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How early should we teach our children algebra (and calculus if will)?
I'm in my 2nd year of university, and it has done wonders to the way my mind works. I know not everybody is good at math, so the question in my topic is sort of rhetoric. I just want your opinions: how can we quicken the education process by introducing to our children more advanced topics at as early of an age as possible? Can we alter the education system so that we can improve the standards of humanity and the capacity for knowledge?
I was pondering this as I walked home after having hung out with some friends and thinking about their debates. The dawn of civilization started ~5000 years ago (maybe give a few more thousands) and we had barely any knowledge when it started. Since then, with the introduction of government, politics, structure of society, then science, philosophy, and entertainment, our knowledge pool has exponentially increased to the point where one can barely learn EVERYTHING (up to their current time) in a lifetime. However, 5000 years is only about 200-250 generations - barely a millimeter's worth of time within the meters of the Earth's history. With evolution (assuming that it happens, for all you fundamentalists ), human brain capacity has grown enough so that we are able to obtain and discover knowledge of up to 130+ year's worth; along with our processing power coming from our pre-frontal lobes, we are pretty advanced beings compared to the rest of the taxonomy. Of course, no one could survey human beings 5000 years ago (or even before the ice age) to find out what the brain capacity was at that point. One can postulate that our capacity has been increasing during these 225 generations as needed (based on the amount of knowledge increased), and if you can imagine a graph, our capacity is slowly increasing while knowledge is an exponential function that has yet to reach the capacity slope.
(For example, we could time travel back several thousand years ago to kidnap obtain an infant and let it live in our age. We can find out the capacity by seeing if it may learn as quick as current humans do, or be labelled a retard by society.)
On a side note, I think many of you who claim to be 16 (+/- 2) years old are actually 20+'s who just want internet credit/to troll professionally. That or I am an above average slow learner who's rate of improvement is diminished by the intelligence you people bring to these forums (or anyplace, for that matter). Not to say you are not to be believed, nor am I an egoist/elitist or stupid.
Actually, continuing from that note (and the thread title), I have been in an unlucky situation where my educational system sucked the life out of my first 17 years; I really wished they taught me algebra and calculas earlier, but unfortunately my school/area/everywhere was/were plagued with people with a lower learning capacity (for knowledge) than me (they may had a higher social capacity, and I may have just traded off capacities WHO KNOWS ). I did not learn about complex numbers until a semester ago when they were introduced so I could do second-order differential equations; Canadian history is uninteresting as my American neighbours had 100+ more years of more interesting history than us (damn you, neighbours!); my entire grade 8 math consisted of a review of grade 7 (which sucked); in physics (my concentration), they did not bother with teaching about waves and optics until I reached my 2nd year and OH GOD WHAT THE **** WAVES AND OPTICS EVERYWHERE. So yeah my elementary and high school education system sucked.
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas) and (today, an hour ago) the definitions of transparent, translucent, and opaque (Glass reflects, but shouldn't we see through glass? Why are certain colours described as "opaque" when opaque means it doesn't let light through/can't see the other side?). Do they have the capacity to understand such though processes? Can they?
As a disclaimer, I am not in biology nor teacher's education. I am a PHYSICIST dealing with REAL PHYSICS PROBLEMS (no, metaphysics is not a part of REAL PROBLEMS).
I was pondering this as I walked home after having hung out with some friends and thinking about their debates. The dawn of civilization started ~5000 years ago (maybe give a few more thousands) and we had barely any knowledge when it started. Since then, with the introduction of government, politics, structure of society, then science, philosophy, and entertainment, our knowledge pool has exponentially increased to the point where one can barely learn EVERYTHING (up to their current time) in a lifetime. However, 5000 years is only about 200-250 generations - barely a millimeter's worth of time within the meters of the Earth's history. With evolution (assuming that it happens, for all you fundamentalists ), human brain capacity has grown enough so that we are able to obtain and discover knowledge of up to 130+ year's worth; along with our processing power coming from our pre-frontal lobes, we are pretty advanced beings compared to the rest of the taxonomy. Of course, no one could survey human beings 5000 years ago (or even before the ice age) to find out what the brain capacity was at that point. One can postulate that our capacity has been increasing during these 225 generations as needed (based on the amount of knowledge increased), and if you can imagine a graph, our capacity is slowly increasing while knowledge is an exponential function that has yet to reach the capacity slope.
(For example, we could time travel back several thousand years ago to kidnap obtain an infant and let it live in our age. We can find out the capacity by seeing if it may learn as quick as current humans do, or be labelled a retard by society.)
On a side note, I think many of you who claim to be 16 (+/- 2) years old are actually 20+'s who just want internet credit/to troll professionally. That or I am an above average slow learner who's rate of improvement is diminished by the intelligence you people bring to these forums (or anyplace, for that matter). Not to say you are not to be believed, nor am I an egoist/elitist or stupid.
Actually, continuing from that note (and the thread title), I have been in an unlucky situation where my educational system sucked the life out of my first 17 years; I really wished they taught me algebra and calculas earlier, but unfortunately my school/area/everywhere was/were plagued with people with a lower learning capacity (for knowledge) than me (they may had a higher social capacity, and I may have just traded off capacities WHO KNOWS ). I did not learn about complex numbers until a semester ago when they were introduced so I could do second-order differential equations; Canadian history is uninteresting as my American neighbours had 100+ more years of more interesting history than us (damn you, neighbours!); my entire grade 8 math consisted of a review of grade 7 (which sucked); in physics (my concentration), they did not bother with teaching about waves and optics until I reached my 2nd year and OH GOD WHAT THE **** WAVES AND OPTICS EVERYWHERE. So yeah my elementary and high school education system sucked.
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas) and (today, an hour ago) the definitions of transparent, translucent, and opaque (Glass reflects, but shouldn't we see through glass? Why are certain colours described as "opaque" when opaque means it doesn't let light through/can't see the other side?). Do they have the capacity to understand such though processes? Can they?
As a disclaimer, I am not in biology nor teacher's education. I am a PHYSICIST dealing with REAL PHYSICS PROBLEMS (no, metaphysics is not a part of REAL PROBLEMS).
Capacity throughout the History of the Human species has remained the same and children have a higher rate of learning than adults, the issue here is efficiently passing on relevant information to the relevant people. Suffice to say, the average person does not need to know advanced mathematical formula and such investment of time and money in doing so would be a folley. The education system is far from perfect, but to be fair - most children shouldn't be learning calculus and algebra etc before age 12; they should be busy being kids and defining themselves. Thereafter one can seek out the further education they need, and should one be motivated, autodictat to themselves alongside standard education.
WarmEye
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas) and (today, an hour ago) the definitions of transparent, translucent, and opaque (Glass reflects, but shouldn't we see through glass? Why are certain colours described as "opaque" when opaque means it doesn't let light through/can't see the other side?). Do they have the capacity to understand such though processes? Can they?
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas) and (today, an hour ago) the definitions of transparent, translucent, and opaque (Glass reflects, but shouldn't we see through glass? Why are certain colours described as "opaque" when opaque means it doesn't let light through/can't see the other side?). Do they have the capacity to understand such though processes? Can they?
That seems a bit extreme. How can the child understand calculus without relevant prior mathematical knowledge? I think that children around the age of 4~6 should be learning the basics in arithmetics, that is, addition, subtraction, multiplication (up to 10x10 or further), and division. I learned calculus last year and was introduced to imaginary numbers 2 years ago.
Personally I find "Child Geniuses" to be something akin to cruelty to children. These kids are drilled calculus and math at an early age, removing likely their ability to interact with others. Furthermore, their despair fuels a sense of self accomplishment in their "genius", which is a hubris that ultimately leads to incompatibility in the workplace and society (no need for cocky geniuses at work, no matter how smart you claim to be). Being homeschooled like that only worsens the situation, as interaction is diminished even further. Parents who subject their children to such regimens are simply living vicariously through their children's successes without fully grasping the ramifications said actions will have on the rest of their children's lives.
The current education system is fine. It works well, and it should be here to stay. No need to push the bill too much, because the learning process is all you can really squeeze into them at an early age. If you drill in algebra and calculus then, you don't instill a desire to learn but instead a desire to memorize. This limits the creativity that sets Western Education apart from Eastern Education (where people memorize like no other). Introducing the option to learn higher math will of course be incremental, but I don't expect them to understand my textbooks on vector calculus anytime soon, and that's just fine with me
The current education system is fine. It works well, and it should be here to stay. No need to push the bill too much, because the learning process is all you can really squeeze into them at an early age. If you drill in algebra and calculus then, you don't instill a desire to learn but instead a desire to memorize. This limits the creativity that sets Western Education apart from Eastern Education (where people memorize like no other). Introducing the option to learn higher math will of course be incremental, but I don't expect them to understand my textbooks on vector calculus anytime soon, and that's just fine with me
How early should we teach our children algebra (and calculus if will)?
I think it's good to specialise earlier than we already do.
When I was 11 years old, I would have just loved for all my Art/DT and History lessons to be replaced with Maths lessons. And I would have probably learnt about calculus earlier, if that had happened.
True, I'd probably end up not being able to draw a picture of anything. But then that doesn't really matter to me.
There are some things which are quite obviously going to be useless to teach a child, because they've already got to the stage where they know what *kind* of things they want to do later. The other good thing about early specialisation is that (apparently) children learn faster when they're young.
When I was 11 years old, I would have just loved for all my Art/DT and History lessons to be replaced with Maths lessons. And I would have probably learnt about calculus earlier, if that had happened.
True, I'd probably end up not being able to draw a picture of anything. But then that doesn't really matter to me.
There are some things which are quite obviously going to be useless to teach a child, because they've already got to the stage where they know what *kind* of things they want to do later. The other good thing about early specialisation is that (apparently) children learn faster when they're young.
When we teach it now is early enough. God kid in the UK seem to grow up to quickly as it is, try to at least give them some sort of childhood.
WarmEye
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas)
I also often think about how to teach my children things such as math (my high school calculas teacher taught her 4 year old calculas)
For what it's worth, some countries in the western world attempted to teach advanced mathematics (such as set theory, functions and algebraic structures such as groups) at an earlier age than was usual. The result was more or less abysmal failure and has largely been abandoned.
I very much doubt your teacher did teach her 4 year old calculus. The rudiments of tangents and approximate areas perhaps, but even hot house 4 year olds will lacks both the necessary background or the maturity to appreciate anything worthy of the name calculus.
Probably when the child knows all his/her stuff clearly and has a solid foundation...that's probably the best time to do algebra and calculus, if that's possible.
If the child is having difficulties with math already...you can delay the process, support his/her foundation in math, and wait until he/she is ready to do so.
If the child is having difficulties with math already...you can delay the process, support his/her foundation in math, and wait until he/she is ready to do so.
I'm more concerned about people getting to grips with the basics. Only about 50% of kids leave school with 5 GCSE's at level C or above (I believe this is what the government believes is to be regarded as a "basic education") and an astoninshing 1 in 5 don't even manage 1 GCSE at level C.
Combine these appalling statistics with the brain drain of the country's brightest and best and I predict that Britain will essentially be a nation of orangutans by about 2030.
Combine these appalling statistics with the brain drain of the country's brightest and best and I predict that Britain will essentially be a nation of orangutans by about 2030.
I learnt the basics of calculus when I was 14, it seemed a complete nightmare for the first 2 weeks(chain rule? wtf?), then it just started to click and make sense. We did the more advanced stuff next year and did complex numbers around the same time as well. I would say 14-16 is the right time to start teaching advanced algebra and calculus, any earlier and most people wouldn't get the idea anyways. Advanced calculus(like vector integretion) must be left to university.
There should be no answer.
Consider this: A is 20, has been learning guitar for 5 years, and plays it with near-professional standard; B is also 20, has been learning guitar for 5 years as well, but still, unfortunately, could not play it. Suppose a tutor is employed to give lesson to both. Should he teach them at the same time with the same materials?
If your answer is no, you should agree that each child is different, and should be taught differently. Some could be taught calculus in 12, while some should never been taught (like those take no Maths/Science in A-levels and proceed to an English/languages course in university).
Consider this: A is 20, has been learning guitar for 5 years, and plays it with near-professional standard; B is also 20, has been learning guitar for 5 years as well, but still, unfortunately, could not play it. Suppose a tutor is employed to give lesson to both. Should he teach them at the same time with the same materials?
If your answer is no, you should agree that each child is different, and should be taught differently. Some could be taught calculus in 12, while some should never been taught (like those take no Maths/Science in A-levels and proceed to an English/languages course in university).
NEVER!!! I learnt a little of it at mths GCSE has done me no good at all and i feel i am doing well academicaly...i find sciences ....um boring 
Howard
I'm more concerned about people getting to grips with the basics. Only about 50% of kids leave school with 5 GCSE's at level C or above (I believe this is what the government believes is to be regarded as a "basic education") and an astoninshing 1 in 5 don't even manage 1 GCSE at level C.
Combine these appalling statistics with the brain drain of the country's brightest and best and I predict that Britain will essentially be a nation of orangutans by about 2030.
Combine these appalling statistics with the brain drain of the country's brightest and best and I predict that Britain will essentially be a nation of orangutans by about 2030.
Your optimism has always been my favorite quality in you.
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