How did you learn maths?

[Scooter]

It's an interesting article and I'm not sure whether to be amused or shocked by the idea of this 'chunking' method.

 

If someone asked me to do a sum of 27x43 I'd do (30x43)-(3x43). I wouldn't consider doing it either their demonstrated long method or chunking it into (20x40)+(20x3)+(7x40)+(7x3) - talk about long winded!

 

 

The way I see it you are looking at this from your own perspective/ability too much. After all you have chunked the original calculation into 2 chunks you are happy to mentally calculate and the add/subtract to get the answer if you were shit hot you'd just reel the answer off ........if someone you knew was not at the stage where 30x43 was simple for them to carry out how would you explain it to them? I think you'd split it into 2 chunks again or explain that when multiplying by 20, 30 etc you can just times the other number by 2, 3 and then add a zero to the end of the result........you may think they are a bit slow but if you can get them to grasp the concepts they can then break it down into (to them) managable calculations.

 

Teaching this way the bright ones will soon realise they don't need to break it down so much (or can arrive at the same and correct answer in a number of ways), some will never gain the confidence or ability to be more proficient but will be able to actually get the result using the more long winded method and some will never 'get it' no matter how long or what method you try.............but the long winded approach just gives more people the chance to succeed

[tbourner]

I know /\ chris k, theres no point filling your head with all that crap that heleped none of us, nowdays if you want to know something, whip out your blackberry and google it, its that simple. Personally school was a waste and i learnt more things outside school that i still use up to today. Biology, physics, maths, english - shakespare....whats the point?

 

The point is, waste half your life at school and the other half working, and thats you out of the way.

 

As I said in another thread:

Talking about intelligence, isn't it more to do with your ability to understand concepts? Whether they be learning a language and being able to wrap your lips around the pronunciation, learning simple to complex math, somebody explaining how something works and you understanding it - that kind of thing?

It's funny how kids always say "When will I ever need to know that" when at school/college/etc., whereas I see it as a test to learn those things - if I've been taught degree level pure maths and then get a good grade in an exam, it shows that I've understood that level of that subject, so in subjects related to it I'm likely to be quite good at understanding them easily at a high level - therefore a degree in pure maths would make me a good mathematician - or Engineer, or any other thing that involves that kind of thinking.

[caseys]

The way I see it you are looking at this from your own perspective/ability too much. After all you have chunked the original calculation into 2 chunks you are happy to mentally calculate and the add/subtract to get the answer if you were shit hot you'd just reel the answer off ........if someone you knew was not at the stage where 30x43 was simple for them to carry out how would you explain it to them? I think you'd split it into 2 chunks again or explain that when multiplying by 20, 30 etc you can just times the other number by 2, 3 and then add a zero to the end of the result........you may think they are a bit slow but if you can get them to grasp the concepts they can then break it down into (to them) managable calculations.

 

Teaching this way the bright ones will soon realise they don't need to break it down so much (or can arrive at the same and correct answer in a number of ways), some will never gain the confidence or ability to be more proficient but will be able to actually get the result using the more long winded method and some will never 'get it' no matter how long or what method you try.............but the long winded approach just gives more people the chance to succeed

 

Ok you've got me on the former there. I think though unless you have a very ordered brain, snapping off multiplication would be through repetitive memorisation of the times tables to the nth degree. Same as I can reel off 2/4/8/16/32/64/128 or 2/4/16/64/256 etc to about the 16Tb limit as a sequence because of memorisation. Yes there are savants and such and learning through repetition.

 

Yes, I suppose breaking it down to the very smallest denominator or very simple denominators does assist in learning, I just think it's possibly though dumbing down teaching and making people only take in the simplest of concepts (maths not just the only field I'd guess). Without difficult problems to solve, or complex methodology to learn I don't think many people would nurture the right mindset to take on challenges and just dismiss complex education as something that modern tooling can do for them.

 

Maybe I just think that this is one of the reasons we're no longer a country that's got a plethora of engineers, scientists and such and why India and China are catching up in the brain race. There's simplification to help people grasp basic concepts, but there's also serving up education parrot fashion.

 

As a side question Scooter, do you think proficiency in a given subject/field then can be taught? I always wondered if at a young age what we learnt/observed wired our brains / mindset to think in a certain matter then after a few years we're fixed. NLP I was quite interested in (http://www.nlpu.com/Articles/artic14.htm) after someone put me through some tests and said my hemispheres were abnormally wired

[Scooter]

 

Yes, I suppose breaking it down to the very smallest denominator or very simple denominators does assist in learning, I just think it's possibly though dumbing down teaching and making people only take in the simplest of concepts (maths not just the only field I'd guess). Without difficult problems to solve, or complex methodology to learn I don't think many people would nurture the right mindset to take on challenges and just dismiss complex education as something that modern tooling can do for them.

 

I think you would be surprised just how many people would struggle with that sort of calculation. Maybe its the lack of regimented times table learning or a dumbing down in general but there are many many people leaving school with little or no maths understanding/ability. I deal with them every day at work! With Maths some people have to work really hard or have set methods to get to someone elses 'take it for granted' standard.

 

Maybe I just think that this is one of the reasons we're no longer a country that's got a plethora of engineers, scientists and such and why India and China are catching up in the brain race. There's simplification to help people grasp basic concepts, but there's also serving up education parrot fashion..

 

I think we still produce a lot of the above its just that the opportunities are greater for the children in the other countries you mention to get higher quality and levels of education than in the past........I would agree that there is a certain parrot fashion going on but that is always going to be the case when you are trying to educate the masses, it's perhaps a teachers job to identify those of higher and lower capabilities and to push and help them respectively?

 

As a side question Scooter, do you think proficiency in a given subject/field then can be taught?

 

I think Maths in particular is a very hard one to teach. You are near always dealing in absolutes, in right and wrong and also crucially as you progress in the subject all the fundamentals are called upon and so need to be remembered, recalled and ideally become second nature, certainly if you want to excel in the field.

 

Passion and good honest hard work/study can get you far in many subjects but I think there may well be a ceiling (certainly when given a certain time frame/time input) on someones mathmatical ability. I could be wrong but I do believe Maths performance is quite hard wired into you and you are almost prediposed to being good, average or bad, with improvement through hard work being limited.

[Snooze]

It's an interesting article and I'm not sure whether to be amused or shocked by the idea of this 'chunking' method.

 

If someone asked me to do a sum of 27x43 I'd do (30x43)-(3x43). I wouldn't consider doing it either their demonstrated long method or chunking it into (20x40)+(20x3)+(7x40)+(7x3) - talk about long winded!

 

Interestingly, someone showed me this method a couple of years ago, as their child had just been taught it at school.

 

My first thought was.... "well, duh."

 

This is actually precisely the way I have been calculating long multiplications in my head for the last 25 years. No-one ever taught me to do it like this - it just seems to be the way I naturally developed to do it - but I'd never seen anyone "formalise" it until then.

I guess I never thought of doing it any other way!

 

Maybe the reason it's taught like this is precisely that - because, whilst it does make it long-winded to write down, it does make mental long multiplication easier (IMO)?

[Fitz]

"I failed maths so many times I cant even count, I was good at history though....no wait, I wasn't. Ah well it was so long ago."

 

Maths has always been a strong point for me, got a B in GCSE maths and then a B in A-Levels for Maths with Statistics. It's pretty much stuck with me although I never had much to do with numbers on My university course (Marketing Management). But, along the same lines as H, I'll work it out in my head before I attempt to smugly prove my answer right on a calculator

[Tannhauser]

NLP I was quite interested in (http://www.nlpu.com/Articles/artic14.htm) after someone put me through some tests and said my hemispheres were abnormally wired

 

NLP is a grade A gold-plated pseudoscience. I looked at your thread on homeopathy, and whilst that's bad enough (homeopathy, not your thread), I hate NLP even more. The reason being that NLP is a lot more sneaky. Homeopathy is obviously bulls**t, but NLP looks really plausible. However, it's all smoke and mirrors. They are responsible for that abomination of "kinaesthetic learners, auditory learners, visual learners".

 

If you're interested,take a look here: http://www.skepdic.com/neurolin.html

[TonyP]

I know /\ chris k, theres no point filling your head with all that crap that heleped none of us, nowdays if you want to know something, whip out your blackberry and google it, its that simple. Personally school was a waste and i learnt more things outside school that i still use up to today. Biology, physics, maths, english - shakespare....whats the point?

 

The point is, waste half your life at school and the other half working, and thats you out of the way.

 

Spaz

[Havard]

Spaz

 

You sit on that fence TonyP. Education is everything. I for one did not take advantage of the information that was given to me. I was too busy messing about, meeting girls and looking forward to break time where I could play football......

 

I was lucky that I was offered an apprenticeship by a friend of mine that got me on the first ladder in Engineering. If that wouldn't have happened then I doubt that I would have the job I have now.

 

Life is what you make of it and school gives you free advice. Always listen to free advice......

 

H.

[TonyP]

You sit on that fence TonyP. Education is everything. I for one did not take advantage of the information that was given to me. I was too busy messing about, meeting girls and looking forward to break time where I could play football......

 

I was lucky that I was offered an apprenticeship by a friend of mine that got me on the first ladder in Engineering. If that wouldn't have happened then I doubt that I would have the job I have now.

 

Life is what you make of it and school gives you free advice. Always listen to free advice......

 

H.

 

Oh well you know me:innocent:I could have explained that education and learning are never ever a waste of time. Even if you think what your learning is irrelevant to you or your life. Most thing you learn through your life you do use along the way, often without even realising. Even my o level latin.

 

But I was a bit pissed at the time so I thought my post summed it all up quite succinctly:d

[caseys]

NLP is a grade A gold-plated pseudoscience. I looked at your thread on homeopathy, and whilst that's bad enough (homeopathy, not your thread), I hate NLP even more. The reason being that NLP is a lot more sneaky. Homeopathy is obviously bulls**t, but NLP looks really plausible. However, it's all smoke and mirrors. They are responsible for that abomination of "kinaesthetic learners, auditory learners, visual learners".

 

If you're interested,take a look here: http://www.skepdic.com/neurolin.html

 

Thanks for the article A guy at work was a big Tony Robbins nut - I think even went to quite a few of his seminars abroad and even started a diet recommended by him. We were constantly ribbing him at work that he had in fact joined a cult.

 

I read NLP and thought about it's observations, but as for how it could be applied like auditory learners etc I thought was bull.

 

Tann what did you think of Myer-Biggs though? I know it's not learning per se but it is personality typing and they did a study of what they thought then a person should do career wise.

 

Statistically they said INTJ was one of the smaller types but it seems on this forum to not be the case

 

http://mkivsupra.net/vbb/showthread.php?t=158016&highlight=INTJ

 

EDIT : I should in fact read my own posts and notice you've already responded originally! I need a coffee.. though admittedly I'm asking about a slightly different context here.

[Attero]

I'm a software developer. Being a software developer, you would expect me to know maths. I am shocking at maths. I can code it, but otherwise I'm crap.

[caseys]

I'm a software developer. Being a software developer, you would expect me to know maths. I am shocking at maths. I can code it, but otherwise I'm crap.

 

Feh, logic is a math structure! True or false statements.

 

So the check in compilation is your crutch?

[martini]

Why do they call it chunking and not an array or matrix?

 

The latter would be more useful for future uses, and also sounds less like vomit and more like a sci-fi movie.

[Rob]

What annoys me about my maths and physics educmacation is that while watching University Challenge, many questions will arise and I will think "I would have known that 20 years ago, but now I've forgotten."

OTOH a lot of questions arise that I don't even understand and just sit there with a vacant gob-open stare.

 

I do the basic, "large" chunking by default now, I think its a natural way to do arithmetic. My Father-in-law is currently doing a basic maths course at Learn Direct for his own pleasure, and reading some of the questions, it was a real struggle to go back to formal, taught versions of long and short division/multiplication.

[Porky1978]

Life is what you make of it and school gives you free advice. Always listen to free advice......

 

H.

 

 

Quality post mate. Unlike you not to add a sense of sarcasm to a post, must be slacking in your old age!!

 

On another note, have you ever had any dealings with Simon Hartley's in Stoke on Trent?? Think it might be Hambaker Hartley's now.

[Attero]

Feh, logic is a math structure! True or false statements.

 

So the check in compilation is your crutch?

 

I'm always worried in case I have to solve mathematical problems on the spot at work, because I can't do it. I just can't.

 

When I'm sat working on it, I have no problem. Do you think that would stop be getting some jobs?

 

I tend to work on content and data management more than mathematical software.

[caseys]

I'm always worried in case I have to solve mathematical problems on the spot at work, because I can't do it. I just can't.

 

When I'm sat working on it, I have no problem. Do you think that would stop be getting some jobs?

 

I tend to work on content and data management more than mathematical software.

 

Interesting. Is that just pressure? Or something else?

 

I don't know, but as Harvard has said, sometimes the job you're in does put you in the spot, maybe for estimates or in a highly pressured situation (like being someone "on-call").

 

Maybe that's more analytical/logical/organisational work then. I suppose you don't do much mathmatical work with arrays and such in your programming? If you have a spare 15 minutes go back and look at the link in my post where I replied to Tannhauser about Myer-Biggs and the personality type test. May tell you a little about your thinking processes

[Attero]

I'll have a go. I think it is pressured situations, but it's also difficult maths I can't deal with. I've got better with certain stuff since school.

 

When I'm working by myself, I can work things out for myself. If I have a problem, a quick research or cheat will get me through the issue.

 

Obviously, I know my maths to an extent, otherwise I would be shit at my job. I can't quite think what the higher-standard maths is right now. But at the end of the day, where I work with content/management data it really isn't all needed.

[Havard]

On another note, have you ever had any dealings with Simon Hartley's in Stoke on Trent?? Think it might be Hambaker Hartley's now.

 

Erm no. Why?

 

H.

[Tannhauser]

What annoys me about my maths and physics educmacation is that while watching University Challenge, many questions will arise and I will think "I would have known that 20 years ago, but now I've forgotten."

 

Isn't that just the pits? I know exactly what you mean. For me, its history. Ive read absolutely masses of it, and mostly, all I can remember is what the front covers of the books looked like.

[Ewen]

Thats rather annoying....I typed out a long post only to have it timed out and lost when logging back on.

Basically, I was chattering on about no one being able to teach us what our brains cannot understand and build on. The methods are unimportant as those with innate ability will evolve beyond what was taught and how.

[Porky1978]

Erm no. Why?

 

H.

 

Just with you saying that you dealt with pressures, flow rates etc. Reminds me of what the ex wifes father does for a living, thought you may have crossed paths lol.