Should Community Colleges Abolish Algebra?
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Instead of removing Algebra, we need to consider better ways to teach this subject to people who do not have a lot of the fundamentals in place already. One of the biggest problems with College Algebra is that it assumes a certain level of math literacy that isn't universal. Algebra simply isn't that hard of a subject to master, but it is something that requires a different sort of teaching strategy than is used at the average community college.
Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. We can go from zero to FOIL, and quadratic to partial fraction decomposition in that amount of time. The key is to listen and to instill a level of confidence as early as possible in this process. Many adults consider math to be "hard" -- not from the perspective of it actually being hard, which it is -- but from the perspective of "this is too hard for me to do, because I'm not a math person." Break this mental block, and anyone can do algebra.
If you get a $1,000 loan at 1% interest each month, how much will you owe in 1 year?
You can buy a phone for $500 or pay Verizon $16.70 / month for 36 months. Which is cheaper?
Pe = nRT is actually the first thing taught in calc 1.
Slightly off topic as I don't think this is college level algebra, in supermarkets in Europe they are required by law to put the "€/liter" price in small on the side, so you can compare easily. In the US it doesn't seem mandatory, or at least the unit is not mandatory because sometimes they use fl oz, sometimes gallons, or for pieces of meat sometimes oz, sometimes lbs, so when you want to compare the prices of 2 similar items, what would just take you 0.5 sec in Europe takes you much longer in the US since you need to add unit conversion in the mix. For example here your "cases" could be of different sizes, that 1 case of water could be 2L ,while those 3 cases could be a gallon each...
Yeah, and then you get aggregate price in "€/package", except that packages are of different size.
As for compound interest, you need WAY more than algebra ...
All of these are literally the sorts of things you'd find on homework assignments and final exams in a community college algebra course... You do need algebra, and don't realize how difficult this "trivial" algebra is for some students because you can do it without even realizing you're doing it.
I mean, there will be some FOIL and quadratic equation examples as well. And a bunch of stuff in-between like identifying graphs of functions.
But CC Algebra is super bimodal, so it's probably not the case that students are nailing these word problems and only failing with the other stuff.
An item at the store is listed for $4.99 each, but under a promotion, the item is buy two, get one free. What is the net cost of each item?
If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop?
I have a 20 foot ladder. It is leaning against a wall such that the tip of the ladder is touching the top of the wall. The distance between the bottom of the ladder to the bottom of the wall measures 10 feet. What is the height of the wall?
You and three office mates decide to purchase fast food for lunch. Each of you order the same item, and your three office mates give you $10 each. The cashier rings up $35.17 as the total. How much change do you owe each of your office mates?
You are traveling by bus and wish to estimate your time of arrival. You notice that it takes one minute and 25 seconds for the bus to travel from one mile marker to the next. Your destination is fifty miles away. Assuming the bus stays at the same speed, how long until you reach your destination?
If these seem contrived, then consider that just about every college educated adult, at one time or another, will need to know his or her way around a spreadsheet. Even basic spreadsheet formulas make little sense unless one can reason algebraically. Just trying to learn how to use a spreadsheet program without understanding algebra is a painful process.
Q: If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop?
A: This can only be answered experimentally for a given car, tire condition & road condition, but a rough estimate would be to apply the square law naively, giving an answer of 80 feet, but of course that's very approximate. The only correct answer that can be given is "more than 40 feet".
That is the power of Algebra, and it is something that all adults should possess.
I used to believe this until I actually tried. Maybe they lied about how much studying they really did, but I've seen people putting in many hours a week and still unable to grasp the basics of algebra. I think many of us have never really been exposed to the thinking power of people at the bottom 10-20% (IQs below 80-87) , they weren't in our classes in high school. And now these people are going to college.
Different teaching techniques are required for different students. For the students at the upper edge of the curve, the homework assignments and lectures are more than enough. For the students near the middle of the curve, some additional exercises and confidence building may be required. For students near the bottom of the curve, it will be necessary to break problems into parts and reinforce smaller parts before building back up to the overall problems. These students must be taught how to break problems into discrete steps, and a lot of emphasis needs to be placed in teaching them how to recognize the patterns. Mnemonics, rhymes, and other catchy phrases can help to reinforce both the pattern recognition and the execution of steps.
Bear in mind that we can teach computers to perform algebra. There is a heuristic involved. This heuristic can be memorized by anyone who can memorize a bible verse, a song, or a poem. You would be surprised what someone with a low IQ can do when time is spent to organize a heuristic in terms that this person can memorize, and enough time is spent to reinforce both this learning and the confidence of this individual.
Well, teaching _motivated_ students is easy and fun. The question is, though, what about the semi-motivated students and do either still understand algebra after they are done with you and in their next class?
I feel like this is equivalent to saying "if you are a STEM major, why even study writing?" I do some technical writing for work, but absolutely none of the kind of writing I did in my college writing classes. Would anyone, especially a non-STEM major, care to make an argument that the two cases are different?
Understanding compound interest at a minimum probably provides an immense benefit to those it keeps from making bad assumptions about taking on and getting out of debt.
A financial planning course, on the other hand, would be immensely valuable. People should be forced to take that, not algebra. Knowing how to save money on tax returns, how to calculate a budget, software to manage it all... If school is being used for job training, then I wish it would train that.
Of course since the argument can't be practical, ie you will use this someday which you won't, opponents talk about the importance of a liberal arts education and being well rounded.
No one should be forced to take such a useless course. Learn algebra and all the non-ephemeral aspects of basic financial planning comes basically for free.
> Knowing how to save money on tax returns
Talk about ephemeral knowledge!
> how to calculate a budget
...is literally the first example used in a lot of college algebra courses.
We're not talking about "strong" math skills. IME most kids who will go on to take AP Calculus mastered at least half of the material covered in a CC Algebra course before even starting high school.
> People are far more likely to benefit economically from strong communication skills than strong math skills
I'm not entirely sure this is true in many local economies. Especially outside of cities, communication isn't as important as competency in skills/trades. And a lot of those skills/trades require a functional understanding of elementary mathematical objects -- understanding ratios, functions, some useful trig properties, and the ability to follow complicated directions (algorithms) precisely are all basic core competencies for most trades.
The article is probably correct -- we could stand to have alternatives to the standard CC algebra course. But an effectively similar level of quantitative skill is required for most trades. And no amount of "pretty talkin'" will prep you for, e.g., CNC machining.
Which trades are you referring to? Truck driving? Retail? Cashiers? Secretaries? Managers, sales reps, school teachers, janitors, waiters, cooks, customer service, freight laborers, stock clerks, maids, receptionists, construction laborers, child care workers, grounds maintenance?
None of those require a wit of algebra. Yet they represent tens of millions of jobs.
It's not good to divorce ourselves too far from the reality of most normal peoples' lives.
None of those are skills (except maybe truck driving). And none of them require a CC degree. Those are all things you do with a GED or less.
I'm thinking of the sorts of things people go to CC for. Dental Hygiene, Paramedics, EMTs, Morgue work, Respiratory therapists et al, various medical diagnostic technicians, vet techs, nursing, CNC, Engineering technicians, etc. Visit your local CC website and look through their programs of study.
> Managers
Depends. Engineering? Construction? Absolutely.
Again, we're not talk about groups and rings. We're talking about stuff like knowing the difference between x and x^2.
> sales reps ... customer service
Outside of cities there are a lot fewer sales jobs... and a lot of them require BA/BS just because they can.
> school teachers
STEM teachers need a LOT more than just CC algebra. At least Calculus. The algebra taught in CC's was once taught in high school, but is now often taught in middle school. Middle school science curricula have kept pace. So, yes, any STEM teacher -- even at the elementary level these days -- needs to know basic algebra.
> janitors, waiters, cooks
Not skills and/or don't require CC, and so irrelevant to this conversation.
> freight laborers, stock clerks, maids, receptionists, construction laborers, child care workers, grounds maintenance?
Again, not skills, and for the most part don't require CC.
It's sobering to see all of the job types listed out like that though, isn't it? Our combined lists represent most peoples' options. Kind of strange to think about.
I think we'll have to agree to disagree that morgue keepers or dental hygienicists benefit from even a little bit of algebra, though.
To re-iterate, most of the jobs you listed do not require a Community College degree!
Whether a truck driver or store clerk needs algebra is utterly irrelevant. People doing those jobs are not required to have -- and usually do not have -- community college degrees. Their needs are irrelevant in a discussion about community college curricula.
Regarding my examples, I'm not "seeing what sticks". I'm literally just listing what are pretty much uniformly the most popular programs at most community colleges. Again, look up enrollment and funding statistics for some of your local CC's.
> dental hygienicists
Again, I think you're over-estimating the difficulty of the material that students need to master in order to pass community college algebra.
As I said in my original post:
>>> The article is probably correct -- we could stand to have alternatives to the standard CC algebra course. But an effectively similar level of quantitative skill is required for most trades.
I think that's spot on for dental hygenists. They absolutely have to understand ratios, for example, and that's one major stumbling block for CC Algebra students.
So do they need CC Algebra? Maybe, maybe not. But IMO a course covering only the portions they do absolutely need is going to be just as much a stumbling block for these students.
I don't think STEM majors should have to take writing courses nor non-stem majors take math courses.
This should not be done in University but earlier. I'm skeptical that forcing these two categories of students take these courses make them effective with in the subject matter or a more enlightened person as the excuse goes.
IMO it is a way to keep professors who teach unneccessary coursework employed.
I wonder how many engineers get hired for their writing ability?
In fact I bet a college educated engineer or at least one who went to college writes well enough as to not interfere with their work.
If you want regular promotions, probably watch your spelling too.
I sincerely wish that this was the norm, but my experience has been that, on average, people with the word "engineer" in their degree can't be bothered with such piddling details as spelling and grammar.
The ability to express ideas, concepts and procedures in writing is a fundamental skill for any professional.
We're not talking about teaching everyone Calculus or Group Theory. We're talking about making sure everyone knows what they should've learned in their middle and high school algebra course.
"Real" math is also about those things, but it's typically not presented that way until it's too late.
"It is also the single most failed course in community colleges across the country".
The author is saying that a lot of people that don't need algebra end up failing it, so if we remove it from their curricula we'll raise graduation rates. That's the end goal.
Not as many people fail writing courses, so there's no need to remove those courses as they're not a barrier to graduating.
This is what's wrong with our education system. Who cares if anyone is actually learning anything, get those useless metrics up!
Employers seem to disagree with you about the usefulness of that metric.
When being able to get a job depends more on what piece of paper you have than what knowledge you have, that is no longer a useless metric.
Students and colleges are responding rationally to what the employers are demanding.
Of course, once they made "college degree" a proxy, everybody on the production side responded correctly and reduced into to its core essence as you said: "pay for this piece of paper and who cares about quality since an interview won't test me anyway".
If it actually mattered, the most rational action is for employers to either 1) interview people without college degrees or 2) train people without college degrees. The fact that neither of these is occurring tells me that the employers aren't really that bothered by the current situation.
If we wanted to raise graduation rates, we could just hand out degrees after two weeks and no exams.
I'm not agreeing with the author, but that's what the author is saying.
FWIW: I have a "Bachelors of Science In Liberal Arts & Sciences" from math.illinois.edu and enjoyed the human sexuality, critical theory, etc courses I took in addition to the math courses.
I have a sneaking suspicion there'd be a revolt if all humanities students had to pass MATH 347[1] to graduate.
However, if I had to pick one mathematical subject everyone should learn, it wouldn't be algebra, it would be statistics.
Plug into SPSS/etc -> p-value calculated -> result = ifelse(p<0.05, success/trueTheory, failure/falseTheory)
This isn't algebra in the "groups and rings" sense, it's algebra in the "use the quadratic equation", "is this a graph of x or x^2 or x^3?", "FOIL" sense. Think middle school or early high school.
It's basically impossible to do any statistics past a bit of hand waving if your students can't identify the difference between a graph of x and a graph of x^2...
The article says, "Their thinking has led to initiatives like Community College Pathways, which strays away from abstract algebra to engage students in real-world math applications."
My interpretation of this is that the article authors are math illiterate enough not to know that "abstract algebra" is thing.
How sad to think that some people think that community college intermediate algebra is so abstract that people can't get it.
I agree, but I don't think more motivation is a bad thing. I hated math (even as an engineer) despite being good at it until I was a junior in college. I got interested in high-level math when I saw what some PhD students were doing for research and that inspired me to dig deeper. Now I appreciate math just for the beauty of it. I wish I had this appreciation in high school, but some people just need a good answer for "why?"
One day, I explained to him that in algebra, X was basically the exact same thing as the empty space in math problems and it made it easier to move it around. Instead of 2+2=_ you could put the "space" anywhere and it was more readable.
He had a fit. He realized had been doing algebra in his head for years to, for example, infer how much damage a particular attack did in a video game. And here books made it sound hard and alien and didn't explain it worth shit.
Maybe colleges need to up their game. Because Algebra really isn't that hard, but a lot of math is just terribly explained and, then, instead of blaming the materials or the professor, we act like the students are just dumb. Which sucks so very much.
It's really funny how helpful the "_" or "cloud" trick is for kids. Even high school kids in AP Calculus find it helpful.
There is a "hump" where "_" vs. "x" doesn't seem to help much, e.g. where we start working with polynomials as more abstract things and so on. I think the right approach there is to make a lot more use of computer algebra.
The point is "here's a generic tool that's useful in lots of specific circumstances", but students get lost during hours of practicing the "useless generic tool" before seeing why that general tool is useful. Computer algebra systems can help there.
I think a lot of people who aren't inclined towards math just don't get it because it's taught the wrong way.
I didn't learn this until well after I graduated from college.
I remember using this argument a lot when I was a smart-aleck kid, that what should I care about Algebra, because when the heck am I going to use it. It feels like total bunk looking back at it now. I just hadn't seen or appreciated math as something worthwhile in its own right, regardless of application. I maintained that view until I got into more advanced math classes in college. For example the being shown the Cauchy–Schwarz inequality in Linear Algebra for the first time, that was just a total 'Ah-ha!' moment of joy. I really doubt I'd have that impression of that moment if the professor had been trying to demonstrate the immediate, concrete utility of that proof at the same time.
I'm not really sure how one can reliably relay onto others the fun in math for its own sake, but it's there. It feels like a cop out to say a particular type of math needs to serve a purpose 'in the real world' instead of just being worthwhile intrinsically, as a fundamental part of reasoning.
I then signed up for the Army and spent 4 years not doing much math. When I got out and went to sign up for community college, I actually had to take the placement test twice to get a high enough score to skip retaking the exact kind of algebra course talked about in this article.
In it he discusses how it is largely mythical that most jobs require knowing anything more than basic arithmetic (and even the need for basic arithmetic is not as solid as most assume). For most that do actually require some math it can usually be taught on the job.
Does this mean we should stop widespread teaching of anything beyond basic arithmetic? No. He concludes that what teaching mathematics really does is teach us how to reason. Sure, you have to learn reasoning in other subjects, such as economics or philosophy or physics, but in all of those the reasoning is either about things that have a large component of opinion, or involve a lot of extra real world factual baggage. With mathematics we get to see reasoning in a more pure context, letting us focus on and better learn to understand and use logic.
Maybe you don't need math. But if you can't pass the course, there may be other serious problems.
It's easy enough to keep pushing kids/adults forward by redefining success in other subjects. Extra credit, dubious essay standards, grade inflation, etc. We need math to keep the system honest.
Most classes in community college have been dumbed down so much that anyone can pass them by showing up and doing mediocre on a few multiple choice tests. You can just memorize a few definitions and get through without learning anything.
I've been programming for 10 years now, and I'm pretty damn good at it if I do say so myself.
I'm not advocating dropping algebra, but your statement is a bit sensationalist.
I guess they'll never know...
But I do kind of question if it's really a good use of everyone's time to learn algebra. For computer science and engineering I can sort of see why you'd want that, but I'll be honest: even in computer science I think most people don't need it. Even when I'm doing algebraic work, it's rarely stuff I learned in a math class. Trig and calculus come more in handy, but unfortunately my day job of writing backend servers does not fundamentally benefit from this. I think many of us could say this.
That's not to say there aren't other benefits of studying mathematics, but if it's really not working then I can see why people are just calling to make it optional. No point in making people suffer through apparently ineffective education.
There are things taught in it (and in other courses of general math) that probably don't need to be—long division comes to mind—but there are some pretty fundamental mental concepts that I'd hate for people to lack.
Ok - I guess it depends on what they include in an algebra course. Here is an intermediate algebra course outline (pdf warning):
https://www.ccsf.edu/dam/Organizational_Assets/Department/Ma...
It goes beyond the basics but certainly should be passable by any ordinary person who works at it. This is one of the major things that a degree (any degree) should indicate : this person can work through learning new things. Removing this makes the degree less valuable.
Something is wrong with a system that make you "learn" information irrelevant to your own life.
You don't "Identify key features of and sketch graphs" when e.g. planning an expensive purchase or reading the news?
No business owner is going to survive if they don't understand how to solve a system of equations (aka figure out feasible pricing before losing all their money). Although we are on a tech VC's news site, so I stand corrected ;-)
Being an informed citizen capable of taking care of yourself does require most of the things taught in middle/high school algebra. (Which are the same exact things taught in CC algebra.) A surprising amount of financial suffering is self-imposed by people who can't or won't do very basic math.
Intermediate algebra isn't particularly difficult but requires a moderate level of attention. It's a basic skill expected to exist for many common career paths, including many in community college. If majorities of students cannot hack that, perhaps they aren't prepared to commit to a meaningful education.
No bigotry of low expectations at play here, none at all.
Not only do I think everyone should be able to understand basic algebra, they should understand basic statistics and probabilities (which is pretty hard to understand without algebra).
These days, not only do people not understand math, but we use numbers and statistics to lie to people and mislead their decision making. Now we seem to just be making it easier to mislead them.
Here is a short printable tutorial for anyone interested: https://minireference.com/static/tutorials/sympy_tutorial.pd...
It's not merely asking, "should we remove algebra requirements from non-STEM degree programs?".
It's asking, "should we remove algebra (courses) from the institution altogether?"
I do a lot of that and the statistics requirements are obvious. I'm having less success identifying the algebra.
Backend or frontend, if you use any quantitative metrics in your year-end performance evals, then some algebra is going to be helpful!
And you never know what will come up. I was once contracted by a regional government to write some code to correct hourly sensor readings (water levels in wells) based on a monthly manual human reading (ground truth). When it was done my boss remarked, "oh, this is just a linear transformation."
And, to be fair, that's probably a GOOD idea. A standard algebra course is a lousy math course if you aren't going any further.
Schools used to have a course that was "shop math" aka how to do the things you might have to do in construction, machining, etc. This included elements of algebra, geometry, trig, and statistics. It was a much better match for people who were not going forward to more theoretical math or science.
One of the community colleges near me has quite a good nursing program. How much "algebra" will they need vs. procedures for medication dosage calculation? "Algebra" has a lot of dead ends for practical use.
A great example is "How do you divide by a fraction?"--a fairly routine algebraic manipulation. Yet, I can't even think of when I have had a real world situation where I had to "divide by a fraction". Multiply by a fraction? Sure. Divide by a whole number? Sure. Calculate a percentage? Sure. Divide by a fraction? Ummmmm.
I would argue that algebra is both too advanced in many places AND too sketchy in others. Geometry is something that people need and don't get because it is after algebra that they fail. The worst part is that a lot of people have better geometric intuition than mathematical and would do better to have geometry first.
Should they have a math course? Yes. Should it be the pedagogical algebra? Not as obvious.
I'm not opposed to that idea in the abstract, but what other math courses are they suggesting?
I'd imagine for a lot of students in community college they care more about getting a job than they do about learning for learnings sake.
Seems reasonable to me.