhere between a Mozart symphony and Hawking's quantum mechanics?

I did think your point about subjective reality was good.

Of course not. College algebra may be the topic of the thread but the post I quoted didn't mention it, it simply said:

education shows you that you can learn anything if you want to and keep at it.

It was the broad statement of "anyone can learn anything" I was objecting to. I was using the two points to illustrate that even the most brilliant people still have specific aptitudes and abilities.

However, to bring the topic back around to the original of college algebra, I do think it's a necessary component in the vast majority of fields for reasons I've stated earlier in this thread

 

[PhotonSSBM]

Your message was about algebra. I can understand how a student can squeak through a GED deficient in algebra. I don't understand how they can squeak through deficient in arithmetic.

Imagine you got a GED, now imagine you waited 5-10 years after you got that GED to go to college. That's a very common story in CC's.

I don't think I agree. California (the system in question) crows about how wonderful its community college to CSU/UCal transfer program is.

I also don't see how a student can get a GED and still be deficient in arithmetic. Didn't they just pass a test on it?

Transfers in my school aren't as common as Cali. I think of the thousands of students we have only a handful make it to a 4 year school. I need to look up numbers for that though.

Also they're not mutually exclusive ideas. I was one of those students nobody wanted and am now doing research in Astrophysics.

 

[symbolipoint]

Your message was about algebra. I can understand how a student can squeak through a GED deficient in algebra. I don't understand how they can squeak through deficient in arithmetic.

That makes sense. A student too deficient in Basic Arithmetic very likely does not succeed in the GED test. At least any student who takes and passes GED who then goes on to a community college will still have the chance to improve in their Math at the C.C. He should be able to relearn or learn better his Airthmetic (through course work), and then move on successfully through Algebra 1 and Algebra 2. If not pass the level of Algebra 2 ("intermediate"), then this is the result of lacking effort by the student.

 

[Auto-Didact]

Again: please specify what you would replace algebra with!

So then what do you propose? Should we just eliminate it and decide later what to replace it with, in the meantime just reducing the education provided?

Graph theory, formal logic, geometry, cryptography, group theory, category theory and information theory are some very useful and much more concrete options than algebra that immediately come to mind. I can't immediately see why these could not entirely replace elementary algebra or some mathematical subjects that are traditionally taught, given that these subjects are presented in a pedagogical manner at a more elementary level than the respective university level courses, by an actual expert, preferably one who is capable of integrating these theories in some subject which interests students and/or is generally useful or practical.

This was mentioned earlier I believe, but it should wholly be possible to replace algebra with some other subject if the goal is to demonstrate a proficiency in exact reasoning; being skilled in pure abstraction is not a necessity for mathematics nor should it be a gateway test for entry into all other forms of mathematics. Unfortunately for the majority of people, the current situation practically excludes them from becoming exposed to other forms of mathematics if they fail some non-obvious prerequisite. I believe during the 60s this was tried to some extent (unsuccesfully) in the New Math programme.

I also want to reiterate the point someone else made of motivation in knowing what something is good for instead of trying to solve some abstract problem i.e. the way in which math is often presented. For example, I learned Calculus 3 prior to learning Electromagnetism; for me, this made some of the concepts and theorems somewhat bizarre, unintuitive and the subject itself increasingly dull. After just a bit exposure to Electromagnetism however, pretty much everything in Calc 3 immediately became crystal clear and not only the most intuitive thing ever, but perhaps far more importantly, extremely enjoyable. For me, this intuition and enjoyment only increased more and more during exposure to Electrodynamics and Hydrodynamics.

Lastly, this all actually is part of a larger, unrecognised, dare I say forgotten problem in STEM and education today, namely that in principle, there seem to be different kinds of mathematical thinkers, i.e. one may naturally be more inclined to think geometrically, while another thinks analytically, another algebraically and again another logically. Of the great mathematicians of the 20th century, both Jacques Hadamard and Henri Poincaré wrote brilliantly on this subject, in respectively 'An Essay on the Psychology of Invention in the Mathematical Field' and 'The Foundation of Science'.

Obviously, everything I am proposing here would require legions of mathematicians going into primary/secondary education and/or a complete restructuring of what it means to be a math teacher. There also should not be some dominant school which dictates by elitist fiat what is absolutely necessary and important for everyone to learn in mathematics; diversity in thinking is not only natural, it is useful. Trying to weed it out, by making mathematics a sterile exercise only to be carried out in the way envisioned by some aristocratic group of overly zealous tradition-bound purists living in ivory towers, severely takes away a lot of the fun and exploration of personal mathematical exploration and discovery for the masses.

There is a democratic revolution in mathematics still waiting to happen here. I firmly believe however the possible benefits definitely outweigh the other option, namely our current situation where the large majority of people not only aren't proficient at any kind of math but openly loath all things mathematics and often wear this loathfulness and ignorance as a badge, while being at a disadvantage in life. I will end on a more positive note, by quoting Grothendieck:

"In those critical years I learned how to be alone. [But even] this formulation doesn't really capture my meaning. I didn't, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these three years of work in isolation [1945–1948], when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law...By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lycée and at the university, that one shouldn't bother worrying about what was really meant when using a term like "volume," which was "obviously self-evident," "generally known," "unproblematic," etc...It is in this gesture of "going beyond," to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one—it is in this solitary act that one finds true creativity. All others things follow as a matter of course.

Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group, who were much more brilliant, much more "gifted" than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone."

 

[Mike Bergen]

CC's and VoTech's train people to make a living. Lots of people need that these days.

Not only CCs and CTE ( no longer VoTech) NEED Algebra as well as Physics to do our job well
HVAC uses "all that stuff": heat transfer, fluid flow and much more to make your AC work this summer

Perhaps that is the real answer with teaching Math etal,question. The students don't see where they need or will use this "stuff" Perhaps if we were to show them that the Scientist lead the way with the general theories then the Engineers APPLY the Science, the Techs like myself APPLY the Engineering. they will understand that their homes or automobiles or any thing else they NEED is based in the Physics world. we then would not have questions like this one that suggest that "They Don't Need That Math/ Science

Just a thought. Mike

 

[StoneTemplePython]

As someone who has lived in California for a good bit, I found this thread interesting.

I have a pragmatic side that says if they were doing away with intermediate algebra so that non-STEM students could instead basically learn (1) the math behind Paulos's Innumeracy, (2) re-visit dimensional analysis (which they should have learned in a Chemistry or Physics course but may not have?) and (3) also the spreadsheet exercises mentioned earlier... that would probably be ok?

I would like to think that holders of Associates Degrees are at least somewhat capable of evaluating evidence on a jury (reference Prosecutor's Fallacy) and evaluating the implications of signing up for a large mortgage. These seem like basic civic considerations (esp. mortgages over the last 10 years). That said, plenty of highly paid, highly credentialed people flunk one or both of these things, so maybe not.

Of course my actual preferred approach is not on the roadmap of how large governmental policies work -- in cases where what's 'best' isn't clear it's generally smart to randomize and run experiments in small doses and track results, then make the 'big' decision some time later (say 5 or 10 years from now) once there is evidence to inform your decision. Instead in politics, it's abrupt scalable changes all at once, and people tend to evaluate complicated things based on affect heuristic or some other form of attribute substitution. Such is life.

 

[StudentOfScience]

Obviously, everything I am proposing here would require legions of mathematicians going into primary/secondary education and/or a complete restructuring of what it means to be a math teacher.

You bring up an interesting point. One of the main points argued in Lockhart's A Mathematician's Lament (https://www.maa.org/external_archive/devlin/LockhartsLament.pdf) is the inadequacy of mathematics education nowadays. The nature of the essay is from a 'purist' perspective of mathematics; that is, real-life application is simply a by-product of mathematics, and mathematics is the elegant study - even art - of patterns. Essentially this is the misconception in today's (well, at least in the US) educational system. Reworking the system so that it portrays the true nature of mathematics: a subject in its own right independent of its real-life applications. I would think this would help in decreasing the number of people debating on whether or not to take elementary algebra. Classes of this sort are more often than not computational and obscure the point of mathematics. So, it's not really math!

However, the above is a long-term solution. Now for the short term, current situation. The issue concerns itself whether or not non-STEM majors striving for an Associate's need to take elementary algebra. Let us step back and ask ourselves the goal(s) of such a course. Teaching real life applications? Well, it's a far stretch to see arithmetic and algebraic manipulation in everyday life. Most of this math is a prerequisite for the intuition needed for later, more advanced courses in math that may be used in, say, physics courses.

For instance, suppose we have person X, and they've taken calculus and classical mechanics. Now, you may apply that knowledge more freely to the real world than, say, the fundamental theorem of algebra. You can analyze various systems (in principle, usually the equations of motion are not solvable analytically). But we are restricted to elementary algebra, it seems, so our range of applications is not as large. Of course, this is not to say this is not applicable at all, as Mark44's answer indicates.

Is the goal of such a course to introduce the student to logical thinking? It seems that 'elementary algebra' teaches mechanical processes more than careful reasoning and deduction. If this was the goal, we may be better off teaching some set theory geared for the non-mathematician.

Of course, I'm not saying elementary algebra is all bad, but perhaps a rework in its curriculum (or replacement with another course which may not even be in the realm of mathematics) could help in focusing the Associate student's education to a particular need, i.e. logical reasoning. It was also mentioned earlier that a course discussing elementary statistics and how they can be manipulated by advertisers to their benefit could work. This seems like an interesting idea.

Disclaimer: I'm a math enthusiast, so I'm a bit biased

 

[symbolipoint]

Why complain about a requirement of A.A. degree for Intermediate Algebra? Good to study and know and have a sense of where it all goes, sure. But why the complaining? GRADES and RESTRICTIONS ON COURSE REPETITIONS. Maybe this is the bigger, hidden problem!

 

[Auto-Didact]

You bring up an interesting point. One of the main points argued in Lockhart's A Mathematician's Lament (https://www.maa.org/external_archive/devlin/LockhartsLament.pdf) is the inadequacy of mathematics education nowadays. The nature of the essay is from a 'purist' perspective of mathematics; that is, real-life application is simply a by-product of mathematics, and mathematics is the elegant study - even art - of patterns. Essentially this is the misconception in today's (well, at least in the US) educational system. Reworking the system so that it portrays the true nature of mathematics: a subject in its own right independent of its real-life applications. I would think this would help in decreasing the number of people debating on whether or not to take elementary algebra. Classes of this sort are more often than not computational and obscure the point of mathematics. So, it's not really math!

Thanks for the link, will check this out.

However, the above is a long-term solution. Now for the short term, current situation. The issue concerns itself whether or not non-STEM majors striving for an Associate's need to take elementary algebra. Let us step back and ask ourselves the goal(s) of such a course. Teaching real life applications? Well, it's a far stretch to see arithmetic and algebraic manipulation in everyday life. Most of this math is a prerequisite for the intuition needed for later, more advanced courses in math that may be used in, say, physics courses.

For instance, suppose we have person X, and they've taken calculus and classical mechanics. Now, you may apply that knowledge more freely to the real world than, say, the fundamental theorem of algebra. You can analyze various systems (in principle, usually the equations of motion are not solvable analytically). But we are restricted to elementary algebra, it seems, so our range of applications is not as large. Of course, this is not to say this is not applicable at all, as Mark44's answer indicates.

Of course all that goes without saying for the student of physics and other STEM. Person X who wants to go on and study math or physics seems to be a different kind of animal than the typical person selected at random from the population, probably even falling one or two standard deviations outside of being an average Joe. I think it is pretty obvious a system of learning or education generally should not be structured around catering to the needs of this minority percentage instead of to the needs of the large majority. The fact that this majority generally has different tastes, motivations, goals and interest should be of paramount importance when presenting them with something as important for them as mathematical reasoning.

People often seem to be bewildered by the fact that other objective and abstract matters like correct grammar and spelling are seen by most people as something that is somewhat or largely important while math outside of arithmetic generally is not; the reason for this I believe is obvious: people quickly come to realize and therefore understand why adhering to grammar is important both for and to them and for and to society, they have put up this goal to be attained for themselves for whatever reasons; in the case of mathematics this kind of personal realization unfortunately seldom occurs, and without this understanding and the setting of goals is impossible.

Because of the above I believe it is important to realize that sometimes it may be better to teach a concrete theory before treating the abstraction thereof, because this may be both more interesting and/or more fun for a larger part of the learners as well as more useful and applicable. For example, Calc 3 historically did not come before EM, but literally the other way around, it is an abstraction of EM. This causes much of the math to be laced with many characteristics and qualities of classical ED, such as being most naturally formulated orthogonally in R^3. If one wanted to use Calc 3 on some other subject than EM in order to analyze that system, one would not automatically know or realize what is mathematically necessary and what of Calc 3 is actually just EM/physics baggage. A case could even be made that perhaps for those not wanting or needing to learn EM, but more generally applied analysis, it may be more fruitful to skip Calc 3 altogether and directly teach them the exterior calculus and theory of differential forms.

Is the goal of such a course to introduce the student to logical thinking? It seems that 'elementary algebra' teaches mechanical processes more than careful reasoning and deduction. If this was the goal, we may be better off teaching some set theory geared for the non-mathematician.

Of course, I'm not saying elementary algebra is all bad, but perhaps a rework in its curriculum (or replacement with another course which may not even be in the realm of mathematics) could help in focusing the Associate student's education to a particular need, i.e. logical reasoning. It was also mentioned earlier that a course discussing elementary statistics and how they can be manipulated by advertisers to their benefit could work. This seems like an interesting idea.

Disclaimer: I'm a math enthusiast, so I'm a bit biased

I think set theory for the non-mathematician would be a great idea as well, even today one would be hard pressed to meet someone outside of math who knows any set theory. The fact of the matter is that these theories are all interesting and important in their own right; as I said before one should not decide beforehand for others what they need to know about mathematics, the choice should be theirs. Obviously choosing such things at a young age is difficult but I believe not impossible, definitely not if exposed to many of these subjects early on in perhaps a playful, lucid but most importantly pedagogically coherent manner, instead of in some arcane compulsive academic formulation.

 

[Dr. Courtney]

The question in the OP is equivalent to, "Should the math requirements in college be lower than the college prep math requirements in most high schools?"

It is also equivalent to, "Just because many high schools are dumbing down math education, should colleges dumb it down also?"

In light of this, it is surprising to find so many shills for the further dumbing down of math education in the US. What next? Remove Algebra 1 and Algebra 2 from the high school college prep sequences? Remove algebra from the ACT because it is a barrier to student success? Stop worrying about all the math teachers passing students in high school algebra courses who are nowhere near proficient? Stop including so many problems that require real high school algebra skills in introductory physics courses?