Down with Algebra II!

[F.U.Shakespeare]

@Dangerosa

When I homeschooled my son, those were pretty much exactly the sorts of math problems Algebra had. They didn’t reach him. He can do them, but reading a graph someone else creates is easy - and he simply showed me how to Google relative values of cell phone plans. In his mind, he doesn’t need to do the math, he knows how to do the research to avoid the math.

@Dangerosa

I thought you were saying that it was worth pushing until indifferent math students had a breakthrough - either a talented teacher or the aha moment when math became the wondrous structure and incredible problem solving skill set math fans see.

Some background is in order.

In grade school, I enjoyed math. But when I got to junior high, the school didn’t have enough math teachers. So for grades seven and eight, we were warehoused and checked out ‘workbooks’ every day. If we didn’t disrupt, we got an “S” for satisfactory on our report cards. But no math instruction for two years. In ninth grade we were put in an algebra class taught by a good but demanding teacher. Most of us did poorly, and assumed that we weren’t capable of learning math. It wasn’t until I’d gotten interested (in my early 20’s) in electronics and wanted to study engineering that I gave math another crack. It was hard for a while, but I eventually succeeded.

I often reflect that I came very close to becoming an adult who assumed that I was ‘not a math person’. Would I as a result have ended up a bum, or a criminal? Probably not. But I shudder to think of career opportunities and accomplishments (not to mention enjoyment) that I would have missed out on.

Because of my experiences, I clearly carry a bias when I hear people describe themselves as incapable of doing math. I believe that many such people have been soured on the study and understanding of math by bad teachers (or, as in my case, badly run curricula). Such discouragements are cumulative - one bad one can turn a person off for life.

As I relate in post #63 upthread, I blame a lot of this on the ‘sink or swim’ attitude that schools took towards instruction when I was a kid (I’m 56).

Is everyone capable of doing math at the college level? Of course not. But not everyone is capable of college level work in any subject.

How can you tell whether you are actually capable of learning math? Well, one indication is if you’re smart at other academic subjects. Especially ones that involve logic and rules, like languages. I’ve met people who are whizzes at foreign languages who think that math requires some rare, savant-like ability. I tell them that I’d be just as clueless communicating in a language I hadn’t learned.

Many people who never learn math do quite well in life. Your son might well be one of them. Much professional work involves researching solutions of problems performed by others.

But if that’s all you do, you are relying a lot more on those others than if you’re able to check their work.

For most people who know math, it’s nothing more, or less, than a very useful skill.

[Dangerosa]

@Thudlow_Boink

Nope. (This may be true for some students, but it’s not what I was saying.)

My apologies for misinterpreting.

[Dangerosa]

@F.U.Shakespeare

Some background is in order.

My son is actually pretty good at math - he doesn’t LIKE it. He’s actually better natively at it than his sister - the one whose AP Calc headed - she struggles to understand - he is just bored and uninterested. (We had a similar issue with band and him - drove his band teacher crazy since he’d pick up instruments with no work, but didn’t enjoy band and never practiced to become exceptional - which he could have been). And, as I said upthread, he wants to be a pipefitter. He’ll need some math, but he won’t need the amount of math he ended up with. In fact, his trade school program has a required math course - it will be the topics he covered in eighth grade.

My issue is that I’ve tutored him (taught him for a year - Alg I and Geometry and then tutored him once he went back to public school) and his friends through Alg II. Applied math problems really don’t resonate with these kids - its still math - plus it adds the problem of translating English to Math - which a lot of these kids really struggle with. And for some of his friends, nothing was working. It wasn’t working when they spent Saturdays at my house, it wasn’t working when they visited the teacher for extra help, it wasn’t working when they were tutored through the volunteer efforts of a local engineering company, and it wasn’t working when their parents paid for Sylvan. Realistic examples didn’t help, different techniques didn’t help. But they had to pass to graduate. A bunch of them got Ps - for passing - after their parents intervened and negotiated the P with the school. (My kid got Cs and Ds, because he didn’t bother to do homework unless his parents hassled him, and didn’t bother to take any time on his tests because doing the math as fast as you can and staring at the wall is more interesting than doing well on a math test. Then, having the graduation requirement under his belt, we had to fight with the counselor to have him pulled from Pre-Calc - because “he needs four years of math.”)

Offering it is awesome. All schools should offer at least Calc and have a path that gets kids who want it Calc. I might have bothered to stay in high school if my school had advanced coursework (I graduated early - having run out of academic courses - and started college at sixteen - which created its own issues). Having Algebra II (and passing it) as a requirement to graduate is decreasing graduation rates - especially in poor and minority populations - for a skill set that many of them will never use. Not having a high school degree limits these kids in what their choices are - they weren’t ever going to go to a great college - but without the degree, they can’t even go to a trade school or community college. They can’t get most full time living wage jobs.

[jz78817]

@Ruken

I’ve been straying from the question of what should be taught as opposed to what is and can be. While I bristle at the notion that something routinely mastered by children is “advance math”, that doesn’t mean everyone should learn it. But I don’t really know what anyone * should* learn about any topic. I think that hinges on the purpose of secondary school, which I don’t see many agreeing on.

I interpret it as “math that the average person will rarely if ever use in their daily lives.” e.g. anything past basic arithmetic.

[Dangerosa]

I just stumbled across this in an article - it shows how varied graduation requirements are by state. My state has one diploma which is a CCR diploma (College/Career Readiness) and includes an Alg II requirement to graduate. If you got a Minnesota diploma, you should be ready for a college level English or Math course without needing remedial work - awesome if you are going to college. On the plus side, this level of rigor means that the graduating seniors who take the ACT tend to do pretty well - and most take it. The downside, the graduation requirements make it difficult to graduate if you are a below average kid.

The Truth Behind Your State's High School Graduation Rate

[Ruken]

@jz78817

I interpret it as “math that the average person will rarely if ever use in their daily lives.” e.g. anything past basic arithmetic.

I’m not sure how much of most high school topics the average person uses in their daily lives, which is why I’m aiming at what the purpose of high school is. There are plenty of broader skills. How to learn, communication, etc. But I have more trouble with individual classes.

[Ruken]

I wonder what math requirements other countries with very high graduation rates have. We had at least one poster weighing in from outside the U.S.

[P-man]

I’ve often wondered if people who have trouble with math also tend to have problems in other specific areas. I have two major problem areas. The first is mechanical reasoning/spatial relationships (I lump these two together because, in my mind at least, they are closely related). I can imagine there being a correlation here, but that’s conjecture on my part. The second, which I doubt has any correlation, is a total inability to tell if a woman is giving “I’m interested” signals. Since I’ve been happily married for almost 20 years that isn’t an issue anymore, but it was maddening in my teens and twenties. For example, I was visiting friends and they kept telling me someone was very interested. Even knowing it, I couldn’t tell. It was obvious to everyone else present. Obviously they were right, since we ended up nekkid.

[Thudlow_Boink]

@Ruken

I wonder what math requirements other countries with very high graduation rates have. We had at least one poster weighing in from outside the U.S.

So do I. For what it’s worth, I did find this PDF showing the math graduation requirements in the U.S. by state (including showing which states currently require Algebra II).

My own state, Illinois, does not currently require Algebra II but does require Algebra I. But I can assure you that substantial numbers of people are graduating from high school either never having really learned, or having completely forgotten, some of the very basics of algebra. My evidence for this is the large number of developmental math classes offered at non-selective colleges, and the (from what I’ve read and seen) increasing number of college students who need to take these classes because they’re woefully unprepared for college-level math.

And I’m afraid that if we say everybody has to pass Algebra II, that means it’ll be dumbed down (or otherwise mistaught) so that everyone can pass. I don’t think everyone should have to learn the content of Algebra II in high school, but I definitely think some kids should. And that’s one reason (among several) that I don’t think Algebra II should be a graduation requirement: for the sake of the kids who actually want or need to take it.

[Ruken]

@Thudlow_Boink

So do I. For what it’s worth, I did find this PDF showing the math graduation requirements in the U.S. by state (including showing which states currently require Algebra II).

I’ve searched around a bit, but I’m coming up dry.

[Martini_Enfield]

@F.U.Shakespeare

I give some examples in this post upthread.

I saw those but I’m not really sure they’re what I was getting at. Needing to work out distances for runners to catch up etc isn’t something I’ve had to do a lot of in my adult life, for example.

@Thudlow_Boink

This doesn’t make sense. The “basic arithmetic” is the part the calculators and computers can handle for us. The “higher math” is the part we still need to know how to do so that we can tell the calculators and computers what to do for us.

The point I’m making is that I don’t actually care what’s going on under the bonnet of a calculator when I ask it to solve an equation for me - to my mind, calculators were invented so we didn’t have to do all that complicated maths jiggery-pokery if we didn’t want to.

I have no trouble at all with basic arithmetic - I worked in retail for more than a decade so I can do addition subtraction, multiplication and division in my head without any problems. But as soon as things like algebra and calculus and trigonometry show up? Nope. Might as well be in Martian.

[Manila_Bay]

A national government-level technocrat or an economist should have a say on this matter. In a developed country, one’s who’s a major technology player, there has to be continuous development in basic skills. That’s one way to stay competitive. You won’t have a new generation of silicon valley moguls, or R&D wizards, if you allow your basic education infrastructure to deteriorate. My country used to be second in Asia. Now it’s close to being last.

[Dr.Strangelove]

@Martini_Enfield

The point I’m making is that I don’t actually care what’s going on under the bonnet of a calculator when I ask it to solve an equation for me - to my mind, calculators were invented so we didn’t have to do all that complicated maths jiggery-pokery if we didn’t want to.

Mathies don’t care about that either. But you still have to know what to punch into the calculator!

Say you’re building something. You know that a thingie (a ramp, or a support beam, or whatever) is 5 units long and makes a 25 degree angle with the horizontal. How far up and over is the end?

You need trigonometry for this. Your calculator has a bunch of trig buttons on it: sin, cos, tan, etc. No one computes that stuff by hand. Even hundreds of years ago, that was true. But without math, you have no idea which one to use.

Could you use a full-fledged 3D modeling program to give you the answer? Maybe, but that’s a heavyweight thing to bring out for a simple project. And without knowing some math, there’s no way to double-check your work, or even do a basic sanity check.

[F.U.Shakespeare]

People seem to be overrating how much calculators can help with *math *(as opposed to arithmetic).

Word processors can check your spelling and grammar. But for the most part, human beings are needed to compose (or reply to) detailed messages.

As Dr. Strangelove notes, there are computer-based tools that can do some math. But these still generally require a user to set up the problem. And if an employer has a choice between buying and maintaining such tools, or hiring employees who don’t need them, well… do the [del]math[/del] arithmetic.

And I repeat, I am not disagreeing with the OP’s premise that some school systems may indeed be requiring too many people to pass too many higher math classes.

But this has nothing to do with preparing people for jobs that require math.

[Derleth]

@Martini_Enfield

The point I’m making is that I don’t actually care what’s going on under the bonnet of a calculator when I ask it to solve an equation for me - to my mind, calculators were invented so we didn’t have to do all that complicated maths jiggery-pokery if we didn’t want to.

Math and arithmetic are two different things. Most math doesn’t involve arithmetic in the slightest; it’s purely symbolic manipulation done to see how various abstract concepts relate to each other.

For example: p = m v. Momentum is mass multiplied by velocity. Based on that equation, we see we can make p large two ways: Large mass or high velocity. See? No numbers involved. We can use numbers, if we want to, at which point I feel morally bound to use a computer, because I am a Homo sapiens sapiens, a member of a species which lifted itself from the dust of the Rift Valley all the way to the goddamned Moon on the strength of its tool use. Ahem.

We can go further. p = m v implies p/m = v. We can rearrange symbols to gain new knowledge. Symbolic manipulation leading to new truths is the essence of mathematics. That is the ultimate, underlying concept first introduced in basic algebra, which most courses utterly fail to communicate in any useful fashion. That is the concept which carries through to literally every other kind of mathematics, and that is why arithmetic is, at best, a faint, pale imitation of mathematics.

Calculators largely take arithmetic out of our hands. I have on my laptop software which takes the “fiddly bits” of literally all mathematics up through multivariate/vector calculus out of our hands. However, in order for that software to be useful, there has to be concepts attached to the symbols. Just shuffling symbols around is indeed an ideal task for computers. Understanding those symbols, and understanding the results, requires an intelligent mind, which computers so far do not have.

[Dangerosa]

@F.U.Shakespeare

People seem to be overrating how much calculators can help with *math *(as opposed to arithmetic).

Word processors can check your spelling and grammar. But for the most part, human beings are needed to compose (or reply to) detailed messages.

As Dr. Strangelove notes, there are computer-based tools that can do some math. But these still generally require a user to set up the problem. And if an employer has a choice between buying and maintaining such tools, or hiring employees who don’t need them, well… do the [del]math[/del] arithmetic.

And I repeat, I am not disagreeing with the OP’s premise that some school systems may indeed be requiring too many people to pass too many higher math classes.

But this has nothing to do with preparing people for jobs that require math.

Absolutely. Jobs that require math you need to do math. I’ve done a whole bunch of modeling in my management career that I’ve needed to develop equations for. And its way better to take your first Calc class from a high school teacher whose first language is English than from a Korean TA in a room full of future Engineers where they are interested in having fewer students in the engineering program. I don’t know that anyone is arguing that no one ever needs it, and that we should drop anything beyond what is needed to make change from high school registration options.

Derleth - as the terms are used in our public education system, math and arithmetic are interchangeable. My kids sixth grade textbook was called “Mathematics” I do know that there is a difference - but not in common usage.

Also, for anyone who hasn’t been in the public education system for years, the kids get “solve for x” really early. I think first or second grade. So first year Algebra flows from the material they’ve had, and variables aren’t strange concepts.

[Martini_Enfield]

@Derleth

Math and arithmetic are two different things. Most math doesn’t involve arithmetic in the slightest; it’s purely symbolic manipulation done to see how various abstract concepts relate to each other.

Last time I checked, arithmetic falls under the heading of “mathematics”, at least in this part of the world. So it is maths.

And I think part of my issue is with non-philosophical abstract concepts

For example: p = m v. Momentum is mass multiplied by velocity. Based on that equation, we see we can make p large two ways: Large mass or high velocity. See? No numbers involved.

That honestly doesn’t make sense to me, though. I’m really not trying to be difficult; I just cannot take those random letters and Why is Momentum called “P”? The letter P does not appear in the word momentum. And why is there no multiplication symbol if I’m supposed to be multiplying things?

This is usually the point I need a cup of coffee and a chocolate biscuit.

We can go further. p = m v implies p/m = v.

Again, might as well be Martian. Sorry. I’ll take your word for it.

We can rearrange symbols to gain new knowledge.Symbolic manipulation leading to new truths is the essence of mathematics. That is the ultimate, underlying concept first introduced in basic algebra, which most courses utterly fail to communicate in any useful fashion. That is the concept which carries through to literally every other kind of mathematics, and that is why arithmetic is, at best, a faint, pale imitation of mathematics.

Complicated gibberish that doesn’t make any sense and I have no use for in my life is the essence of mathematics

Seriously though, I appreciate you taking the time to try and lay it out, but it just doesn’t make any sense to me and my brain shuts off at the merest hint of an equation that isn’t related to working out change or something practical like that.

As an educated chap I get all that stuff about theoretical symbolic manipulation and building blocks of the universe and so on - but it still looks, sounds and quacks like witchcraft to me.

Fortunately, the world is full of people who love maths, so I don’t have to do any of that stuff.

On the other hand, my strength is writing - and a lot of people treat my ability to work with the English language in the same way I look at your ability to worth with advanced mathematics - as some impenetrable skill that’s very impressive and also completely unfathomable at the same time.

[Nava]

@Ruken

I wonder what math requirements other countries with very high graduation rates have. We had at least one poster weighing in from outside the U.S.

I’m not even sure how you’d count graduation rates for Spain; for the last 12 years or so, anybody who needs to repeat a year or who graduates “late” is deemed a “failure” in our statistics, even if they do finish ESO. I find that completely stupid; one of the kids in my nephew’s class started school late for medical reasons, so he was classified as “a failure” before even setting foot in class :smack:

Our compulsory education is supposed to last until 10th grade or age 16. Would we be looking at that or at people who stay in school for Bachillerato, until 12th grade?

I can tell you that while I don’t know what the exact requirements are now, it’s not possible to take college courses without finishing your Bachillerato and passing your University Entrance Exam (even schools which don’t require a specific grade require it to be passed) and some of the things I’ve seen mentioned in this thread are stuff I had in my second year in college… if we’re using the same names, that is. If multivariate calculus means “systems of N differential equations with N variables”, that was 2nd year in college - specially mind-boggling given that the stuff I had in grad school in the US was almost completely formed by repeats of stuff I’d seen in my 1st or 2nd year of college. I’m sure our school system isn’t any kind of “best in the world” or anywhere near some sort of “perfect equilibrium point”, but it seems to me as if the US system can manage to be too high and too low at the same time (multivariate calculus in HS paired with college students who don’t know how to “call it x” or write in the passive voice).

[Dr.Strangelove]

@Martini_Enfield

That honestly doesn’t make sense to me, though. I’m really not trying to be difficult; I just cannot take those random letters and Why is Momentum called “P”? The letter P does not appear in the word momentum. And why is there no multiplication symbol if I’m supposed to be multiplying things?

It seems like you’re having a hard time getting past the syntax. If you’ve always had that as a stumbling block, it would be tough to progress further.

It doesn’t matter what letters you use. Momentum could have been p or Q or happyface-symbol. It’s just a symbol meant to represent a variable quantity. It can be anything as long as you stay consistent. (Not that it matters, but the p comes from the Latin petere. They would have used m but it was already used for mass.)

It’s just a shortcut that two letters next to each other (or a number and a letter) get multiplied. You can put in a * or an X or a · if you wish.

There are ways of teaching math that avoid the syntax completely and focus on the actual principles. For instance, the common expansion (a+b)(c+d) = ac + ad + bc + bd becomes quite obvious when shown as rectangles that you can arrange in a 2D plane. Some people learn better from the physical manipulation of objects. This is just as much math as manipulating symbols on paper. The principles at work are exactly the same–they go deeper than syntax or indeed any other single representation.

It’s too bad that our schools don’t have the resources to work with each student to find the methods that work best for them. The one-size-fits-all approach leaves some students out in the cold.

[Martini_Enfield]

@Dr.Strangelove

It seems like you’re having a hard time getting past the syntax. If you’ve always had that as a stumbling block, it would be tough to progress further.

That’s always been a problem. I also struggle with languages in non-Roman alphabets too. I’m fine with things like French and Spanish and even Malay, but I’m completely hopeless with things like Mandarin, Japanese, or Russian.
Again, my brain basically says “Whatever that is, you can’t read it, and even if you could translate those symbols in English letters, it still wouldn’t mean anything to you.”

There are ways of teaching math that avoid the syntax completely and focus on the actual principles. For instance, the common expansion (a+b)(c+d) = ac + ad + bc + bd becomes quite obvious when shown as rectangles that you can arrange in a 2D plane.

It’d be interesting to find out more about those, since that equation you give looks to me like something one might see in a forbidden tome used to summon Cthulhu.