Math Education: Encouraging Mediocrity and the Negative Effects of Algebra

[Vorde]

I think one thing that needs to be thought of is that school is part preparation for life, and part just teaching the student.

I could easily make the argument that 90% of what I learn in a history class is useless for any (non-historical) professional career, but I still think we should be taught it.

 

[Drakkith]

I'm with Zooby and his article on this one. I don't have anything to back my opinion up other than my own experiences, but I would expect that most people never use algebra outside of the classroom.

I think one thing that needs to be thought of is that school is part preparation for life, and part just teaching the student.

I could easily make the argument that 90% of what I learn in a history class is useless for any (non-historical) professional career, but I still think we should be taught it.

Absolutely. I believe that knowing basic history is essential to having a basic understanding of the world and how it works. But I dare say that learning the countries of the world or the history of the middle ages is a far cry from struggling through mathematical concepts that you will probably never use and the understanding of is far from necessary to a successful life.

 

[zoobyshoe]

Regarding the "considerable training occurs after hiring" part. Can't say I have been in many jobs where that happens to be honest. Most jobs I have worked at require you to have the necessary skills before you start working for them.

But that's just me I guess. Maybe I am the odd one out?

That information comes from a guy who has specifically studied this:

John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college, which has tailored classes in “machine tool mathematics.”

There may be other 'educational psychologists' with dissenting opinions, but it's not the kind of assertion you can challenge without actually collecting data about what's going on in the U.S. workplace.

 

[zoobyshoe]

I'm with Zooby and his article on this one. I don't have anything to back my opinion up other than my own experiences, but I would expect that most people never use algebra outside of the classroom.

I'm not on the author's side about the solution, necessarily. I posted it because he highlights the problem well.

I, personally, never failed an algebra course, but I also never exceeded a B. What bothers me is that it all evaporated from my mind within a year of getting out of high school, that is: as soon as it wasn't reinforced any more. I learned algebra to pass algebra and it never had the least application to my real life. It was a weird, tedious problem solving exercise that got more and more complex without having any purpose.

 

[Mech_Engineer]

Why do you think this would happen? I doubt the stuff that gets used and reinforced constantly in real life would ever be questioned as necessary to teach.

Well I guess I'm trying to make the point that there will always be a "hardest class" that some students may struggle with. I've heard this argument for calculus before and agree that lots of people don't need it, but algebra seems so fundamental to me...

Maybe instead of algebra they (we) could implement a series of "applied mathematics" courses that focuses more on real-world problems in statictics and finance and and less on understanding abstract algebraic math. Still, it seems to me that algebra has so many useful real-world examples its method of teaching doesn't have to be abstract at all...

 

[WannabeNewton]

If the argument being made is let's not teach algebra to students who have no interest in it and/or will never use it later in life then why can't I say the same thing about history or literature classes? I doubt I will ever in my life use what I have learned about the Mesopotamian era or the Ottoman empire or even the Puritans. These things many would not find essential but I find it hard to believe that people would think high school algebra is not an essential job skill for a reasonable amount of jobs. My mom is a biologist who deals mainly with immunology and there is a good amount of math that crops up in the articles she reads but should such math not be important to an aspiring biology student simply because he/she is not "interested" in it?

 

[micromass]

If the argument being made is let's not teach algebra to students who have no interest in it and/or will never use it later in life then why can't I say the same thing about history or literature classes? I doubt I will ever in my life use what I have learned about the Mesopotamian era or the Ottoman empire or even the Puritans.

Right. It's not only about algebra being necessary in later life. I will concede that many people will never use math in their later life (although many people will, which is already a reason to teach it).
But that's not the point here. High school is supposed to give a general education. How can you call somebody well-educated if he never heard of Shakespeare before? How can you call somebody well-educated if he doesn't know who won the US civil war? Likewise, somebody cannot be well-educated if he never learned to do basic algebra.
Algebra is truly one of the triumphs of human reasoning. It is truly terrible that people do not want to learn it.

 

[Vorde]

I think the problem here was highlighted by someone else when they were talking about the apprentice system. In the old days, you became an apprentice to learn the skills needed for your job, and you went to school to be taught many different things. Both aspects of those two things are combined in modern day schools.

It sort of comes down to what you expect a high school diploma to contain. Drakkith seemed to draw a distinction between math and literature (history really) and their relevance to modern day life. I see no such distinction.

If you are going to say school is about learning skills for life then I would say the curriculum should consist of Foreign Language, Engineering, Writing and Economics/Statistics. If you are going to say school is about being taught, then I would say that History, Literature, Science and Mathematics are all on equal footing with regards to their relevance.

From that equality, you can't righteously remove a course because people are struggling in it, you need to examine your way to teaching it to see what's wrong with it.


Edit: Micromass said a very similar thing in a more concise way.

 

[zoobyshoe]

If the argument being made is let's not teach algebra to students who have no interest in it and/or will never use it later in life then why can't I say the same thing about history or literature classes?

If people were being barred from college based on widespread failure in History and Literature, the same question would apply to those subjects. The fact is, it's not that hard to pass History and Literature even if you have little interest in them.

 

[WannabeNewton]

If people were being barred from college based on widespread failure in History and Literature, the same question would apply to those subjects. The fact is, it's not that hard to pass History and Literature even if you have little interest in them.

I can't say this with generality but at my high school the history and literature classes were tougher than math classes simply because of the hours and hours of daily work we would receive from those classes. I loved US history but the daily multiple page written home-works would easily make my LA or DE class look like heaven on earth. It was a pretty controlled experiment at my school because both the US history teacher and the LA \ DE teacher (same one for both) were excellent; it came down to the nature of the classes. I think getting good marks on a math test would be considerably easier than pulling off consistent A's on history essays given that the math teacher is a good one. We need to have better math teachers not discard algebra from being a mandatory high school class. That would be absurd in all honesty.

 

[zoobyshoe]

Algebra is truly one of the triumphs of human reasoning.

This is probably true, but is it an insight you arrived at yourself, or was algebra presented to you in this enthusiastic way?

 

[zoobyshoe]

We need to have better math teachers not discard algebra from being a mandatory high school class. That would be absurd in all honesty.

Word. I think I would have loved algebra if it had only been taught differently.

 

[micromass]

If people were being barred from college based on widespread failure in History and Literature, the same question would apply to those subjects. The fact is, it's not that hard to pass History and Literature even if you have little interest in them.

So since when is it wrong to challenge the children? Should we dumb everything down and make everything easy for them??
The fact is that algebra isn't even that hard. The children should just apply themselves and struggle through it.

 

[micromass]

This is probably true, but is it an insight you arrived at yourself, or was algebra presented to you in this enthusiastic way?

My algebra teacher was very bad. I hated it. But it was important and I studied for it anyway. In the end, I'm glad I know it.

 

[WannabeNewton]

Word. I think I would have loved algebra if it had only been taught differently.

Unfortunately it would be a monumental task getting such teachers in each high school in the country or even a majority of the high schools.

 

[Andy Resnick]

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?" Historically, professional schools (Medical, Law, Graduate science programs, etc.) trained future professionals, while K-12 and liberal-arts undergraduate programs provided a broad education. The rise of standardized testing has introduced the notion of training K-12 and undergraduate students, and as a result, increasing numbers of educators (like Professor Hacker) are rightly questioning the fundamental purpose of education- should schools provide a 'learning environment', or 'train the future workforce'?. That is the correct question to be discussed.

For an excellent critique of the current state of K-12 Mathematics 'training', Paul Lockhart's 2002 essay "Mathematician's Lament" is required reading.

 

[D H]

This is probably true, but is it an insight you arrived at yourself, or was algebra presented to you in this enthusiastic way?

On my own (there was no internet in the stone age), I came up with a proof that 0.999... is 1. I showed it to my 9th grade algebra teacher. He said I was wrong. He was quite adamant. He ranked right up there in teacher quality with my 9th grade history teacher, whose main job was football coach. He made rocks look downright intelligent. At least my high school algebra teacher was smarter than a rock. But not much.

 

[zoobyshoe]

Unfortunately it would be a monumental task getting such teachers in each high school in the country or even a majority of the high schools.

I don't think it's a matter of replacing teachers, but of getting the ones that are in place to understand what they're doing wrong and how to correct it.

However, I'm not sure anyone knows exactly what's being done wrong or what they should be doing instead. All that might be certain at this point is that there's a big problem.

 

[zoobyshoe]

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?" Historically, professional schools (Medical, Law, Graduate science programs, etc.) trained future professionals, while K-12 and liberal-arts undergraduate programs provided a broad education. The rise of standardized testing has introduced the notion of training K-12 and undergraduate students, and as a result, increasing numbers of educators (like Professor Hacker) are rightly questioning the fundamental purpose of education- should schools provide a 'learning environment', or 'train the future workforce'?. That is the correct question to be discussed.

For an excellent critique of the current state of K-12 Mathematics 'training', Paul Lockhart's 2002 essay "Mathematician's Lament" is required reading.

Very good point.

On my own (there was no internet in the stone age), I came up with a proof that 0.999... is 1. I showed it to my 9th grade algebra teacher. He said I was wrong. He was quite adamant. He ranked right up there in teacher quality with my 9th grade history teacher, whose main job was football coach. He made rocks look downright intelligent. At least my high school algebra teacher was smarter than a rock. But not much.

This gives me an idea for another thread with a poll.

 

[Drakkith]

Warning: Read the following at your own risk. Author may not know what he is talking about. You have been warned.

But that's not the point here. High school is supposed to give a general education. How can you call somebody well-educated if he never heard of Shakespeare before? How can you call somebody well-educated if he doesn't know who won the US civil war? Likewise, somebody cannot be well-educated if he never learned to do basic algebra.

I would argue that a knowledge of the basics of history allow us to judge current events and keep bad things from happening. And this doesn't require an advanced understanding of all of history, only the most basic understanding is needed. How does algebra help the average person? If it's JUST so they can be considered "educated", I would say to hell with that. Let's not invent reasons just to have some.

Algebra is truly one of the triumphs of human reasoning. It is truly terrible that people do not want to learn it.

I could argue the same thing about almost anything, such as Quantum Mechanics. But the fact is that we don't teach QM to most people because it's pointless and they don't care about it.

I can't say this with generality but at my high school the history and literature classes were tougher than math classes simply because of the hours and hours of daily work we would receive from those classes. I loved US history but the daily multiple page written home-works would easily make my LA or DE class look like heaven on earth.

Wow, sounds pretty hard. I don't remember having anywhere near this amount of homework.

I think getting good marks on a math test would be considerably easier than pulling off consistent A's on history essays given that the math teacher is a good one. We need to have better math teachers not discard algebra from being a mandatory high school class. That would be absurd in all honesty.

Would you say that writing a paper on U.S. History requires that you know the history of Ancient Greece? I would say no. However, getting A's on an Algebra test DOES require you to know stuff from previous years of math. But, when does anyone actually use math as a kid? Only on schoolwork. Math more advanced than maybe multiplication just isn't commonly used. You don't talk about it, you don't think about it, nothing. You don't need it to understand the world around you for almost all purposes. It doesn't give you insight into every day matters, help you make decisions, or serve as a moral compass. It does NOTHING. That's why it's so hard for people to care about it. Because for them, it does nothing. It's only useful as a tool for doing other things, and if you don't do things that require you to know algebra, then why would you want to learn it?

So since when is it wrong to challenge the children? Should we dumb everything down and make everything easy for them??
The fact is that algebra isn't even that hard. The children should just apply themselves and struggle through it.

I don't understand this common mentality of "X person should just do Y thing". It's a BS statement that means nothing. It is a FACT that algebra IS difficult to many people. If you have to "just apply yourself and struggle through it", you have failed. Even if you passed the class, you have failed. The fact that you struggled through it probably means that you don't really understand it and only memorized enough information to get past the tests and will likely not be able to do a real life problem involving algebra. This contrasts to classed like history where you can forget the exact date that Abe Lincoln got shot and it doesn't matter. You know he got shot, you know the general idea of why and how and the events leading up to it (Civil War), and that's about all that really matters. (My personal opinion of course) And if you don't know those things, THEN you have failed history.

Now, I am NOT saying we should stop teaching algebra. I really have no idea how useful it is to most people. I'm saying that IF it is useless for the great majority of people, THEN we should probably not teach it.

 

[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..

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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.