As a fervent math addict whose enjoyment reaches into my choice of programming language (functional) and who would be delighted to be gifted a text on differential forms, I think this question deserves to be asked.
Math teaching is being carried along with a thousand year momentum and while the current curriculum made sense when many jobs involved building catapults, bridges, ships or cathedrals and jobs as a carpenter or mason were more numerous, they make little sense now.
Notice also that most of these subjects were set at a time before education was necessary so that if you went into say a gymnasium; odds were you wanted to be a teacher, academic or engineer. So topics like trigonometry, geometry, calculus and higher algebra (matrices, analytic geometry) made sense.
But these days, the vast majority of people do not need these subjects. On top of that there is a great crime. The most pertinent topics to modern living are given short thrift. Subjects like understanding basic statistics (including mean, mode, median, stdev, and variance), probability (including expected value), basic decision theory and estimation. All of these would have far more use to every day life and could be fully taught in the context of how they would help in real life (media, gamblers fallacy, money management etc).
Advanced topics would be things like distinguishing conditional and joint probabilities, counting (combinatorics), graphs and networks, exponentiation and logarithms, common plots (logistic, exponential, parabolic), rate of change, and the relationship between a circle and triangle (must be taught with animations). These things actually still have use to many people.
There is also the question of should math be taught at early years at all? A 12 year old can probably compress their previous 7 year math eduaction to 1. Maybe just numbers, (Z,+) or (Z,*)? I don't know but I think the question of if math education starts too early deserves to be looked at. The current hatred is in part due to a cycle of teachers who hated the subject having to force learn it in college and then having to teach it by force in addition to other subjects they may be stronger in.
Instead let the child's curiosity guide them. So they would arrive not by force and a bunch of unmotivated subjects but by curiosity. To augment the lack of math classes there will be game classes to teach reasoning. Not just video games but also card, dice and board games - with the caveat that the game must be PSPACE complete. Just let the kids play and compete. Maybe they will learn the same type of reasoning that will be useful to learning about chains, posets, groups, first order logic or probability. The more determined may even go read about the topics.
For video games the game must allow scripting. I think such a policy would just about eliminate thoughts of the pointlessnsess of math.
Kids are not dumb, they will do impressive things if it interests them. Adults make this mistake of underestimating kids all the time e.g. whenever they say things like "whaoh that was done by a 12 year old?!"
Math teaching is being carried along with a thousand year momentum and while the current curriculum made sense when many jobs involved building catapults, bridges, ships or cathedrals and jobs as a carpenter or mason were more numerous, they make little sense now.
Notice also that most of these subjects were set at a time before education was necessary so that if you went into say a gymnasium; odds were you wanted to be a teacher, academic or engineer. So topics like trigonometry, geometry, calculus and higher algebra (matrices, analytic geometry) made sense.
But these days, the vast majority of people do not need these subjects. On top of that there is a great crime. The most pertinent topics to modern living are given short thrift. Subjects like understanding basic statistics (including mean, mode, median, stdev, and variance), probability (including expected value), basic decision theory and estimation. All of these would have far more use to every day life and could be fully taught in the context of how they would help in real life (media, gamblers fallacy, money management etc).
Advanced topics would be things like distinguishing conditional and joint probabilities, counting (combinatorics), graphs and networks, exponentiation and logarithms, common plots (logistic, exponential, parabolic), rate of change, and the relationship between a circle and triangle (must be taught with animations). These things actually still have use to many people.
There is also the question of should math be taught at early years at all? A 12 year old can probably compress their previous 7 year math eduaction to 1. Maybe just numbers, (Z,+) or (Z,*)? I don't know but I think the question of if math education starts too early deserves to be looked at. The current hatred is in part due to a cycle of teachers who hated the subject having to force learn it in college and then having to teach it by force in addition to other subjects they may be stronger in.
Instead let the child's curiosity guide them. So they would arrive not by force and a bunch of unmotivated subjects but by curiosity. To augment the lack of math classes there will be game classes to teach reasoning. Not just video games but also card, dice and board games - with the caveat that the game must be PSPACE complete. Just let the kids play and compete. Maybe they will learn the same type of reasoning that will be useful to learning about chains, posets, groups, first order logic or probability. The more determined may even go read about the topics.
For video games the game must allow scripting. I think such a policy would just about eliminate thoughts of the pointlessnsess of math.
Kids are not dumb, they will do impressive things if it interests them. Adults make this mistake of underestimating kids all the time e.g. whenever they say things like "whaoh that was done by a 12 year old?!"