Should Algebra Be Required At Community Colleges?

[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?

 

[PhotonSSBM]

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?

What do you propose as a solution to the problem if not replacing intermediate algebra with something else to, as you suggested, work out the mind? Or do you believe these numbers for CC graduation/transfer rates to be sustainable/acceptable?

 

[Auto-Didact]

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?

I feel again this is unnecessarily far too confrontational a view, focusing again largely on the luxury problem that without algebra one is handicapping students to properly be able to do our most beloved subject, instead of focusing on the larger societal problem, namely that there needs to be an alternative way of dealing with the situation that most people do not want or feel they need algebra in life per se, a position which the educational system acknowledges to some extent, but one which they seem to be incapable of meeting head on by adequately offering to teach other mathematical subjects instead.

It goes without saying but most people do not plan to nor enter into STEM, let alone specifically physics or mathematics. If one does not plan on entering into STEM or one of the practical sciences (mostly public servants such as health care and CSI) there is a case to be made that mastery of elementary algebra is not an essential skill in life. Empirical research has shown well and above that most people are actually capable of getting by fine in life without it. Hell, there are even a substantial amount of people who aren't able to read yet still are able to get by in life, sometimes even fully unnoticed by others (NB: contrary to popular opinion this requires some considerable reasoning skills).

Research has also shown that both mathematicians and non-mathematicians naturally tend to be more proficient at some particular mathematical field or point of view, instead of generally being 'mathematically strong or weak'. This is obvious really: having a knack for say tensor calculus says absolutely nothing about having an a priori knack for set theory as well. The fact that we act otherwise today is because we confound the entire question by artificially making it only possible for a select few to learn these skills and then stare ourselves blind on them.

The select few are of course those capable of passing the traditional teaching strategy, while anyone else regardless of their natural skills aren't even considered. The select few tend to be called mathematicians, but the point here to take away is exactly one need not be a mathematician to be able to do some mathematics, and the existence of physics as a separate field of study and of physicists with their own particular flavor of mathematics is the perfect example of this. There is therefore a case to be made that perhaps elementary algebra could perhaps be replaced with some other mathematical subject, and if deemed absolutely necessary down the road, be developed from the point of view of this other perspective or just learned later down the road, just as how we tend to teach these other subjects to a select few much later down the road.

This would first and foremost likely exacerbate any naturally occurring differences in different mathematical skill sets among children; one is for example no longer broadly labeled as 'mathematically weak' if one happens to be shown at the same time to be very skilled at say logic or graph theory. The chances that one has no mathematical strengths at all is of course a possibility albeit a somewhat unlikely one; this would most likely be indicative of a learning error, teaching error or perhaps both. Moreover, I severely doubt this would significantly decrease the number of applicants to STEM or mathematics specifically, and I'd even wager that it might actually increase the number of applicants to interdisciplinary fields with unexplored but strong mathematical overtones which are at the present moment still in their infancy stages.

This really is a behavioral hypothesis to be tested in practice of how things actually are, not merely philosophised about in regard to some ideal fantasy of how we would like things to be. Any further questions of the utility of teaching such widely varying skill sets to different people and the possible effects thereof on future science, mathematics and society remain open questions which can only be answered by carrying out large controlled educational trials and comparing different teaching strategies with respect to different goals. In any case, it should be patently clear that a 'one size fits all' approach is far from the optimal strategy to adhere to when teaching elementary mathematics, especially when the consequences of this are so dire for all levels of society.

 

[Dr. Courtney]

What do you propose as a solution to the problem if not replacing intermediate algebra with something else to, as you suggested, work out the mind? Or do you believe these numbers for CC graduation/transfer rates to be sustainable/acceptable?

Your errant assumption is that most of those who do not become proficient in algebra can't become proficient in algebra. Having taught high school algebra, college algebra, and algebra-based physics (high school and college), my observation is that most students willing to make an honest effort at the homework every day, CAN become proficient in algebra. I've seen this personally from high schools in the rural south to community college in the midwest. If you let student's claim they "can't" and provide alternate pathways, they won't. Take away the alternate pathways, and suddenly most are able to do it when they DECIDE to work hard enough.

And for those who either cannot or will not become proficient in the algebra that is universally required on college prep tracks in US high schools, their pathways should then be limited to education and career options that do not require college degrees. As soon as you get serious about saying, "Your college dreams are over unless you learn algebra" most students who truly aspire to college will learn algebra. The battle is one of the will, not of the abilities.

 

[PhotonSSBM]

Your errant assumption is that most of those who do not become proficient in algebra can't become proficient in algebra. Having taught high school algebra, college algebra, and algebra-based physics (high school and college), my observation is that most students willing to make an honest effort at the homework every day, CAN become proficient in algebra. I've seen this personally from high schools in the rural south to community college in the midwest. If you let student's claim they "can't" and provide alternate pathways, they won't. Take away the alternate pathways, and suddenly most are able to do it when they DECIDE to work hard enough.

And for those who either cannot or will not become proficient in the algebra that is universally required on college prep tracks in US high schools, their pathways should then be limited to education and career options that do not require college degrees. As soon as you get serious about saying, "Your college dreams are over unless you learn algebra" most students who truly aspire to college will learn algebra. The battle is one of the will, not of the abilities.

It's very good to hear that your experiences have led you to the conclusions in your first paragraph. Honestly, I was truly hoping that someone who taught at various levels of mathematics in the past would post here.

I do feel as though everything you said is true, and have for the course of the thread. My teaching experiences have led me to the same conclusions with respect to ability and willpower. But at the end of the day, I always go back to the numbers of my school and others that encouraged me to make this thread. So many fail, and so many give up, all because of math. We're already at a place where alternate pathways are non-existent. You have to learn algebra or drop out, and that drives the vast majority of CC students to failure (again, 72% for the school I tutored at).

Perhaps I'm giving these numbers more credit than they deserve. Maybe they are acceptable in some way. I'm just having a hard time rationalizing them and finding them acceptable. Which is one reason I made the thread. I can see that you do not believe there is a problem from the perspective of a student, but what would you say to a school with these issues. You've taught for decades. If California's CC system came to you and asked, "How do we fix this?" What would you tell them?

 

[Dr. Courtney]

If California's CC system came to you and asked, "How do we fix this?" What would you tell them?

Prosecute the high school teachers who pass these students in Algebra 1 and Algebra 2 for fraud and corruption. Put them in jail as the criminals they are: collecting their paychecks, not doing their job, and passing the students on to downstream situations where they will have a much harder time succeeding.

 

[Haelfix]

I just finished tutoring my fiance the entirety of middle school and high school math, which she hadn't practiced for a decade. As a student, bright as she may be, she was singularly unsuited for the subject and had all the usual red flags (fear of failure, predilection for putting of the hard work, desire to memorize instead of understanding etc). I of course would not let her do any of those things, and drilled her pretty harshly in the way that teachers refuse to do anymore in the US.

It wasn't pleasant for her, but in the end she just aced her university entrance exams and would have likely scored well on an advanced placement test for calculus. The whole exercise took 5 months, and about 2 hours a day.

The point is it really isn't that difficult, and I firmly believe that almost anyone can do it if they're instructed properly. We used to not allow students to get away with failure, and there is absolutely no reason why anything should have changed. Indeed if anything it's tremendously easier to learn new things in the Information Age . The only failure I can see is in the will of the instructors, and those administrators who contemplate ridiculous measures like the above.

 

[bhobba]

I live in Queensland Australia and thought I would give my perspective based on that.

We do it a bit differently here. Where I am is undergoing a bit of a change so I will describe how it was when I went through - it will be slightly different in future to bring us in line with the the other states of Australia.

First we start grade 1 at 5 - not 6 and finish grade 12 at 17 (the change underway is to start at 5.5 and finish at 17.5 ie increase it by 6 months).

We combine your algebra and geometry into one subject done over two years in grade 7 and 8 - but since we start a year earlier that would be your grade 6 and 7 in what you call middle school. We then do a combined algebra 2 and some pre-calculus in grade 9 and 10, but some private schools stop at grade 9 ie when you finish middle school. Also some of the better students are accelerated and finish then to start on calculus. This is to maximize year 11 and 12 results by doing it over 3 years instead of 2 while the better students do university math in year 12 ie at 16 years of age. In 11 and 12 we do a combined pre-calculus and calculus either as one subject (equivalent to you calculus AB) or as two subject equivalent to your BC plus a few extra things like beginning linear algebra, beginning Markov chins, some mechanics etc etc. Then at 17 they go to university, but since they have done what you in the US do in first year uni its only 3 year degrees here - we start with multi-variable calculus, differential equations etc first year. The best students do that in year 12 so they start on our second year math subjects when they go to uni at 17

So from our experience here we would say - what - middle school students do algebra here and calculus in the age group of your high school students. I, and I suspect most people here would be shaking their heads - you guys need a different more rigorous system - you should have well and truly finished with algebra by community college level - you should be doing calculus - and advanced calculus at that.

Now is calculus required to get a degree here? There is a big debate about that out here right now. It used to be required for most degrees because common subjects like Economics required it, but they have now dumbed it down so its now not necessary. Such a pity.

Guys over there in the US - wake up to yourself - finish algebra and geometry in your middle school and do pre-calculus and calculus at HS. Community college is not the place for it.

Thanks
Bill

 

[symbolipoint]

Should Algebra be required for A.A. Degree from Community Colleges?
Yes. AT LEAST through Intermediate Algebra.
Why? Basic finance, common citizen & consumer knowledge such as Richter Scale (a measure of earthquales), more assured understanding of linear interpolation, momentary cost-purchase budgeting, constant rates applications (which often form either linear equations or quadratic equations); too many other examples which other members may discuss.

 

[cristo]

Guys over there in the US - wake up to yourself - finish algebra and geometry in your middle school and do pre-calculus and calculus at HS. Community college is not the place for it.

I think it's important to keep in mind the mission statement of a community college. As opposed to a four year university, a community college aims to provide affordable education for anyone who seeks it. The student body is diverse, and does not only include students fresh out of high school, but also older students who perhaps dropped out of high school, or who the public school system failed. It includes parents, perhaps single parents who were unable to complete their schooling but are wanting to return to obtain an education. So to say to "wake up" is really missing the main point of a community college.

So the community college has a diverse student body, which can be essentially split into traditional and non-traditional students. The former are looking to get a jump on their four year degree at a lower price, while the latter are looking for education that they should have got at an earlier age, but for whatever reason life prevented that. Having both sets funneled through the same algebra sequence is, in my opinion, a problem. How to fix this problem is, of course, a non-trivial question.

 

[bhobba]

or who the public school system failed.

Yes - that's a big problem here as well.

We have a school taking an entirely different approach because of it with very good results:
https://tc.vic.edu.au/

Everyone is on an individual learning plan. You leave when you are ready and its total flexible learning. No university entrance - they have arrangements with universities that you go when they think you are ready - that may be 15 or 20 - it doesn't matter - it's when you are ready:
http://www.theage.com.au/victoria/school-dumps-cutthroat-vce-ranking-20160226-gn4gk0.html

Here in Aus HS starts grade 7 - some start university entrance type subjects right from the start and leave in 3-4 years. Others take longer thn the usual 6 years - while others never go, instead doing what's called TAFE (that's equivalent to your Community College) and prepare for trades, shop assistants etc - you know ordinary everyday jobs you don't need a university degree for but of course in some cases like being an electrician it won't hurt. My father was a qualified electrician and had an engineering degree (the reason why is a bit complex to do with silly regulations that have since gone away requiring to do any work on stuff with voltages greater than some voltage you need to be a qualified electrician - engineers were not considered qualified electricians)

They actually bypass grade 7 and go straight to grade 8. Most have no issues and when finished have done the equivalent of your geometry and algebra. From that point on they do what they feel like. You cannot progress from that grade (called it's foundation year) until you have passed it. Some are so good they skip it by passing subjects more advanced than grade 8 while some need 2 or 3 years to do it - but everyone must do it and pass it - it's not negotiable. You can't leave that school until you have mastered the basics and algebra, correctly, is considered a basic. Sure they may only rarely use it if they want to be say a pharmacy assistant, which they can study for there, but algebra teaches you sound thinking practices of breaking a problem into chunks you can write equations for as well as some pretty basic financial things they will surely use later eg understanding why if you take out long loans you end up paying much much more than short term ones.

To me its much more rational approach than trying to correct these deficiencies at what you call CC and we call TAFE - in fact TAFE is integrated into HS for those that want that path.

Thanks
Bill

 

[vela]

I live in Queensland Australia and thought I would give my perspective based on that.

I'm curious. A major part of the problem in the US is the public's attitude toward math. Here it's acceptable to fail, and people will often brag about their inability to do math. Do you face the same attitudes in Australia?

 

[bhobba]

I'm curious. A major part of the problem in the US is the public's attitude toward math. Here it's acceptable to fail, and people will often brag about their inability to do math. Do you face the same attitudes in Australia?

Most definitely not.

Everyone here knows its importance.

The only issue is taking advanced math in 11 and 12 ie calculus. That is falling dramatically because, as I said, common subjects even liberal arts students take, most notably economics, no longer requires calculus as a prerequisite. This means people tend to opt out - why - well its perceived as hard - but failing it when its compulsory in grades 1-10 is very frowned upon. They are trying to do something about it by giving bonus points in university entrance if you take it. Its not required, for example, in medicine, but unless you take it its doubtful without the bonus points you will have a high enough entrance score to get in.

That is for parents that actually care about education - as you probably know many don't regardless if its math, English, science or pretty much anything - that's a much bigger problem.

Thanks
Bill

 

[jfmcghee]

Prosecute the high school teachers who pass these students in Algebra 1 and Algebra 2 for fraud and corruption. Put them in jail as the criminals they are: collecting their paychecks, not doing their job, and passing the students on to downstream situations where they will have a much harder time succeeding.

It seems to me that this falls on the administration and government at least as much as on the negligent teachers. At my school it's not even up to the teachers if the student moves on, it's up to the score the student makes on the state required test. Of course then if the student doesn't pass they get endless opportunities to try again or even take a different, "equivalent" test, just so graduation rates stay acceptable. I'd lose my mind if I had to teach math. We lost half of our math department last year. It's no wonder lots of students go to post-secondary school with completely inadequate math preparation.

 

[Dr. Courtney]

It seems to me that this falls on the administration and government at least as much as on the negligent teachers. At my school it's not even up to the teachers if the student moves on, it's up to the score the student makes on the state required test. Of course then if the student doesn't pass they get endless opportunities to try again or even take a different, "equivalent" test, just so graduation rates stay acceptable. I'd lose my mind if I had to teach math. We lost half of our math department last year. It's no wonder lots of students go to post-secondary school with completely inadequate math preparation.

Then the power to fail students needs to be given back to the teachers, so that specific individuals can be held accountable if students are passed who are not proficient in the material.

 

[jfmcghee]

The teachers unions would sure try to stop that from happening. I still don't have a contract for the last school year because our bargaining unit can't do it's job, but if something like holding individual teachers accountable were to be proposed you can be sure they'd find a way to crush it. They also don't want to reward individual teachers for doing a good job, it has to be for everybody. I think this whole "let's treat everyone the same, let's not punish or reward anybody"- from the students all the way up speaks directly to the problem of the OP. The solution is simply to change the culture of the U.S. No big deal...