You can find a whole bunch of my Quora answers at my Quora profile, down below all the list of subjects that I find it interesting to read or write (or both) about. All that
may not teach you anything except what it amuses me to write about when I'm bored and procrastinating.
Anyway, Lauren Godfrey asked a cool question, and here's how I answered it, and I hope it's as good an answer as her question was:
- Most adults are not good at math (they are after all products of a system that notoriously doesn't teach it successfully). Some of them transmit de-motivating feelings to kids around them, such as:
- fear of math
- fear the kid will quickly excel them
- anger at having to study math
- defensive attacks on math as unneeded or useless
- Well-taught math has a solid conceptual base. A kid who never develops an understanding of that conceptual base is going to be lost and helpless sooner or later (the usual years for that problem are about 9-12, and the usual sticking places are long division, fractions, decimals, and elementary algebra).
- Kids who understand better conceptually and don't get any conceptual instruction are primed for a particularly infuriating flavor of failure because they won't be able to do what the problems are asking later on, but they will understand that they should be able to.
- Kids who learn better by other means (patterning is the most common) will try to learn more advanced math by those other means, and at some point it can't be done. Then, since the only tool they have is a hammer, and they are out of nails, they quit.
- Well-taught math is constantly related to other subjects (science, history, geography, many more) and kids who aren't shown those relationships usually don't figure them out for themselves, so they give up because "this has nothing to do with anything."
- Many people don't use math where it would be to their advantage to use it, because they don't know how; their children learn that buying too much paint or too little tile, adapting a recipe to the scarcest ingredient and having it come out tasting funny, never really knowing how much is in your bank account, etc. are just how life works; in extreme cases there are adults who simply do not believe in math at all (i.e. they don't think that things that are routinely calculated can be known by any means other than trial and error).
- Many teachers were attracted to subjects because they thought they were unmathematical. It isn't necessarily obvious to an English teacher that much of the plot of Shakespeare's double-tetralogy of histories (from Richard II through Henrys IV-VI to Richard III) depends on logistics, travel times, and various other things you can calculate; there are math problems under nearly every human activity, but a teacher who doesn't know them can't show them.
- Many math teachers really like abstract problems because they like doing nifty puzzles; more concrete real world problems aren't as much fun, and they tend to stint them (and not know enough about the related subject to teach them).
- Well-taught math demands quick effective recall (like knowing the operations tables, the simple algorithms, some ordinary relations between fractional and decimal representation, and so on, with almost instant recall of accurate information). Memorization has been very out of fashion in education for a long time (somebody ask me sometime why that was bad. Don't ask this weekend, I'm going to be too busy. Just remember to ask it, later). This has unfortunate consequences:
- Kids don't learn how to memorize for effective recall, so they don't know how to put the basic information into their heads.
- Kids are rarely asked to use any power of effective recall so they don't know how to pull the information they need out of their heads and use it.
- Teachers don't know how to teach either of those skills so they can't help.
- Kids and teachers therefore avoid memorization because they're not good at it and it mostly just makes them unhappy.
- Inane curricula re-written by textbook consultants who didn't understand what the textbook author was trying to say or why it mattered. Honestly, truly, there are some textbook publishers who appear to prefer a clear and easy to read style in the words, and nice looking graphics, to accuracy in the math.
- The luck of the draw in teacher quality and/or connection; every so often a kid just gets a teacher who kills math for him/her. That will always happen to some extent, just as it happens for every other subject. (I enjoy working in visual arts now, but hated it as a kid; I had 3 awful art teachers back to back, and it took one great one in 7th grade most of a year to win me back to art. On the other hand, as it happened, I had so many good math teachers that by the time I had my first bad math teacher, I was incurably a math kid).
- Some otherwise successful-enough people seem to stick at the concrete-operational Piaget stage, which pretty much limits you to below-algebra math.
- Other people have a hard time sequencing multiple steps (lack of executive function) for any of several possible reasons, so again they're limited to math problems that can be done in a number of steps they can sequence.
- And yet more kids have problems with branching algorithms: in long division, for example, you have to remember that if the remainder is bigger than the divisor, you need to back up and add one or more to the last digit on the dividend. Comparing two numbers to decide which of several possible things to do to a third number is genuinely beyond many seemingly normal 3rd-5th graders (almost everyone can do it by 6th grade). If the kid has to do some kinds of math before his/her brain grows into it, that can be the end of math for that kid.
- Some students develop a habit early on of simply grabbing all the numbers in a problem and more or less randomly applying algorithms to them. "Bobby is riding in a car and reading a book. He is 9 years old, 52 inches tall, and weighs 63 pounds. He reads 72 pages, and there are an average of 208 words on each page. The car takes 2 hours to travel 100 miles. What is the average speed of the car?" There are people who can't solve that problem because they have no sense that to compute a speed, all they need is distance traveled and time taken. So when the teacher demonstrates the answer, their reaction tends to be that "seven" was a perfectly good answer because they divided the weight by the age correctly, or that the teacher is unfairly shutting down their answer of 10,816 (number of words on a page multiplied by height) even though they had to multiply much bigger numbers to get it. Obviously teachers just make up the rules as they go to cheat the kids, and to hell with this. (Sound extreme? I have worked with four children just like this).
Many kids give up on math earlier than is optimal for them or for society, but we probably want to achieve a more optimal distribution of give-up points, not fill the retirement homes with would be Galoises and Gausses.