Should Algebra Be Required At Community Colleges?

[brainpushups]

From what I heard on the radio last week my understanding is that the proposal is to replace the requirement of algebra with a different mathematics course that is more 'practical.'

This gets right to the heart of the question. The answer is because what mathematics teaches us about logical thinking.

If this is indeed the reason for requiring all students to take math (seems reasonable to me) then what California should do is come up with a clear set of standards about logical reasoning, advertise which courses allow students to demonstrate their level mastery in these standards, and allow students to pick the course. Students could perhaps opt for a course in propositional logic, philosophy, or rhetoric to meet the requirement. If quantitative reasoning is part of what is valued then a math or science course is probably inescapable. Why not allow a student to use a geometry course as evidence of logical reasoning instead? Of course, many of the courses would likely need an overhaul in pedagogy based on

Unfortunately, [insert any course name here] can also be "practiced" to a limited degree with very little thought. If a student simply learns "When you see this sort of problem, you execute these steps to solve it," that has little or no value. But if the student learns to think about what he is doing, why this leads to the solution, then we have the value of algebra for the non-technical student.

 

[symbolipoint]

You forgot probably the biggest; the other side of the coin from #1: high schools aren't preparing students.

What? When you go to a car dealership, do you say "Here is a big bag of money, just give me any car you feel like giving me."? Why are you suggesting that here? No, I certainly did not go to college in order to get a worthless piece of paper. De-valuing it will make the problem(worhless college educations) worse, not better.

In either case, you are wrong about the business model: colleges don't get paid for graduating students, they get paid for enrolling them.

Make it harder to enter college and make it harder to graduate high school (and advance at every level).

From what I heard on the radio last week my understanding is that the proposal is to replace the requirement of algebra with a different mathematics course that is more 'practical.'
If this is indeed the reason for requiring all students to take math (seems reasonable to me) then what California should do is come up with a clear set of standards about logical reasoning, advertise which courses allow students to demonstrate their level mastery in these standards, and allow students to pick the course. Students could perhaps opt for a course in propositional logic, philosophy, or rhetoric to meet the requirement. If quantitative reasoning is part of what is valued then a math or science course is probably inescapable. Why not allow a student to use a geometry course as evidence of logical reasoning instead? Of course, many of the courses would likely need an overhaul in pedagogy based on

Some often ask the question, why is Algebra difficult, and also the question, why are students failing algebra 1?
Those asking or others, should also ask, why did those students who did succeed in Algebra 1, do so?

 

[PhotonSSBM]

You forgot probably the biggest; the other side of the coin from #1: high schools aren't preparing students.

I agree and discussed this earlier, but this is a problem that CC's have to address now, as I'll show next.

What? When you go to a car dealership, do you say "Here is a big bag of money, just give me any car you feel like giving me."? Why are you suggesting that here? No, I certainly did not go to college in order to get a worthless piece of paper. De-valuing it will make the problem(worhless college educations) worse, not better.

In either case, you are wrong about the business model: colleges don't get paid for graduating students, they get paid for enrolling them.

That's not what I'm saying or suggesting in either statement here. You keep assuming I want to get rid of Intermediate Algebra without adding something back. I made this point earlier, but apparently you didn't feel the need to read it, or you disagree with it but didn't feel like addressing it.

I am not wrong about the business model. You completely missed the point, which is that people will stop enrolling if failures and dropouts continue to go unabated, and federal grants will no longer be issued to those school if they can't graduate more students.

Make it harder to enter college and make it harder to graduate high school (and advance at every level).

I have to think about this more before I agree or disagree with it.

 

[PhotonSSBM]

The table in there shows at that college, MATH 108 is Intermediate Algebra at that school.

Correct, I don't think I suggested anything to the contrary.

 

[PhotonSSBM]

It's pretty basic stuff, and they want to cut it from the requirement? Our country is already stagnating as it is. Technology is rapidly improving and society simply needs to get smarter to keep up. The days of simple tasks are more or less coming to an end. So the rational thing to do is to improve education and skills as much as possible, not keep cutting standards.

I see your point, but nobody is suggesting that intermediate algebra not be offered to students, just that it shouldn't be mandatory. AND that we should replace the unnecessary portions of the class with practical skills. As I said earlier, learning how to code a spreadsheet is way more practical AND marketable than being able to factor a fourth degree polynomial.

 

[PhotonSSBM]

Some often ask the question, why is Algebra difficult, and also the question, why are students failing algebra 1?
Those asking or others, should also ask, why did those students who did succeed in Algebra 1, do so?

This is why we opened a tutoring center at our school specifically for math, where I worked for two years. People who took to those tutoring sessions were much more likely to pass with a C in a course. It was ours, and I assume, California's initial response to the problem. But with thousands of students, all of whom have to take the classes, it's almost impossible to help everyone. But you are absolutely right, and this IS the mentality successful students in these courses have.

 

[FallenApple]

I see your point, but nobody is suggesting that intermediate algebra not be offered to students, just that it shouldn't be mandatory. AND that we should replace the unnecessary portions of the class with practical skills. As I said earlier, learning how to code a spreadsheet is way more practical AND marketable than being able to factor a fourth degree polynomial.

How is someone supposed to write code if they don't know how to move x's and y's around? Maybe the math courses needs to be restructured a bit, but it should stay. Often a mathematical relation is determined on paper before putting it into a program. What is practical is higher level thinking( logic, deduction, mathematical relations etc) which is becoming more and more important these days. In the future, people will not be asked to do simple tasks such copy and paste manually across cells in spreadsheets, or data entry. They will need to actually tell the spreadsheets what to do, which follows mathematical logic.

 

[symbolipoint]

I see your point, but nobody is suggesting that intermediate algebra not be offered to students, just that it shouldn't be mandatory. AND that we should replace the unnecessary portions of the class with practical skills. As I said earlier, learning how to code a spreadsheet is way more practical AND marketable than being able to factor a fourth degree polynomial.

Makes one wonder: He can create a spreadsheet to do something with numbers, but can he think? (Maybe he can think, but factoring a fourth-degree polynomial before the invention of spreadsheets was possible).

 

[russ_watters]

That's not what I'm saying or suggesting in either statement here. You keep assuming I want to get rid of Intermediate Algebra without adding something back. I made this point earlier, but apparently you didn't feel the need to read it, or you disagree with it but didn't feel like addressing it.

No, I'm aware you want to switch it out for something else, but you can't get around your own reason for the suggestion: algebra is too hard. You only ask "do we need it" after declaring its too hard and should be gotten rid of. It doesn't even enable entertaining the opposite possibility: maybe we should require more math?

You completely missed the point, which is that people will stop enrolling if failures and dropouts continue to go unabated...

Maybe they should! I'm most certainly not missing it: That's the outcome I'm arguing for!

 

[symbolipoint]

How is someone supposed to write code if they don't know how to move x's and y's around? Maybe the math courses needs to be restructured a bit, but it should stay. Often a mathematical relation is determined on paper before putting it into a program. What is practical is higher level thinking( logic, deduction, mathematical relations etc) which is becoming more and more important these days. In the future, people will not be asked to do simple tasks such copy and paste manually across cells in spreadsheets, or data entry. They will need to actually tell the spreadsheets what to do, which follows mathematical logic.

What PhotonSSBM tried to say was, creating the spreadsheet to help factorize the polynomial, or for finding "roots" is easier (for those who have learned Spreadsheets well enough) than using other methods, such as pencil & paper, or writing a program in C or Fortran or Python or BASIC or whatever.

 

[PhotonSSBM]

How is someone supposed to write code if they don't know how to move x's and y's around? Often a mathematical relation is determined on paper before putting it into a program. What is practical is higher level think which is becoming more and more important these days. In the future, people will not be asked to do simple tasks such copy and paste manually across cells in spreadsheets, or data entry. They will need to actually tell the spreadsheets what to do, which follows mathematical logic.

You'd be surprised what someone who's taken College Algebra is capable of, and what someone who's taken Intermediate Algebra is not. I believe you, like others, overvalue what is being taught in the class. And I will have to disagree that it requires more than college algebra to be able to work a spreadsheet from my experience in tutoring our CS courses involving excel.

 

[FallenApple]

You'd be surprised what someone who's taken College Algebra is capable of, and what someone who's taken Intermediate Algebra is not. I believe you, like others, overvalue what is being taught in the class. And I will have to disagree that it requires more than college algebra to be able to work a spreadsheet from my experience in tutoring our CS courses involving excel.

Depends on the topic. For example, finance often uses spreadsheets and finance itself involves formulas that are often polynomials or exponentials. That simply needs to be coded in if they want to get the answers.

 

[PhotonSSBM]

No, I'm aware you want to switch it out for something else, but you can't get around your own reason for the suggestion: algebra is too hard. You only ask "do we need it" after declaring its too hard and should be gotten rid of. It doesn't even enable entertaining the opposite possibility: maybe we should require more math?

Maybe they should! I'm most certainly not missing it: That's the outcome I'm arguing for!

Now we're getting somewhere. I am curious then, not in a passive aggressive way, how you see the role of education. And if you believe that the role of education is to be highly competitive and difficult to achieve, what do you suggest that low skill workers do to gain the skills to move up the ladder of society?

 

[PhotonSSBM]

What PhotonSSBM tried to say was, creating the spreadsheet to help factorize the polynomial, or for finding "roots" is easier (for those who have learned Spreadsheets well enough) than using other methods, such as pencil & paper, or writing a program in C or Fortran or Python or BASIC or whatever.

I actually wasn't, but that is a good point :)

 

[FallenApple]

What PhotonSSBM tried to say was, creating the spreadsheet to help factorize the polynomial, or for finding "roots" is easier (for those who have learned Spreadsheets well enough) than using other methods, such as pencil & paper, or writing a program in C or Fortran or Python or BASIC or whatever.

My idea is more general. Many applications, more often than not, require formulas. To get the answer to various aspects of the problem, the formula needs to be changed around. So that requires some thinking and a bit of pencil work beforehand. Finance, physics, engineering, computer science. All those fields require some symbolic manipulation of mathematical ideas before placing it into a finalized code. This is because programs can't be pre built to handle every situation. A simplified example is this: Say there's a program that gives kinetic energy as the output and mass and speed as the input. If my job requires that I get the speed as the output using mass and kinetic energy as the input, then I need to do the math first on paper to see the functional relationship, then go into the code and tweak it around a bit. So just knowing algebra helps.

I remember working on a personal project and had to do a considerable amount of algebra before reaching the final expression, of which I didn't know how to solve for the roots analytically. It didn't matter, I just looked up Newton-Raplhson code, pasted it and plugged in the formula, changing the symbols around. The key point was that I needed to do algebra the whole way though, even re-modifying someone else's code required that I know exactly what each part does so that I can taylor it to my specific problem, which basically most problems are, specific problems.

 

[russ_watters]

Now we're getting somewhere. I am curious then, not in a passive aggressive way, how you see the role of education.

With no irony/coyness intended: the goal of education is to educate people.

And if you believe that the role of education is to be highly competitive and difficult to achieve...

Being difficult is not a role or a goal on its own except insofar as in order to be worth something, it has to require some effort. You have to accomplish something in order for the reward to be meaningful.

...what do you suggest that low skill workers do to gain the skills to move up the ladder of society?

Get an education and/or acquire more skill. I'm not being coy here by repeating your questions back to you as declarative statements: to me the answers really are that self evident. The government has a responsibility to probide a quality education. The students have a responsibility to make the most of it. If one of those groups (or both) is failing, it is up to them to fix it. The issue could not be any more straightforward.

[Edit] I'm reminded of a quote from Starship Troopers: "Something given has no value." It means that if you deem something to be too difficult and start giving it out for free, it becomes valueless. So that isn't a strategy that gets you around the problem of not enough people achieving it.

 

[PhotonSSBM]

With no irony/coyness intended: the goal of education is to educate people.

Being difficult is not a role or a goal on its own except insofar as in order to be worth something, it has to require some effort. You have to accomplish something in order for the reward to be meaningful.

Get an education and/or acquire more skill. I'm not being coy here by repeating your questions back to you as declarative statements: to me the answers really are that self evident. The government has a responsibility to probide a quality education. The students have a responsibility to make the most of it. If one of those groups (or both) is failing, it is up to them to fix it. The issue could not be any more straightforward.

[Edit] I'm reminded of a quote from Starship Troopers: "Something given has no value." It means that if you deem something to be too difficult and start giving it out for free, it becomes valueless. So that isn't a strategy that gets you around the problem of not enough people achieving it.

I think we agree when it comes to that quote and it's meaning. However, again, I would like to emphasize that whatever value you seem to perceive as being taken away by reducing the math requirement, can easily be amended and then some with more pragmatic skills being added as a graduation requirement. So imo there's no net loss if it's done correctly. When you look at the success rates of students in classes, every other class, even physics, has a lower rate of failure than mathematics by a wide margin. And graduation rates are, on average, around 30%. I don't believe these numbers are acceptable or sustainable for the schools or the students.

So based on your second point above, who do you believe to be at fault for these numbers: the schools/government, or the students? And whatever your answer, what would you suggest community colleges do to change these numbers? Or do you find the numbers acceptable and suggest they admit fewer students?

 

[symbolipoint]

I think we agree when it comes to that quote and it's meaning. However, again, I would like to emphasize that whatever value you seem to perceive as being taken away by reducing the math requirement, can easily be amended and then some with more pragmatic skills being added as a graduation requirement. So imo there's no net loss if it's done correctly. When you look at the success rates of students in classes, every other class, even physics, has a lower rate of failure than mathematics by a wide margin. And graduation rates are, on average, around 30%. I don't believe these numbers are acceptable or sustainable for the schools or the students.

So based on your second point above, who do you believe to be at fault for these numbers: the schools/government, or the students? And whatever your answer, what would you suggest community colleges do to change these numbers? Or do you find the numbers acceptable and suggest they admit fewer students?

How then did the successful Algebra students do it?

When you try to look for what parts of Mathematics to remove and what ways to replace them with what're practical, you need to look at too many different kinds of students in too many different fields. This cannot be neat. What we should have right now, is Basic Elementary Algebra, Intermediate Algebra, and for so many students at CCs still, College Algebra. Nobody knows who will choose which major field, and nobody knows exactly which parts of Algebra anyone person will or will not need, so students must learn or study all the contents of Mathematics for their program.

 

[russ_watters]

However, again, I would like to emphasize that whatever value you seem to perceive as being taken away by reducing the math requirement, can easily be amended and then some with more pragmatic skills being added as a graduation requirement.

Such as? Caveat: You've already lost me by getting rid of algebra and not history or gym, so I'm not sure there is an answer that will satisfy me, but I'd still like to hear it.

So imo there's no net loss if it's done correctly.

IMO, basic algebra is an essential skill of minimally functional people. So losing it is a major loss.

So based on your second point above, who do you believe to be at fault for these numbers: the schools/government, or the students?

Both, but primarily the students (and their parents).

And whatever your answer, what would you suggest community colleges do to change these numbers? Or do you find the numbers acceptable and suggest they admit fewer students?

I suggest they admit fewer students.

 

[Dr. Courtney]

Now you're starting to get to the heart of the matter. I looked at the AA/AS requirements and also the graduation requirements for California high schools. In English and Math they are the same: one course post-HS. So what's the problem? Probably that the high schools looked the other way when their students didn't really know Algebra I and graduated them anyway.

Exactly right.

If a student enters CC without knowing arithmetic, the K-12 system has failed. They have taken someone who didn't know the material and kicked the can down the road to the next station in the chain, most likely several times. I mean we're talking junior high material being still unlearned for someone who wants to start college. Yipes!

I agree this is a problem. I disagree the solution is to do the same thing as what got us into this mess: relax the requirements and kick the can further down the road.

Exactly right.

You forgot probably the biggest; the other side of the coin from #1: high schools aren't preparing students.

In either case, you are wrong about the business model: colleges don't get paid for graduating students, they get paid for enrolling them.

Make it harder to enter college and make it harder to graduate high school (and advance at every level).

Exactly right.

I don't really care what California does. I am not a citizen of California, and the decisions of their public colleges should be left to their citizens and the republican process by which they are governed.

I would recommend we cease ALL federal financial aid for colleges that do not require algebra for their college degrees, and I would hate to see the state where I reside or where my children attend college stop requiring algebra for degrees.

Here's why:

Since all high schools require algebra for their college preparatory course sequences, failing to require algebra in college is essentially requiring less math to graduate for college than they are requiring in their college prep sequences. It is giving tacit permission to all those high schools who are passing students in Algebra 1 and Algebra 2 to award credit in those high school courses for students who are nowhere near proficient in those subjects. The message is "Don't worry about preparing students for college, we'll just lower our standards to accommodate the quality of students we get."

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 factors that create the value of that profession: working with the hands and strength (manual labor), putting oneself at risk for the good of others (military and police), and solving problems with one's mind. The smaller one's ability to solve problems with one's mind, the more one's livelihood will have to depend on manual labor and/or putting oneself at risk. Math through college algebra greatly enhances and strengthens the ability to solve problems with one's mind, even if one never puts pencil to paper.

 

[gmax137]

How then did the successful Algebra students do it?

I think this is a question that really needs to be answered.

How do you all square this thread, whose premise seems to be "too many kids flunking out" with this other thread whose point is "too many kids graduating for the positions available"?

 

[russ_watters]

How do you all square this thread, whose premise seems to be "too many kids flunking out" with this other thread whose point is "too many kids graduating for the positions available"?

Probably already evident from my posts, but I'll answer anyway: I believe both of those are true and place the blame on an over-emphasis on going to college. Too many people going to college results in both too many dropouts and too many graduates with de-valued degrees.

I don't drink much juice, so why waste my money buying a juice maker?

 

[XZ923]

IMHO, here's the best reason for keeping math: its status as an opposition to subjective reality. More and more we're seeing this idea pervade society (and no more so than in contemporary higher education) that reality is entirely subjective, that the way you interpret it and especially the way you feel about it is more important than actual reality itself. By "actual reality" I mean empirical, scientifically-provable data. In [fill in demographic category here] studies, sociology, philosophy, etc. programs students are being taught this idea of subjective reality, usually portrayed as "your/my truth" as opposed to "the truth". This whole concept teaches that reality must bend to the individual and not the other way around.

Enter mathematics, the counterpoint to all that I've described above. Math is either right, or it is wrong. To use Orwell's example, 2+2=5 is incorrect, no matter how you feel about it. As a general rule, across all disciplines, it is essential that we keep reminders of the difference between subjective and objective reality, and there's no better subject for this than math.

 

[CarlM]

Having had to deal with community college grads that come in and try to represent their education as being just as rigorous as a four year engineering degree I am definitely opposed to making their programs weaker. One of the biggest problems with community college programs is the overconfidence which a two year program instills. It is like the old saying "You cna always tell a sophomore but you can't tell him much." Community college grads come out as sophomores brimming with overconfidence. Introducing a little self doubt with a tiny bit of mathematics is a good thing. If they are not willing to work for the degree they do nto deserve it.

 

[vela]

Get an education and/or acquire more skill. I'm not being coy here by repeating your questions back to you as declarative statements: to me the answers really are that self evident. The government has a responsibility to probide a quality education. The students have a responsibility to make the most of it. If one of those groups (or both) is failing, it is up to them to fix it. The issue could not be any more straightforward.

Implicit in your viewpoint is that the schools are providing the right mix of courses. FallenApple is questioning that assumption, but you and others keep dancing around it or misrepresenting the issue.

 

[russ_watters]

Implicit in your viewpoint is that the schools are providing the right mix of courses. FallenApple is questioning that assumption, but you and others keep dancing around it or misrepresenting the issue.

I don't think either I or others have been unclear, but I'll say it again: IMO, algebra is a necessary course.

But as for who is responsible for what in the argument, maintaining the status quo is the easy, default position. It requires no justification. The side wanting to make the change needs to articulate what and why, and so far has not fully articulated what: he (nor anyone else) has not said what algebra should be replaced with that would make a positive change. So the argument is void and there is nothing to respond to yet...

...except that by not providing the other half of the recommendation, it makes it look to me like a red herring, with the true argument being what it looks like when you only include half; remove algebra because it is hard, not because it isn't useful.

 

[vela]

I don't think either I or others have been unclear, but I'll say it again: IMO, algebra is a necessary course.

Why? This is exactly the question posed that, again, you are avoiding. I don't think many here are arguing that being able to reason mathematically is a skill that should be omitted or removed from most degrees, but that's not the same as saying that everyone has to know the fundamental theorem of algebra otherwise their education is deficient.

 

[russ_watters]

Why? This is exactly the question posed that, again, you are avoiding.

Why does one have to justify the status quo? It is bad form to propose an hypothesis, refuse to justify it, and demand others prove it wrong lest it be declared valid by default! I'm pretty sure that is in our quality guidelines somewhere.

Nevertheless, irrespective of the attempted burden of proof shift, others have answered why it is useful:
1. People use it (even without realizing it).
2 It teaches you to think logically.

I don't think many here are arguing that being able to reason mathematically is a skill that should be omitted or removed from [some liberal arts] degrees, but that's not the same as saying that everyone has to know the fundamental theorem of algebra otherwise their education is deficient. [Goalpost shift removed]

Isn't it? How do you learn to think mathematically without learning math?

 

[vela]

Why does one have to justify the status quo?

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

It is bad form to propose an hypothesis, refuse to justify it, and demand others prove it wrong lest it be declared valid by default! I'm pretty sure that is in our quality guidelines somewhere.

Intermediate algebra is what's called a gatekeeper course. If students can't get past it, they're shut out of tons of opportunities. 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. There's the justification for questioning whether the intermediate algebra requirement, as it's presently constituted, is the right one.

Nevertheless, irrespective of the attempted burden of proof shift, others have answered why it is useful:
I would say
I think it's really
1. People use it (even without realizing it).
2 It teaches you to think logically.

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

Isn't it? How do you learn to think mathematically without learning math?

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

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.

 

[XZ923]

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

Yes, opportunities that require at least some math proficiency in order to perform correctly.

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

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.

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

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?

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.

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