what does algebra leave people with such dread?

what does algebra leave people with such dread?

This really baffles me. I forget how we got onto this but i was talking to a friend today who said he went up to his teacher and asked "you prove one time i will ever need algebra" My responce was "you use it all the time" and the example I used was converting my cars fuel economy from Km\L into L\100Km (because i was plugging it into my GPS recently) and his responce was "i dont need to know fuel economy". Then i rembered he was a nurse so i asked him "do you ever do drug calculations?" (knowing dam well he did them all the time), his responce "but thats not algebra, thats drug calcs". I just rembered that this conversation is an almost exact duplicate of a conversation years ago between my mum (a teacher) and a friend of hers who was also a nurse.

So what is it about the way algebra is taught which turns something used everyday (for instance working out the price difference between 2 different items at a supermarket which almost everyone ESPECIALLY women do automatically) into something which seems to fill people with dread?

 

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I have grappled with this. I used to get 100% in geometry and barely make it in algebra. I hold algebra responsible for many tears, frustrations and unhappy test results, I also hold it responsible for bringing down my average so that I never ever came first in school [always 2nd or even 3rd]

I only discovered a liking for it after I found a copy of Hall and Knight at a used book sales, which I picked up because I had liked a poem about it.

Hall and Knight
or 'z + b + x = y + b + z'

When he was young his cousins used to say of Mr Knight:
'This boy will write an algebra - or looks as if he might.'
And sure enough, when Mr Knight had grown to be a man,
He purchased pen and paper and an inkpot, and began.

But he very soon discovered that he couldn't write at all,
And his heart was filled with yearnings for a certain Mr Hall;
Till, after many years of doubt, he sent his friend a card:
'Have tried to write an Algebra, but find it very hard.'

Now Mr Hall himself had tried to write a book for schools,
But suffered from a handicap: he didn't know the rules.
So when he heard from Mr Knight and understood his gist,
He answered him by telegram: 'Delighted to assist.'

So Mr Hall and Mr Knight they took a house together,
And they worked away at algebra in any kind of weather,
Determined not to give up until they had evolved
A problem so constructed that it never could be solved.

'How hard it is', said Mr Knight, 'to hide the fact from youth
That x and y are equal: it is such an obvious truth!'
'It is', said Mr Hall, 'but if we gave a b to each,
We'd put the problem well beyond our little victims' reach.

'Or are you anxious, Mr Knight, lest any boy should see
The utter superfluity of this repeated b?'
'I scarcely fear it', he replied, and scratched this grizzled head,
'But perhaps it would be safer if to b we added z.'

'A brilliant stroke!', said Hall, and added z to either side;
Then looked at his accomplice with a flush of happy pride.
And Knight, he winked at Hall (a very pardonable lapse).
And they printed off the Algebra and sold it to the chaps.

-E. V. Rieu ( Emile Victor 1887-1972)

But I am still prejudiced against it. :bugeye:

 

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I think the problem is that the schools separate mathematics from reality and treat it like this abstract never-never land garbage and then years later they want to reatach the mathematics to reality.

They never should have disconnected it in the first place. There should not be math teachers in grade school. There should be physics teachers that teach the math as the need it to understand the physics. Then the kids will never separate the math from reality.

Our educational system compartmentalizes knowledge too much and confuses people more than it helps them. It creates lots of jobs for educators though.

That is another problem with school. You are not supposed to be motivated by curiosity. You are supposed to be motivated by competition. If you don't care about the competition then the teachers think there is something wrong with you. Do the 3 hardest of 10 homework problems and throw it in the garbage but always get A's on the tests then the teacher give you a B because you didn't do the homework. But A's on the test prove you know the subject. Tell the teacher to kiss your ass. But then you get detention. ROFL

psik

 

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psikeyhackr I totally agree. Another way to bring mathematics back to reality could be to teach chaos science in elementary or middle school - not only because it would be captivating to kids with its seemingly "alive" and beautiful shapes but also because its basics are the simplest of algebra equations. There would be instant reward for the work the students put in and also freedom for more curious students to explore the world of strange attractors on their own.

 

Algebra seems to be one of those things that males learn (and use) much easier than females do.

I read a news article not long ago in which a study was made that apparently explained at least a part of why that is so. Female math teachers feel somewhat inadequate at the task and project that inadequacy onto their female students. Another thought was that girls don't grasp logical formats and symbolism as readily as boys do.

And yet another thought - which I totally agree with - is that at the moment a girl feels overwhelmed by some subject like algebra, they completely loose their place in the learning process and cannot progress very well from that point. It's sort of like "I'll never understand this stuff" so they cannot build upon the little they've already learned and more or less just stop trying.

If any of you have ever missed a week of algebra class due to the mumps or whatever, you KNOW how difficult it is to ever catch up again! For some it's practically impossible.

 

I have had some success, with some students, completely disconnecting the algebra from any reality at all.

I recall one student suddenly "getting it" after taking the suggestion that the little letters were just letters - they didn't "stand for" anything - for example.

Others seem to do better by involving as much physical manipulation as possible - moving stuff around, using an actual physical balance beam, drawing their own graphs by hand, physically "feeling" the "pressure" of the relationship being graphed.

People do not all think alike - that's not just a truism.

What seemed to me to be the biggest handicap facing most students in their first year of calculus was a lack of basic theory, a gap where there should have been something they could go back to when their rules of thumb failed them. This was startlingly visible in, for example, confusions involving negative numbers in complicated expressions.

Physical models or illustrations of negative numbers - temperature scales, forward and backward motion, etc - need to be detachable in such circumstances. They can make things much harder than necessary.

And the fact that they don't need to be considered - that physical interpretation can be left to the initial setup and the final interpretation, and ignored in between - is maybe a great insight, and source of power, of mathematics in the world.

There's a statistical problem: At the levels of schooling at which female math teachers predominate, most teachers seem inadequately prepared in the subject, at least in the US.

The parallels between the reasons advanced for girls underperforming in algebra now, and girls underperforming in Latin and Greek back when, are close enough to recommend a certain humility in the speculations.

 

Dread over... algebra...? I always thought the really difficult things in math (roughly in descending order of difficulty) are :

• minus signs,
• index/variable substitutions in summations/integrals, and
• normalisation constants, factors of \(2 \pi\), etc.

 

i agree 100% with your comment about women losing confidence but i disagree with the coment that women generally cant do this. To go back to my origional post who does the shopping? If you have a 400g packet for x and a 500g packet for y which is better value?

Then there are the drug calculations Registed nurses do EVERYDAY so that the pts get the right doses of medication (which is the nurses responcability, not the doctors)

These 2 groups especially tend to be both women. In the case mum was talking about the nurse felt she was unable to help her son with his grade 6 maths homework because "i dont get algebra". We arnt talking about the advanced stuff like calculs which is used mainly by engerners but the basic stuff like 2x+50=100

 

If it was taught in context people would and do appreciate it more. When it is taught out of context, dry and boring, as it generally is in school, that very boredom makes it scary. People learn things more easily in context. They have motivation then, even excitement. But we pulled education out of life, abstracted it, turned into what often feels like busy work. Lazy, uncreative pedagogy.

Me, I as afraid of trigonometry

and I am pretty damn sure I have not needed it since.

 

i agree with you, i was facinated by maths right up to the point that i learned the square root of neg 1 was i and my comment was "so what? whats the point?". Since school i havent used calculas or trig or square root of neg numbers ect but i have used basic algebra everysingle day. Possably not fully expressed but rather in my head to switch things around so that i could plug them into a calculator to work out an answer (or to be able to look at a drug chart and get a doseage). As i said the first thing which poped into my head was the fuel economy because i had only just done that (i was driving around for a week trying to work out why the GPS thought i was using 40L\Km before i realised it was per 100ks rather than k\L) but drug calcs and while shopping are also times when everyone uses it without even thinking about it

 

Aww, that's too bad, complex numbers are such beautiful and fascinating things

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they are also compleatly useless, so what if the square root of neg 1 = i it doesnt tell you ANYTHING and has almost no practical aplication in the real world. You could just as easerly say it equaled Unicorn with as much importance

 

I do hope that was meant as a joke.

 

i said ALMOST (i know its used in vibration of bridges)

 

Imaginary and complex numbers are not useless, they are used extensively in Maths and Physics. Obviously it doesn't matter whether you call it i, Unicorn or Jeremy Paxman, the conceptual leap involves realizing that the square root of -1 is a number yet it clearly does not lie on the 'normal' (real) number line.

 

They're useful because of Euler's formula and because you can write any complex number as \(z \,=\, A e^{i \theta} \,=\, A \bigl( \cos(\theta) \,+\, i \sin(\theta) \bigr)\). In physics and engineering, a complex number is most usefully thought of as a sort of "number" with both an amplitude and a phase, which usually makes complex numbers useful almost anywhere you're dealing with waves or oscillations. Exponentials are usually much easier to deal with than sines and cosines.

 

One of the scariest experiences for first year students at Uni, is when they go to their first computer lab.
Here, they are supposed to be clever enough to write some code that formulates some problem (print the area of a circle, given a radius, say), and are required to use a compiler like, say FORTRAN, or C++, or whatever (usually the first year lab is obliged to use the language decided on by the lecturer).

It's an exercise in applied math, using an algebra that corresponds to instructions, loops and tests etc. The scary thing I noticed as a lab assistant/tutor was that most of the male students see this as a test of their ability to perform, on some level.

I recall having a definite sense of dread about my first lab, and how a totally irrational fear arose in my mind about doing something wrong (maybe blowing the computer up), which was completely groundless, because I had done electronics and I knew already that it was just a dumb electronic machine--it wasn't going to take revenge on me for daring to challenge its logic, for god's sake.

So I suppose the fear was me redirecting some other anxiety--which these days I qualify as "being able to perform mathematically, on demand". This is a challenge for anyone, but males seem to feel it more acutely; the ability to be rational and "do the math" is an advantage, obviously, so perhaps male students are unconsciously competing for this advantage...? Which explains why math is so confusing, for males with a female teacher.

 

Why does algebra cause so much dread?
I would have thought it was obvious:

W.v[sup]2[/sup]=k.d[sup]3[/sup].(t/d)[sup]n[/sup]

Just solve that for k and you've got the answer...

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Hello Asguard

Algebra is so dreadful because it asks you to use your brain, and use it analytically.

LC, Ph.D., Los Alamos National Laboratory.
Los Alamos, New Mexico