Math Education: Encouraging Mediocrity and the Negative Effects of Algebra

[Drakkith]

Andrew Hacker is asking the wrong question. While his logic is sound, the underlying question is not "Is Algebra Necessary?", but "Should Schools Teach or Train?"

An excellent point Andy.

 

[Evo]

The problem with being taught a specific skill(s), you are then at risk of becomming obsolete. When new technology replaces your work, what are you going to fall back on?

I saw this in the communications industry. Many people couldn't make the jump to newer technology. Even though many were offered new jobs within the company, I actually heard comments like "this isn't the job I was hired for". I told them, the job you were hired to do no longer exists, this device called the "computer" has made your job copying microfilm obsolete.

 

[Drakkith]

The problem with being taught a specific skill(s), you are then at risk of becomming obsolete. When new technology replaces your work, what are you going to fall back on?

What can you be taught that isn't a "specific skill"? Can you teach adaptability?

 

[Evo]

What can you be taught that isn't a "specific skill"? Can you teach adaptability?

If you have a well rounded education, you are more likely to be able to adapt and learn, because you had to adapt and learn in school. These people usually only had limited education, many didn't even graduate high school, which would be the equivalent of removing subjects from the curriculum.

 

[Drakkith]

If you have a well rounded education, you are more likely to be able to adapt and learn, because you had to adapt and learn in school. These people usually only had limited education, many didn't even graduate high school, which would be the equivalent of removing subjects from the curriculum.

I'm not sure I agree, but I can't offer anything concrete as to why. I've known people who have graduated and who have not graduated and don't see a real difference between the two in terms of adapting to new situations.

Plus I don't think we are talking about having large gaps in education from the removal of algebra from most peoples curriculum. But again, that depends on how much use the average person gets out of it, which I can't say I know for sure.

 

[collinsmark]

But, when does anyone actually use math as a kid? Only on schoolwork.

I can think of a few, hypothetical situations. (And these are just off the top of my head. There's lots of stuff like this.)

Imagine you're a teenager/young adult, and you finally take that summer trip to Europe to experience first hand all that art, culture and history that you learned about in your American school.

When you arrive you discover, much to your chagrin, that the thermometers are all in Celsius! (Being an American, your only experience is with Fahrenheit.) You can see such a thermometer from outside your permanently closed hostel window. Not packing a computer with you, you can't rely on the Internet for help in conversions. Should you wear a sweater or shorts? You happen to remember that water freezes at 32^o F and 0^o C, and that it boils at 212^o F and 100^o C. Using only that information, can you find the general conversion formula?

Later in the day while hiking on the trail, you find that all the trail signs and roads show distances in kilometers. You know that you become fatigued after a certain number of miles. You happen to remember from high-school sports that 5 km is right around 3.1 miles. Can you find the general conversion formula?

You have $200 left and you still need to buy a 70 € Eurorail pass. How many baguettes will you be able to afford per day for the rest of your trip? (I didn't give enough information to actually solve this one, but you get the idea. )

 

[Evo]

I'm not sure I agree, but I can't offer anything concrete as to why. I've known people who have graduated and who have not graduated and don't see a real difference between the two in terms of adapting to new situations.

I'm just basing it on personal experience. My company laid off over 100,000 people in a year (AT&T). The people most likely to not be able to adapt to another job, although they had the chance, were those that were less educated. They were under achievers. They didn't want to try at school, and they didn't want to try at work. They wanted the path of least resistance.

I don't see the harm in taking algebra, it was a 9th grade subject at my school. The teacher was the worst, so those of us that did well were self taught. Do I use it, not really, but I don't regret knowing it. Obviously I'm not talking about anything advanced, just basic algebra. What I really got nothing from was balancing equations in chemistry.

 

[Jimmy Snyder]

What I really got nothing from was balancing equations in chemistry.

Balancing equations in chemistry is a direct application of algebra. Specifically, systems of linear equations.

 

[Evo]

Balancing equations in chemistry is a direct application of algebra. Specifically, systems of linear equations.

It was boring! All I remember of it is a loop of ack,ack,ack.

Now biology :!)

Courses I didn't like, at least I felt a sense of accomplishment by doing well, and a sense of relief that I didn't have to do it again. It was doing things I didn't want to do and doing my best that I found had more impact on my career successes rather than remembering the actual subject.

 

[Drakkith]

I'm just basing it on personal experience. My company laid off over 100,000 people in a year (AT&T). The people most likely to not be able to adapt to another job, although they had the chance, were those that were less educated. They were under achievers. They didn't want to try at school, and they didn't want to try at work. They wanted the path of least resistance.

Perhaps it wasn't that they were less educated, it was that they were lazy?

I don't see the harm in taking algebra, it was a 9th grade subject at my school. The teacher was the worst, so those of us that did well were self taught. Do I use it, not really, but I don't regret knowing it. Obviously I'm not talking about anything advanced, just basic algebra. What I really got nothing from was balancing equations in chemistry.

I did very well in school, including math. I remember very very little of it now though, and have never once used it as far as I know. I recently bought a Calculus book and quickly realized I'd have to relearn Algebra again even though I took college algebra back in 06.

 

[micromass]

Perhaps it wasn't that they were less educated, it was that they were lazy?

Could be. But I think the two are very related. If you were never challenged, then you expect everything to be easy. You need to have classes where you struggle and then feel the accomplishment of eventually getting it. These are very important experiences for young people.

Dumbing everything down only creates the expectation that everything will be easy. So I guess this creates an attitude of laziness.

 

[Drakkith]

Could be. But I think the two are very related. If you were never challenged, then you expect everything to be easy. You need to have classes where you struggle and then feel the accomplishment of eventually getting it. These are very important experiences for young people.

Dumbing everything down only creates the expectation that everything will be easy. So I guess this creates an attitude of laziness.

It isn't about "dumbing it down", it's about whether Algebra is useful to learn or not.

 

[micromass]

It isn't about "dumbing it down", it's about whether Algebra is useful to learn or not.

It is about dumbing it down. The post in the OP indicates that too many people fail algebra and that it therefore must be scrapped. I don't see anybody making the case that history should be scrapped. Even though history, arts, literature, foreign languages, biology, physics, chemistry are all equally useless than algebra.

Algebra is basic knowledge that everybody should have. Knowing how evolution or genetics works is not useful, but children should see that.

If we only want useful things, then we can scrap the entire science education.

Honestly, I find it extremely sad that people are arguing about this on a science forum.

 

[chiro]

One thing IMO about math is that people with a bit of math are sharper and aren't able to be as fooled or conned as easily.

The person that knows what fractions really mean in a deep context and what exponentials and compound interest mean are going to be a lot sharper IMO when some shady person offers them a loan as opposed to someone who doesn't: when people have a sense of these kinds of things, they are able to detect if someone is trying to screw them.

Similarly, the person that knows enough about probability to know that the game is rigged and that the house in the long run always comes out on top are in a different position than the person who just believes that if they rub that rabbits foot, then they will get back what they invested all their time and money (and possibly other peoples money) into.

To me, this idea of getting general skills to keep you sharp is something that everybody at one stage of their life will need regardless of what they end up doing. People are screwed when they don't have this capability, and one way to overcome this is to introduce math in a way that shows people how math can help in this regard.

It could be that the guy wants to look around for a home-loan and upon understanding his math, he realizes the impact of how much extra he (and possibly his wife) will have to pay for the next 20-30 years, and in this particular situation he will be glad he took a a math class or two.

 

[Drakkith]

It is about dumbing it down. The post in the OP indicates that too many people fail algebra and that it therefore must be scrapped. I don't see anybody making the case that history should be scrapped. Even though history, arts, literature, foreign languages, biology, physics, chemistry are all equally useless than algebra.

Algebra is basic knowledge that everybody should have. Knowing how evolution or genetics works is not useful, but children should see that.

If we only want useful things, then we can scrap the entire science education.

I disagree completely. With every other subject you mentioned, you at least come away with some knowledge about how the world works, some basic skills that allow you communicate better than before, or something. But what about algebra? What do you come away from an algebra class with? Effectively nothing if you aren't going to be using it immediately. It it no way pertains to real life for the majority of people. And this is assuming you pass the class to begin with. Is algebra difficult for many people? Yes. Does this mean we should get rid of it? No, not solely for that reason. Every subject is difficult to someone.

To be fair I can't think of a better way to do things that we already do them. I have no idea how you would separate people who would require algebra and those who wouldn't. I honestly don't see an option but to continue teaching it for now.

Honestly, I find it extremely sad that people are arguing about this on a science forum.

Why?

 

[Drakkith]

One thing IMO about math is that people with a bit of math are sharper and aren't able to be as fooled or conned as easily.

I agree that a better knowledge of math is generally helpful, but I question whether the average person could actually do all of this. Especially the interest on a mortgage part. I know I have no idea how to find that out. Also, how much of what you said requires algebra?

 

[Vorde]

I have no idea how you would separate people who would require algebra and those who wouldn't.

I think that is the key.

Ideally there would be some people who benefit from algebra and the higher maths, and some people that wouldn't, but there isn't a good way to separate the two.
If you looked at my middle school algebra grades you would absolutely put me into the class that doesn't do any serious mathematics, yet here I am 5 years later near the top of my class.

Algebra needs to be taught because it is the basis of all mathematics (at least all mathematics anyone who isn't studying math will ever encounter). The same reason something like basic Biology is taught to everyone: just so they know the subject.

 

[micromass]

I disagree completely. With every other subject you mentioned, you at least come away with some knowledge about how the world works, some basic skills that allow you communicate better than before, or something. But what about algebra? What do you come away from an algebra class with? Effectively nothing if you aren't going to be using it immediately. It it no way pertains to real life for the majority of people.

So what are you saying, that mathematics and algebra doesn't give knowledge about how the world works?? Since when do people not need numbers and calculations any more? Since when is mathematics not part of the world anymore?

And tell me, how does history, literature arts, foreign languages, physics, biology, chemistry pertain to the real life for the majority of people? I personally never had to use any of these in my life, and I don't think I ever will. In fact, if they never taught me those things, I think my life would not be significantly different than what it is now.

Good luck figuring out what kind of loan to take out without algebra. Good luck doing anything science or engineering related without mathematics. I agree that mathematics isn't immediately useful to most children. In fact, its uses become apparent only later in your life.

Furthermore, how would children get a feel for math if they don't ever take it? How would you get people interested in sciences and mathematics if nobody takes courses on those subjects anymore?

 

[Drakkith]

So what are you saying, that mathematics and algebra doesn't give knowledge about how the world works?? Since when do people not need numbers and calculations any more? Since when is mathematics not part of the world anymore?

Algebra specifically isn't part of the world of the average person. Math in general is though.

And tell me, how does history, literature arts, foreign languages, physics, biology, chemistry pertain to the real life for the majority of people? I personally never had to use any of these in my life, and I don't think I ever will. In fact, if they never taught me those things, I think my life would not be significantly different than what it is now.

The SPECIFICS of each one aren't important. (Well, maybe in foreign languages they are. But those are generally electives, not requirements. At least at my school) What matters is that you come away with a general understanding of each one. But I feel it's hard to compare those subjects overall to algebra specifically. It's like saying that no math should be required in school. That would be ridiculous, as basic math is very much a requirement and will get used by most people.

Good luck figuring out what kind of loan to take out without algebra. Good luck doing anything science or engineering related without mathematics. I agree that mathematics isn't immediately useful to most children. In fact, its uses become apparent only later in your life.

Furthermore, how would children get a feel for math if they don't ever take it? How would you get people interested in sciences and mathematics if nobody takes courses on those subjects anymore?

Why is this suddenly about ALL of math? And of course algebra is required for engineers and other careers that would use it.

 

[zoobyshoe]

It is about dumbing it down. The post in the OP indicates that too many people fail algebra and that it therefore must be scrapped.

No, not scrapped. I think the author of the article would make it optional as opposed to required. That is all.

I don't think that's about to happen, so you shouldn't get so upset. I think it's important, though, to be aware of this big problem, that roughly a third of students seem to be unable to handle it.

 

[SW VandeCarr]

I had a rocky start with algebra in the 8th grade. The teacher said unknown constants are represented by lower case letters from the beginning of the alphabet while unknown variables are represented by lower case letters from the end of the alphabet. He gave an example with something like $ax-b=0$. Solving for x we get $x=b/a$. I asked why x is a variable and a and b are constants. If you fix the values of a and b, you also fix the value of x. I don't remember his exact answer, but it was something like you're given a and b and solving for x. For some reason, I had a problem with that.

 

[xdrgnh]

They should teach algebra based physics so the students see how useful algebra is. They said in the article that algorithms are mathematical reasoning which is wrong. If they actually taught mathematical reasoning then this would not be an issue because the value of algebra would be imminent.

 

[Vorde]

They should teach algebra based physics so the students see how useful algebra is. They said in the article that algorithms are mathematical reasoning which is wrong. If they actually taught mathematical reasoning then this would not be an issue because the value of algebra would be imminent.

Mathematical reasoning sort of falls into your lap once you get sufficiently comfortable with algebra, I don't think that is something that can really be taught.

 

[xdrgnh]

Mathematical reasoning in the real world means being able to quantify. Algebra teaches that just fine

 

[Drakkith]

Mathematical reasoning in the real world means being able to quantify.

What does this mean?

 

[xdrgnh]

It means getting sense of how much and how little a specific quantity is and being able to express it as a mathematical model. The problem is that mathematical modeling isn't really taught. All they teach are algorithms and students get the idea that it's trivial.

 

[genericusrnme]

I think a big problem with maths education is that in modern western society it is seen as 'cool' to suck at basic stuff.
The number of times I've heard someone tell me about how they "can't do maths" in an attempt to impress me or god knows what else.. it's unreal.
I've witnessed the same thing about cooking - someone asks me what I did last night, I tell them I made bolognese or something simple like that and I get regaled with tales about how they manage to burn baked beans.
It's not that I'm trying to be superior to anyone because I can cook and do maths, it's just enfuriating that people seem to think being unable to do simple things is something to brag about..

edit;
dang it, how come I always get to start a new page >.>

 

[lisab]

I think a big problem with maths education is that in modern western society it is seen as 'cool' to suck at basic stuff.
The number of times I've heard someone tell me about how they "can't do maths" in an attempt to impress me or god knows what else.. it's unreal.
I've witnessed the same thing about cooking - someone asks me what I did last night, I tell them I made bolognese or something simple like that and I get regaled with tales about how they manage to burn baked beans.
It's not that I'm trying to be superior to anyone because I can cook and do maths, it's just enfuriating that people seem to think being unable to do simple things is something to brag about..

edit;
dang it, how come I always get to start a new page >.>

This is something I've noticed, too, that I just don't get! Why is it so acceptable to be bad at math?

What would people think if they heard someone say, "Oh, reading? I don't read at all, I've always been so bad at reading! I can't read beyond an elementary level -- really! Can someone read this menu aloud for me, heehee?"

Is that really supposed to be cute?!?

/rant


well ok not really /rant because I'm still worked up it really ticks me off!

 

[AnTiFreeze3]

The Western society has a firm grasp of the notion that mathematics is only for the geniuses who are naturally gifted at it, and that their lowly minds can't handle such strenuous activities. Therefore, they may feel like they are in common company when they, oddly enough, brag about not understanding math.

Everywhere else seems to have held on to the idea that hard work can accomplish a lot, and it just so happens that hard work seems to do wonders for learning math...

Now comes the problem of dumbing down the curriculum in a pathetic attempt to raise percentages. Somebody earlier mentioned how laziness may or may not directly correlate with poor math scores: I believe that it does.

In elementary and middle school, everything was easy for me. I am by no means smart, but I was able to pull off straight A's without ever studying. I got put into an ELP program (Extended Learning Program) which was for the "gifted" students. Even in that class, it was merely a replacement for English and Literature classes, so I was pushed to write well, improve my grammar, and give in-depth presentations; math was never mentioned.

Needless to say, I developed the nasty attitude and misconception that I could breeze through school without ever cracking open a book outside of class. Even in my freshman year of high school, I got mainly A's, with two B's, with that same shoddy work ethic. (Not surprisingly, one of the B's was in math).

My epiphany came during my sophomore year, where I realized that I needed to actually work hard if I wanted to do something with my life.

Essentially, a severely dumbed down curriculum (at least to me, maybe not to everyone) led to my development of a bad work ethic, and eventually caused me to not fully apply myself in math classes, which is why I am now self-studying to make up for my previous rejection of anything to do with math. Dumbing down academic curriculum is harmful for the very reason that the real-world is not dumbed-down; you're essentially giving children the idea that they don't need to work hard in order to excel in life, which couldn't be further from the truth.

 

[chiro]

Absolute agree ^.

An interesting thing is that at least for mathematics, it has been found that while Asian students are less confident about their abilities, they do better than their US counterparts who are funnily enough, more confident about their abilities in mathematics.

I would have no problem in supporting your conclusions mentioned above especially in the context of the above statement.

 

[Zarqon]

This is something I've noticed, too, that I just don't get! Why is it so acceptable to be bad at math?

What would people think if they heard someone say, "Oh, reading? I don't read at all, I've always been so bad at reading! I can't read beyond an elementary level -- really! Can someone read this menu aloud for me, heehee?"

Is that really supposed to be cute?!?

/rant


well ok not really /rant because I'm still worked up it really ticks me off!

My guess would be that it's simply a human defense reaction. If you've already realized (even if just unconsciously) that you are not very good at math, and don't want to spend much time on it, then I guess the brain would much rather turn the whole thing into a "choice", like you chose not to learn math (because who needs it anyway) rather than live the rest of your life knowing that you failed it.

 

[Drakkith]

This is something I've noticed, too, that I just don't get! Why is it so acceptable to be bad at math?

I'd guess that it's because most people don't use any math more advanced than basic arithmetic. Combine that with the stereotype of a smart person or scientist being a complete bumbling idiot in "real life" and I can easily see why.

 

[zoobyshoe]

Participate in my poll, people:

https://www.physicsforums.com/showthread.php?t=624784

 

[zoobyshoe]

I think a big problem with maths education is that in modern western society it is seen as 'cool' to suck at basic stuff.

It's sour grapes: when the fox couldn't reach the grapes he 'decided' they were probably sour anyway.

 

[DragonPetter]

I think a big problem with maths education is that in modern western society it is seen as 'cool' to suck at basic stuff.
The number of times I've heard someone tell me about how they "can't do maths" in an attempt to impress me or god knows what else.. it's unreal.
I've witnessed the same thing about cooking - someone asks me what I did last night, I tell them I made bolognese or something simple like that and I get regaled with tales about how they manage to burn baked beans.
It's not that I'm trying to be superior to anyone because I can cook and do maths, it's just enfuriating that people seem to think being unable to do simple things is something to brag about..

edit;
dang it, how come I always get to start a new page >.>

It reminds me of an ignorant and superficial version of jante law as an attempt to conform.