Math Is Fun Forum

<-- not as young as you think. 23 is still young but past the age where I have time to discover myself. Luckily I have a general idea of my passions. I admire your Pollyannaism though. I'll just enjoy the subject for the moment.

This is a GCSE syllabus question for 15-16 year olds usually which is taken at the end of school here in the UK. They don't covere parabolas at that level. They just touch on reciprocal graphs. Also this question was on the first or second page and not at the back and they don't require you to understand that much.

What's the last answer? oh - 5

x = -1 and y = -1

I think I understand what you're saying. It's the same with this game Street Fighter I used to play. In fighting games you could learn certain combinations of keys to do different moves and combos. Some of these were very easy to learn. Towards the end commbos would become more difficult to learn because of how advanced they were. Even after learning a large portion of procedures you can use, it still didn't make you good. You would need to be almost fluent to pull them off in game.

Certain knowledge bases were only useful for certain situations. The advanced procedures were rarely ever used because of not being feasible. It would often be best to use the most simple techniques in creative ways rather than the advanced stuff. All of that would come with experience.
The people considered the great players would raise the bar by using some known procedures in ways nobody really has before. They would understand the mechanics in ways nobody had noticed and exploit it.

Outsiders watching couldn't see what was so interesting about a game. However any decent player could tell that the person assessed multiple different possible outcomes in a fraction of a second and reacted with the best procedure given their circumstances. The best players would figure out the mechanics of the game somehow. They would find out that this has priority over that, moves at this speed so if they react to x,y or z in 1/3 of a second then they can counter it.

It only took maybe 100 hours to get decent at the game but to compete at a high level it would take a lot longer because you would have to turn procedures and their best use in different situations into a reflex or instinct. It was like you could get into the top 60 % of players with only 200 hours learning and practice but for each 10% bracket higher you went the effort to get there doubled.  To get from the top 40% to the top 30 you would need to put in 400 hours or something. Some people were naturally good at these things. I competed in the B league and everytime I got to A I was kicked out. I reached a brick wall where I couldn't compete unless I could relegate complex combinations, mechanics, and reaction times into instinct and focus on reading the opponents.

Getting good at mathematics will probably be similar I guess. Part of problem solving is knowing the problem, and knowing what tools are relevant to solving it. I got good at these games by learning the techniques, seeing how the greats used them, and experimenting myself. You can't really watcha mathematicians thought process and step by step solutions to a problem right? Anyhow this has given me some insight into the issue.

Welcome young mathmaknight knightstar.

This means I haven't really mastered anything in mathematics. Not even number theory lol.

Thanks again. How do you find all ths stuff?

Gracias. I can't get answers to questions like this from textbooks.

lol yes mathematics is a form of escapism for me too. My mind focuses on the problem and every other issue in life dissolves into non existence for the moments I'm solving the problem.

Are you in the USA? I went to a school in Michigan there and the education was bad but I didn't think it was that bad. So what are the people over there working as if they're poorly educated?

The issue with public education is that it's not there to educate students and bring out their potential. That is an indirect effect if it happens. It is there to mold the children to fit roles that society supposedly needs at the time. Success in school is determined by your ability to follow orders, memorize and regurgitate what you're told. That's training children to be obedient rote memorizing machines.

Some children become terribly bored with this robotic process spanning the course of years so don't do well. These children may be good at a subject but don't get into it because in school its a boring passive process. Society doesn't care about their talents unless it benefits society. Society will try to mold people into what it needs. In my grandparents era they molded them into factory workers. In my mums they molded the lower classes of people for clerical work, construction etc. Just things needed for the functioning of society. The politicians, think tank workers, scientists almost exclusively come from the upper classes unless the person from a lower class stands out and makes it through thte school system to an Ivy league university.

Society's needs take precedence over individuals needs. A person may want to paint, act, sing, do stand up, but there's ample supply of entertainers. The education with my generation totally failed because technology progressed so fast and the recession hit in 2008. There aren't many low skilled jobs anymore for which we were trained. There are service and retail jobs which are usually given to the attractive young women. There are trades like plumbing, bricklaying etc which are almost exclusively done by men.

The government is now trying to change the school curriculum and are offering companies cash incentives to employ young people for 6 months or more. People can be good at lots of different things but the bottom line is "can they make money doing it?" It can be useless so long as it makes money. Look how successful Coca Cola is for contributing to diabetes. Then companies make things that brake as quickly as you will put up with so you will buy more often. Rather than making things that last and saving resources.

You have to somehow fit your skills into this societal structure to survive. This is why children are steered away from their interest to focus on topics that will lead to more lucrative prospects. You can be an artist and do animation or something, or like discovering things and do research for a company but the children will need to adapt their talents to the market.