Time to return to basics?

Pherekydes

http://www.insidebayarea.com/argus/oped/ci_4348937

The gist is that students are not being taught the basics correctly.

My opinion is that the kids are not learning the basics properly. When I was young :rolleyes: we didn't have calculators. We had to learn off our tables, our rules of precedence, how to handle brackets and such stuff well. (OK, it was beaten into us) My son just started secondary and a calculator was a requirement. They're putting the cart before the horse, IMHO.

So what do y'all think?

vallo

I couldn't agree more. First year students just don't know their tables any more and right through to 6th year, students take out a calculator to work out simple calculations like 60/3.
Many students rote learn everything and expect to be given a set of steps to solve problems that'll come up in exams. The result is that they do not understand what they are doing or what types of problems can be solved by the mathematical techniques they learn.
Many maths teachers (possibly most) are focussed on getting the best grades from the bulk of the students and see mindless rattling off of steps to solve problems as the best way to achieve this.
We are producing generations of citizens who fear numbers, fall prey to scams and get short-changed without knowing it.
On the day of the leaving cert results, the minister for Ed actually said the words "horrible things like algebra" - there should have been an outcry. We need to dramatically overhaul the maths syllabus and the way it is taught but that doesn't look likely any time soon.

breadmonkey

Any person that found maths difficult that I have ever helped was missing the fundamentals; inability to manipulate equations and expressions being the most common and most crippling imo.

Tingo

Is it really fair to base the standards of Irish students on an American article? The are two different systems with different approaches. The article doesn't taken in account to the way, things are taught here ot how they're taught. The Leaving Cert and Junior Cert are hardly like the SATs, are they? Otherwise, there are chapter tests I presume, and well they're easy enough to do well in, before promptly forgetting all the information. There's no need to retain the skills.

The article claims that students 'never mastered the fundamentals they need to be successful at higher-level maths like algebra and geometry.' From my experience that isn't the case. Some people struggle with that, but it's the concepts that are the problem not the basic maths skills.

The article says that United States ranked fifteenth on an international maths test. Does anyone have any ideas where Ireland is on that list? The course is large, but I think in most areas in has depth. There's definitely focus. Trig and calculus are covered very well, although some sections like statistics are lacking.

A calculataor may be a requirement but I don't remember using in that much in first year in maths. It hardly helped for things such as, like the article mentioned, algebra and geometry. A maths set is also a requirement, and I know I rarely used anything in it.

Vallo, you complain about students learning things off by rote but you say that don't know their time tables? They are basically rote learning. Some things do need to be learned by rote. In the article it's actually encouraging learning off by rote over problem solving.

Using a calculator for stupid questions? I'm a hundred percent guilty of that, but is it not in someway justifable that if you're in the middle of a complex question, there are dozens of factors in your mind, and your trying to keep them all straight. It's easier to grab a calculator, because you can only hold so much in your head at once. Or maybe that's just me. I'm easily confused.

I love my calculator. :rolleyes: It helped me overcome my incredible fear of fractions when all I had to do was put in numbers. Then one day, I opened my maths book and saw some algebra question involving a quadruple fraction with a lot of X's lurking around the place. If I remember correctly, I did solve in eventually (with use of my calculator I'm sure), and it took an entire refill pad page.

Calculators have their advantages and disadvantages like everything. :cool:

I think in the Junior Cert sometimes there was questions involving rounding off numbers and getting an approximate, and then the next part involved getting the exact answer rounded off to three decimal places or whatever. That shows the basic skills are still being taught, or at very least challenged. I vaugely remember being all confused, and wondering why they were asking us something basic like that, not when they could torture us with trig or something else. Although not beaten into me, I know the bomdas and birdmas rules for handling brackets and order and what not. I doubt I'm the only one in my maths class to feel the same.

And in the Leaving Cert? Well, the last two years look like its putting more emphasis on problem-solving which means those who rely on their calculators aren't getting away with it so easy anymore.

So, does anyone have anything else to add? I'm feeling all defensive about my basic maths skills.

Nietzschean

I dunno i'd agree with the original posters, massive empasis these days is put on rote learning, though alot of that comes from revision books and the student themselves. Vast majority of my class way back when (5 odd years i suppose), would have rote learned as many questions as they could for mathematics. Its a pretty viable approach to getting at least a B1 in hons maths. Frankly LC maths is just way too easy and predictible, and the number of students who don't get even that does imply there is something wrong well before they get there...

As for cacluators, i concur, students just arn't getting enough experence even creating estimates in their heads, which are something that comes in very handy in later life. Once they leave school the odds of them having a calucator beside them is pretty low. Though correct me if i'm wrong, i though students weren't allowed use calculators doing the JC?

As for the LC, its very lacking in statistics, group theory could be done more, but mainly stats is just woefully inadaquite. Poor subject choice to teach them too, there is alot of real world applications whose statistical backgrounds can be looked at to better engage a class.(i.e. poker, gambling, odds, etc... might stop people becoming future gambling addicts too if they realise how shafted they are before they start...though i imagine anyone doing lc hons maths knows that anyway..)

[edit]
with respect to not knowing their tables, well i must say i was never very good at learning my tables off, though there isn't a need, if students get enough practice doing multiplication in their heads(which really should be done instead of rote learning tables anyway) such memorisation isn't needed.

I honistly can't think of anything up to the level of LC maths which requires rote learning.
[/edit]

Tingo

Nietschean wrote:

Frankly LC maths is just way too easy and predictible, and the number of students who don't get even that does imply there is something wrong well before they get there...

Repeating myself here. Predictible? I'm told something appeared on the LC higher maths paper last year that wasn't even on the syllabus. You can't predict that. The last two years everyone has been shocked by the maths papers. I don't know anyone complaining that they're easy. That's hardly emphasising rote learning.

Though correct me if i'm wrong, i though students weren't allowed use calculators doing the JC?

They changed the course a couple of years ago, and since then students have been allowed use their calculators. I don't know the exact year. 2001 maybe, or thereabouts.

Once they leave school the odds of them having a calculator beside them is pretty low.

It's unlikely they they'd have a proper calculator with all the fancy buttons and functions, but most mobile phones have basic calculators in them, and practically everyone (or so it seems) has a mobile now. Anyone who needs a more advanced calculator, well if they're at a computer it's no bother to google calculator and get one up onto the screen. It's easy enough to get around the problem, although granted it would probably be easier to just grab a pen and paper.

Poor subject choice to teach them too, there is alot of real world applications whose statistical backgrounds can be looked at to better engage a class.(i.e. poker, gambling, odds, etc... might stop people becoming future gambling addicts too if they realise how shafted they are before they start...though i imagine anyone doing lc hons maths knows that anyway..)

Apparently they're not allowed put gambling stuff on the exam papers. It was in my maths book, but my teacher commented that we'd never see it in the papers. It's not politically correct or it goes against some religion or something along that line, and it can't be inculded. I can't remember the exact reason he gave, just that it was stupid.

with respect to not knowing their tables, well i must say i was never very good at learning my tables off,

You teacher didn't try to make a game out of it? I vaguely some sort of thing. I think it was called Kings and Queens, but I might be making that up. It was basically a competition to see who knew their tables best and the winner got a sticker. I don't think the method was ever that effective though. :rolleyes:

I honistly can't think of anything up to the level of LC maths which requires rote learning.

Theorms. It's preferable to understand them, but if you wanted you could just memorise off everything and reproduce it. Likewise I'm sure you can understand them and not be able to write them out.

ecksor

Gah! Rote learning of theorems is worse than Hitler.

If you understand it you can puzzle it out, and more to the point you can spot any errors in reasoning you make. Proving theorems should be good for both providing understanding and illustrating proof techniques, which should be examined by presenting the student with something they haven't seen before to prove.

the_syco

Someone mentioned the dreaded tables. Never used them since I left school. Never understood them, as we were told to use them to do equations, but never told why we should use them, or what for.

As for calculators, everyone had a different type, and thus there were four groups, each learning off a different calculator, how to do a particular sum.

Someone mentioned about not having a calculator handy... good luck in finding a log book.

Delphi91

The leaving cert ordinary paper is very predictable. Each year, virtually the same questions, just different numbers. Give someone enough time and a maths book and they'll manage to get them all right in the exam. That doesn't mean that they understand what they're doing. As for this years Honours paper being different, it was the first time that students were asked to APPLY what they'd learned rather than regurgitate it. Surely that's what maths is about?

As for calculators, kids coming out of primary school use them. But I wonder how many of them actually KNOW numbers? Can anyone comment on the amount of mental arithmetic that is being done in primary schools these days?

Prof. Richard Feynman tells a very interesting story in one of his books where he is challenged to a calculation competition against an abacus salesman by the owner of a bar. Initially the abacus salesman got the result first each time, but as the calculations became more complex, Feynman took the lead. AFAIR, Feyman was doing the calculations in his head. He explained his success in the end by stating that the abaus salesman knew how to use an abacus, but he knew numbers. He was aware of relationships and approximations between numbers, logs, etc that allowed him to get answers much faster.

I wonder if we are producing a generation of abacus salespersons instead of people who know numbers?

vallo

Of course you use your tables in daily life - of all the convoluted stuff we teach, tables are thee most useful in basic everyday life. They can be rote learned as this saves time - though if students want to work out 7x6 as 7x3(=21)x2=42 thats fine by me as long as it is quick and accurate.
What I object to is rote-learning of methods, without any concern about why each step in the method is carried out or the overall purpose of the exercise. For example a bunch of 16-year-olds learned how to factor quadratic trinomials. We factor an example on the board (say x^2 + 4x + 3 = (x+3)(x+1) ) -when I ask them what will we get if we multiply (x+3) by (x+1) they haven't a clue. Some of them venture 3x^2 + 3 or something like that which shows that although they can factor some complicated quadratic trinomials they haven't a clue what the result is and although they can multiply a pair of expressions by each other in their sleep, they don't know what to do if the context is even slightly unfamiliar.
It all comes down to whether or not we are interested in students getting their points or producing a numerate population.

Nietzschean

Tingo wrote:

Repeating myself here.

My experence with LC maths finishes in 02, at which point i was slightly miffed at people being able to get decent enough grades without any understanding at all. If thats changed well then i'm happy.......

They changed the course a couple of years ago, and since then students have been allowed use their calculators.

Dumbing down maths? eww, that can't be good...

It's unlikely they they'd have a proper calculator with all the fancy buttons and functions

Its also unlikely they will need the answer to 10 decimal places, most things one can quickly work out to a resonable degree of accuracy in the brian faster than you could get a phone out.

Apparently they're not allowed put gambling stuff on the exam papers.

Well thank god they don't take that silly approach in uni, though i guess we are being sorta trained to be able to work for bookmakers and finance companies so it makes sence to know. But i dunno i can't see how showing how much the odds are stacked against you when you do gambling should be a problem....

You teacher didn't try to make a game out of it?

Nope, yet another thing i failed in early exams

Theorms.

requires is what i said, and as you've pointed out, its not needed at all....

Nietzschean

I must say if this thread has taught me anything , it'll be if/when i ever have kids i won't be trusting any teachers to teach them maths......

[no offence to any teachers present....but your as aware as anyone how woefull people you work with can be....]

Nietzschean

the_syco wrote:

Someone mentioned the dreaded tables. Never used them since I left school. Never understood them, as we were told to use them to do equations, but never told why we should use them, or what for.

Why? syco you use/work with computers, whats 16 by 16? any sort of programming you run into frequent calculations, which really come down to tables sort of multiplication.... (unless your very lazy)

As for calculators, everyone had a different type, and thus there were four groups, each learning off a different calculator, how to do a particular sum.

while indvidual calculator's properties learning can be usefull to speed some stuff up if you understand the overall concepts of programming calculators you should be able to swap between them handy anyway....

Someone mentioned about not having a calculator handy... good luck in finding a log book.

Emm how about using your brian? you tend to bring that aroudn alot i presume

breadmonkey

Using a calculator for stupid questions? I'm a hundred percent guilty of that, but is it not in someway justifable that if you're in the middle of a complex question, there are dozens of factors in your mind, and your trying to keep them all straight. It's easier to grab a calculator, because you can only hold so much in your head at once. Or maybe that's just me. I'm easily confused.

I love my calculator. It helped me overcome my incredible fear of fractions when all I had to do was put in numbers. Then one day, I opened my maths book and saw some algebra question involving a quadruple fraction with a lot of X's lurking around the place. If I remember correctly, I did solve in eventually (with use of my calculator I'm sure), and it took an entire refill pad page.

I'm sorry but you're proving mine,vallo's, slow coach's etc point here. You needed your calculator for very rudamentary things. You were afraid of fractions ffs.

Someone mentioned the dreaded tables. Never used them since I left school. Never understood them, as we were told to use them to do equations, but never told why we should use them, or what for

This is rediculous to say the least. I would say it's actually harder to not use tables on a daily basis than to do so.

Aero787

I'm a 6th year student. I was very fortunate to have an UNBELIEVABLE maths teacher for my Junior Cert. He gave us an excellent foundation in maths.

Do I use a calculator? Yes, to speed up certain calculations (particularly in accounting) if I'm in a rush. Sometimes for inverse sine, log functions, if I have to go well into decimals, etc. the calculator will come out to speed things up. However, I use my head as often as I can because it can be faster than using a number cruncher. Calculators are to be used sparingly.

Rote learning theorems? I learned to understand them. I thought that was the point.

As for the LCHL course, I think it's fine. I suppose the area where it truly is lacking is the real world application of maths. Students don't know how certain parts of the course are used!

I do agree that there can be a fear of maths among people. That's presumably one of the reasons why interest in engineering courses is waning and why people are going for business courses.

Next year I'll be doing engineering in college. I think it'll be a fresh start and I'm really looking forward to it. Challenging - yes, I hope so!

You can pick faults with any education system, but overall the LC isn't too bad. There should probably be some syllabus changes, particularly for Maths, Irish and English, but overall it provides a good broad education. Rote learning can be a problem, but I was fortunate enough to be taught to think for myself. I prefer to understand things rather than learn by rote - is this a detriment to my LC results? I hope not. But, I'll get over the faults.

If anyone wants to tell me what engineering maths is like at college, please do!

Don't tar everyone with the same brush!

Aero787

I forgot to say that the LC Maths textbooks (well mine anyway) is crap. We need proper books with proper questions! (The same could be said for accounting. My teacher teaches accounting from the exam papers!)

Sir Digby Chicken Caesar

This is rediculous to say the least. I would say it's actually harder to not use tables on a daily basis than to do so.

you'd think so, but I've been asked by about seven differnet people in the past month while playing board games (none of whom I would have thought were particularly stupid) whart 6X4 was, or 8X5 ...

it's scary.

breadmonkey

Aero787 wrote:

Do I use a calculator? Yes, to speed up certain calculations (particularly in accounting) if I'm in a rush. Sometimes for inverse sine, log functions, if I have to go well into decimals, etc.[/U][/B]

Aero, these are situations where using a calculator is obviously the way to go. No one is saying that we should re invent the wheel for every little question. There is no sense in trawling through your tables to find sin-1(0.12769872349873). It's using it to do basic mental arithmetic that is the problem (among other things).

breadmonkey

Mordeth wrote:

you'd think so, but I've been asked by about seven differnet people in the past month while playing board games (none of whom I would have thought were particularly stupid) whart 6X4 was, or 8X5 ...

it's scary.

That is scary.

Sir Digby Chicken Caesar

yeah, I have a sliding scale for those sort of questions... anything X 7 I'll give the person the benefit of the doubt and assume they're just not willing to add a number 7 times... but 6X4?

Tingo

breadmonkey wrote:

I'm sorry but you're proving mine,vallo's, slow coach's etc point here. You needed your calculator for very rudamentary things. You were afraid of fractions ffs.

I didn't have a calculator then. It was in primary school when I was ten. I'm pretty sure then I was probably afraid of ghosts and monsters under my bed too. :rolleyes: Hardly substantional fears.

It just helped me understand the relationship between fractions and decimals. I never consciously understood until then why, for example, a fifth equalled .2. Pretty obvious, yeah, but I guess I must have been daydreaming or something when that was taught. I never copped it until I was messing about with my dad's calculator (after reading some short story in school about a calculator that spelled words ) I learned fractions the good ol' fashioned way before coming across a scientific calculator...and it's just too much of a pain to put in fractions for the effort to be worth it, I find. It's not the right reason for not using a calculator. I do use mine too frequently, but I'm not completely dependent on it.

Someone mentioned the dreaded tables. Never used them since I left school. Never understood them, as we were told to use them to do equations, but never told why we should use them, or what for

Are you talking about times tables or log tables? I wouldn't call those basic sums equations, so I'd think latter, but everyone else seems to think differently so...:p

breadmonkey

No offence Tingo but if you couldn't understand why 1/5 = 0.2 then you were daydreaming while they were teaching division.

Tingo

breadmonkey wrote:

No offence Tingo but if you couldn't understand why 1/5 = 0.2 then you were daydreaming while they were teaching division.

Quite possibly. Teachers always tended to put my beside the window, and it was my undoing.

It wasn't the division as such. From what I remember, we were basically given a list of fractions and their decimal equilvents. This means that. One fifth is .2. And that was that. Learn them all off by heart. There should have been more. Maybe there was. Either I'm way better at not listening than people give me credit for or I was out sick for a few days. I don't know.

At any rate myunderstanding of fractions was limited. I was too occupied with using the skills I just learnt, adding and subtracting them and all the rules that came with that, to think about fractions in a wider context. I was disinterested in the whys and hows, and maths in general once I got the right answer.

And with the pretence of being on topic, by reading this thread the message (Well in part) seems to be that rote-memorisation is necessary in primary school, that's how the kids should learn tables and everything, and then when they go into secondary school, forget memorisation, you have to understand it, and problem-solve. Problem-solving is the only way to throughly understand a concept. And that in reality kids are doing in backwards, not memorising their basics, but trying to memorise everything for the Leaving Cert. Or am I just taking people's words out of context?

breadmonkey

Nobody is saying that rote memorisation is how everything must be learned in primary school. This was only said in reference to tables. Learning decimal equivalents is fine I suppose as long an understanding of how to get them is also learned.

JimG

Read through this thread tonight for first time. I'd just like to say that despite the comments in the newspapers by people who should know better, there was no truth in the assertion that a Calculus question on a Maths paper (Higher) a few years ago needed a knowledge of Applied Maths to solve. Such "authoritative" statements by "experts" do a disservice to everyone, especially the students.

breadmonkey

JimG wrote:

Read through this thread tonight for first time. I'd just like to say that despite the comments in the newspapers by people who should know better, there was no truth in the assertion that a Calculus question on a Maths paper (Higher) a few years ago needed a knowledge of Applied Maths to solve. Such "authoritative" statements by "experts" do a disservice to everyone, especially the students.

I think that was year I did the LC but I wouldn't have noticed since I was doing applied maths as well. WHat was the question?

JimG

I think it was Question 8(c)(iii), Paper 2, 2003

breadmonkey

JimG wrote:

I think it was Question 8(c)(iii), Paper 2, 2003

Lol, I don't have the ol' papers any more! I was the year after though.

Michael Collins

breadmonkey wrote:

Lol, I don't have the ol' papers any more! I was the year after though.

Good Aul (as Bertie would say) examinations.ie has the answers (or in this case...the question)

http://www.examinations.ie/archive/exampapers/2003/LC003ALP200EV.pdf

breadmonkey

I dunno, are the equations of motion on the Leaving Cert Maths syllabus?

Tar.Aldarion

I didn't do applied maths for the LC, you didn't nned to for that question. People thought you did. If you can solve something with applied maths, doesn't mean you have to.
People always give oput about things on the maths papers, when we were going through past ones my teacher would point out the controversial ones. The 'hardest' one was where you had to let t equal to a number and it was very awqward, it would have taken ages, unless they had a bit of cop on and put t as 0.
Simplist question on the paper then.

Reading this thread almost makes me want to go and start teaching maths...