Merged No more algebra?

[DazzaD]

I get really frustrated when very well educated people bemoan the mathematics education that students get. You very rarely find a well educated mathematician going on an (ill informed) crusade about how "knowing dates in history is not useful in real life".

Much of the education a student receives is going to be used generically. In history they may not have to recall the exact facts, names, figures, dates etc but an understanding of why things happened and how things happened can be incredibly useful in understanding the world around you.

I teach mathematics and the higher level mathematics you have learned the more you appreciate just how it is involved in every single aspect of daily life. You may not CHOOSE to sit down and write an equation of motion for walking across the road but that does not mean you are not using mathematics in a variety of ways.

It can be mundane (working out change when shopping) or quite advanced and interesting maths (working out the quickest route to the shops) or involve linear algebra (some economics perhaps pertaining to the industry that is producing the goods you are going to the shops to buy).

Whatever mathematics it is it has an unreasonable effectiveness in everyday life.

Learning algebra isn't meant to instil a magical calculation machine to solve quadratic equations in a child's mind, it is meant as introduction to methods of problem solving, setting up problems, analysing them, rewording them, simplifying them.

I would be interested to hear this gentleman's opinion on whether students should be able to problem solve in the workplace.

Admittedly, there are some aspects of the curriculum I might choose to replace.

e.g. in the UK, instead of doing, say, circle theorems, I might choose to go back to learning matrices at an early age, these can be developed and used to do transformations and solving simultaneous equations at GCSE - which IS done, but only in the further mathematics A Level. While circle theorems instil a sense of pure mathematics, elements of proof and abstract maths, I still think that learning matrices would be a better stepping stone to solving problems and give a better foundation for mathematics, economics, physics, engineering etc.

 

[Careyp74]

The Betas don't want to learn, and the Gammas can't, so only the Alphas should get a good education.

(Direct from His Flivver.)

Well, he argues that a lot of those betas and gammas are not getting any education at all because of the algebra requirement causing them to drop out. I also don't think he is trying to remove anything from the curriculum, just keep the requirements lower. I took calculus in high school, and it wasn't a requirement. I finished all of my requirements early, and the last year had plenty of electives (including calculus) and study halls.

The problem I see is, that there isn't a guarantee that these types that cannot grasp algebra will benefit at all from completing a high school curriculum that doesn't require it. Not from the lack of algebra, but from the lack of being able to use mental processes in general. If you dumb down the curriculum, you make it easier to get through without any feedback as to learning ability.

 

[Hazel]

I get really frustrated when very well educated people bemoan the mathematics education that students get. You very rarely find a well educated mathematician going on an (ill informed) crusade about how "knowing dates in history is not useful in real life".

Much of the education a student receives is going to be used generically. In history they may not have to recall the exact facts, names, figures, dates etc but an understanding of why things happened and how things happened can be incredibly useful in understanding the world around you.

I teach mathematics and the higher level mathematics you have learned the more you appreciate just how it is involved in every single aspect of daily life. You may not CHOOSE to sit down and write an equation of motion for walking across the road but that does not mean you are not using mathematics in a variety of ways.

It can be mundane (working out change when shopping) or quite advanced and interesting maths (working out the quickest route to the shops) or involve linear algebra (some economics perhaps pertaining to the industry that is producing the goods you are going to the shops to buy).

Whatever mathematics it is it has an unreasonable effectiveness in everyday life.

Learning algebra isn't meant to instil a magical calculation machine to solve quadratic equations in a child's mind, it is meant as introduction to methods of problem solving, setting up problems, analysing them, rewording them, simplifying them.

I would be interested to hear this gentleman's opinion on whether students should be able to problem solve in the workplace.

Admittedly, there are some aspects of the curriculum I might choose to replace.

e.g. in the UK, instead of doing, say, circle theorems, I might choose to go back to learning matrices at an early age, these can be developed and used to do transformations and solving simultaneous equations at GCSE - which IS done, but only in the further mathematics A Level. While circle theorems instil a sense of pure mathematics, elements of proof and abstract maths, I still think that learning matrices would be a better stepping stone to solving problems and give a better foundation for mathematics, economics, physics, engineering etc.

Well said. I feel that all aspects of education have a purpose and should be taught. If the less able never get past the basics, they at least know what it is about. And yes, they are often using things they learned without even realizing it. A simple example that comes to mind is adjusting recipes in the kitchen.

That said, two little sayings: The mark of a good education is not knowing a slew of facts but knowing how to find the facts when you need them. I don't envy the British student trying to keep all the Henrys, Edwards, and Johns separate but I keep a book at hand that re-enlightens me whenever I need to know "which Edward?"

My other favourite saying all teachers need to keep in mind. The mark of an intelligent person is the abillity to explain to the person of lesser ability without talking down to him. I've lost interest in more than one topic - and almost failed one at university - because the teacher was using ten-syllable words and technical terms far beyond my ken.

Hwyl

 

[Hazel]

Well, he argues that a lot of those betas and gammas are not getting any education at all because of the algebra requirement causing them to drop out. I also don't think he is trying to remove anything from the curriculum, just keep the requirements lower. I took calculus in high school, and it wasn't a requirement. I finished all of my requirements early, and the last year had plenty of electives (including calculus) and study halls.

The problem I see is, that there isn't a guarantee that these types that cannot grasp algebra will benefit at all from completing a high school curriculum that doesn't require it. Not from the lack of algebra, but from the lack of being able to use mental processes in general. If you dumb down the curriculum, you make it easier to get through without any feedback as to learning ability.

Your last line says it all. And, as I'm trying to say, this is exactly what is happening. It doesn't start in high school and certainly not at university. It starts in elementary school where so many (academic?) subjects have been eliminated - some deliberately by the school districts and some by teachers who simply say they don't have time to teach that particular subject - or don't want to.

I have a friend who is a librarian and a university. She says she meets too many students who cannot use references adequately because they do not know the alphabet. I have heard reports from universities about students who cannot read at high school level, let alone college level. Having taught sixth graders who were still reading at third grade level, I believe it.

A lot of this is attitude such as "Algebra, do we need it?"

Please let me add, though, that not all elementary schools are doing this damage. We have some excellent school districts in this huge country who are still teaching history, geography, spelling, science, even music and art. But, too many are not and we who see it fear for the future.

Sorry, I get didactic, don't I?

 

[dlorde]

I have a friend who is a librarian and a university. She says she meets too many students who cannot use references adequately because they do not know the alphabet. I have heard reports from universities about students who cannot read at high school level, let alone college level.

How on Earth do they get to university - even just for interview - without knowing the alphabet or being able to read?

 

[Careyp74]

She says she meets too many students who cannot use references adequately because they do not know the alphabet.

Oh, THAT'S what that is used for.

I suspect that I have gone to University with many students like this. While many do still try, others believe that simply paying tuition should be enough to acquire a diploma, and if the subject is too difficult, they should be walked through it. Where did they pick this up?

 

[Hazel]

How on Earth do they get to university - even just for interview - without knowing the alphabet or being able to read?

Good question. I don't know that they are interviewed. Perhaps. When I went - back in the dark ages - we had to take exams which showed our skills, where we were strong and where weak. Then we were told what subjects we had to take - not needed or suggested but required. Things were more rigid back then, I suppose.

 

[Rasmus]

How on Earth do they get to university - even just for interview - without knowing the alphabet or being able to read?

The alphabet is just the ability to go A, B, C, D .... Y, Z and know that N comes before U and Q after L.

Nobody would ever test that stuff, because it is assumed that everybody knows.

And then there is something called a "functional analphabet" - a person who knows how to read, can read ... but not well enough to ever actually do it beyond the base minimum level that's required to get through life, and certainly not well enough to enjoy it.

We had a guy in high-school who was - a bit - like that. He didn't like reading, so he never read. So he couldn't read out a paragraph or two fluently in class. Bright kid, otherwise. And he knew how to read, else he wouldn't have gotten the grades he did. But he got through 10 or 11 years of school without it ever being noticed and/or appropriately addressed. (For what it's worth: We graduated together.)

 

[Hazel]

Oh, THAT'S what that is used for.

I suspect that I have gone to University with many students like this. While many do still try, others believe that simply paying tuition should be enough to acquire a diploma, and if the subject is too difficult, they should be walked through it. Where did they pick this up?

Exactly. Back in the 60s and 70s, students were going on strike against universities that refused them entry or tried to fail them. As you said, they paid tuition and considered that as purchasing a diploma whether you'd learned anything or not. Like buying a baseball ticket.

Where did it start? In kindergarten. It has become verboten to fail any child in school. It might damage his psyche. So, the first grader is too immature to grasp what is being taught. Instead of holding him back, you move him on into second grade. He gets "babied" along there with hopes he'll catch up. Not so. By third grade, he is lost. By fourth grade, he has learned to say 'you can't make me do homework'.

 

[Careyp74]

Exactly. Back in the 60s and 70s, students were going on strike against universities that refused them entry or tried to fail them. As you said, they paid tuition and considered that as purchasing a diploma whether you'd learned anything or not. Like buying a baseball ticket.

Where did it start? In kindergarten. It has become verboten to fail any child in school. It might damage his psyche. So, the first grader is too immature to grasp what is being taught. Instead of holding him back, you move him on into second grade. He gets "babied" along there with hopes he'll catch up. Not so. By third grade, he is lost. By fourth grade, he has learned to say 'you can't make me do homework'.

I know many a smart person who was held back once in their lives. Didn't hurt them.

NOT holding them back would hurt them. The fact that I can understand this, and the parents that cry about it don't know this, tells me that I was fortunate to get a good education, and can use that for the good of future generations. Either they didn't get one, and are continuing to help the problem, or they are being irresponsible with what they were given. (or a third alternative not listed.)

How on Earth do they get to university - even just for interview - without knowing the alphabet or being able to read?

by bus?

 

[Hazel]

The alphabet is just the ability to go A, B, C, D .... Y, Z and know that N comes before U and Q after L.

Nobody would ever test that stuff, because it is assumed that everybody knows.

And then there is something called a "functional analphabet" - a person who knows how to read, can read ... but not well enough to ever actually do it beyond the base minimum level that's required to get through life, and certainly not well enough to enjoy it.

We had a guy in high-school who was - a bit - like that. He didn't like reading, so he never read. So he couldn't read out a paragraph or two fluently in class. Bright kid, otherwise. And he knew how to read, else he wouldn't have gotten the grades he did. But he got through 10 or 11 years of school without it ever being noticed and/or appropriately addressed. (For what it's worth: We graduated together.)

Dyslexia, perhaps?

 

[Zelenius]

I still have no idea how I graduated from high school. Even my family was shocked, they kept thinking I would drop out.

As hostile as I was to any form of schooling, even I understand the need for requiring algebra in high school, for career preparation, or to help deal with every day problems. I don't think it is even possible to be a well-rounded, informed citizen without at least some understanding of algebra. Even "some understanding" I think is all that is required, not mastery.

I also believe in getting statistics into the high school mathematics curriculum. This seems to be the most neglected area of mathematics, at least in this part of the country. It is amazing how even some educated people I know do not know the first thing about statistics.

I frequently have to use algebra and higher in my own work. It's amazing I am able to do it at all, considering I almost always failed it in high school, but I can do all the necessary equations required to get everything working properly without a problem. Luckily, these days, computers do most of the work.

 

[Hazel]

Luckily, these days, computers do most of the work.

And that may be a drawback because people (myself included) rely on it so much that they don't bother to learn or apply what they've learned. Some day the whole internet will crash and then what? Who will figure compound interest for the banks?

 

[OrangeCatz]

As a chemical engineer from 1950-1990, my dad had to work out a lot of equations by hand and cheap TI calculators. When younger engineers would come up with results, my dad and his older colleagues would glance at the value and say, "That can't be right!". The young engineers would say, "But that's what the computer gave me."

 

[Dinwar]

As a chemical engineer from 1950-1990, my dad had to work out a lot of equations by hand and cheap TI calculators. When younger engineers would come up with results, my dad and his older colleagues would glance at the value and say, "That can't be right!". The young engineers would say, "But that's what the computer gave me."

My dad's a civil engineer, and similar things have happened to him. One design spec came in with a triangular room whos corners added up to more than 180 degrees. Took my dad fifteen minutes to explain to the kid that this couldn't possibly happen, and that the structure could not be built.

Math isn't just useful in real life, it's often a matter of life and death. I've staked my life on my calculations a few times, and I've staked it on the calculations of others every day (work on the 9th floor of an office building in California--if the engineer forgot to carry a 1 the first good earthquake would also be my last).

 

[Hazel]

My dad's a civil engineer, and similar things have happened to him. One design spec came in with a triangular room whos corners added up to more than 180 degrees. Took my dad fifteen minutes to explain to the kid that this couldn't possibly happen, and that the structure could not be built.

Math isn't just useful in real life, it's often a matter of life and death. I've staked my life on my calculations a few times, and I've staked it on the calculations of others every day (work on the 9th floor of an office building in California--if the engineer forgot to carry a 1 the first good earthquake would also be my last).

Like Spell Check but far more serious. A teacher once asked me to look at a problem that she and the student "knew they had the right answer to" but the computer kept telling them they were wrong. It involved decimals. I looked at it. No decimal point. I suggested they put the decimal point . "Oh, that isn't necessary", said the teacher. I insisted. They did. The computer said 'correct'. Always that human element.

Yes, computers can be wrong and so can simple calculators. Electronics goes haywire like anything else. Students should not be allowed calculators of any kind until they understand the concept. Then they'll spot the error when they see it. But can you convince anyone of that?

 

[OrangeCatz]

In my Calc class exams, we had to leave our calculators on a table in front. We would finish part one of the exam, then turn it in for part two and our calculator. Part two would be much harder.

 

[Fredrik]

To this day I don't understand what a "set" is,

What your books and teachers have failed to explain to you is that you're not supposed to know. Since a definition of a term can only be fully understood by someone who understands the terms used in the definition, it's impossible to define everything. So something must be left undefined. Obviously, we would like to leave as few things as possible undefined, so it's pretty cool that mathematicians have found that it's sufficient for (I think) all known applications of math to leave exactly two things undefined: what a set is, and what it means for a set to be a member of a set.

You probably already understand statements like "2 is a member of the set whose members are 1,2, and 3" and "pi is a member of the set of real numbers". If you do, you already understand the two undefined concepts almost as well as a mathematician. The next step for someone learning about sets would be to learn in what ways you are allowed to construct new sets from the ones you already have.

 

[timhau]

How on Earth do they get to university - even just for interview - without knowing the alphabet or being able to read?

by bus?

Certainly not by the A-train.

 

[Rasmus]

One design spec came in with a triangular room whos corners added up to more than 180 degrees.

Did it come with blueprints?