I think the fundamental thing that many refuse to accept is that some people are, in fact, smarter than others. Until we can accept that fact in society, we're always going to end up reducing to the lowest common denominator.
Yet, as someone teaching electronics and programming to art students, many of whom "hate maths" there are many people who would have understood it in school if it was explained right and/or if someone gave them a good motivation why they should bother understanding it in the first place.
The truth is that many math teachers suck. I had a math teacher that managed to do integrals with us for a year without ever explaining to us (in a school specialized on mechanical engineering) what real world problems would be impossible to solve without it.
> I had a math teacher that managed to do integrals with us for a year without ever explaining to us (in a school specialized on mechanical engineering) what real world problems would be impossible to solve without it.
I sure did. She said it doesn't matter, or we don't need to understand right now. As I said, shw was not a good teacher.
As an educator myself the point I am trying to make here is that the why is crucial in complicated topics and if someone who was mentally there even feels the need to ask the why you should probably reconsider the way you chose to teach things.
I vividly remember the moment when I researched integeals for an exam. I found the typical simple examples and wondered why the hell that teacher didn't mention this once. In fact today I am convinced the right way to teach such topics is to always bring up the examples even (or especially) as you dive deeper into the material. This reminds people what they are actually dealing with.
> if someone gave them a good motivation why they should bother understanding it in the first place
Being bad at math means you'll likely not manage your finances very well, and that will hurt.
I saw a documentary recently on Netflix (or Amazon?) on what happens to athletes who became overnight millionaires. Very few managed to hold on to that wealth very long. Some pretty sad stories.
Do you have kids? Telling them their finances are a reason for learning maths is bullshit, because not every person that age has to worry about their finances.
And even if you choose that as a story you will have a hard time explaining to them why they need to learn trigonometry or something like the aforementioned integral.
As an educator I have found most people don't really need a hard rational incentive to learn a thing. All they need is a story that convinces them to learn that. E.g. when I helped unruly teens with their homework and they had an abstract geometric problem to solve, it costed me literally nothing to come up with some story of how they comanding the knights in a castle and to prevent their enemey from entering they have to figure out how much material they need to chop in the woods.
The same boring problem suddenly was tied to a heroic story of them saving the day and oh wonder, they were more interested in solving the issue.
I've seen 'em right up through high school saying that there was no purpose to learning math, and that math wasn't "relevant". And then they go into the workforce and mismanage their finances into perpetual poverty.
I also see them choose college majors apparently on the basis of avoiding all contact with math, and wind with degrees that employers aren't interest in.
Your hero story worked, good on ya! I would have related the true story of hiring a contractor to build an elliptical patio. He charged by the square foot. He laid it out, and had the bricks delivered. Something seemed off. I measured the L+W+H of the brick pallet, and the volume of one brick, and computed the area the bricks would cover. Then, measured the L+W of the patio layout, and used the area for an ellipse formula. The bricks was the right number for the area, but the area was only 2/3 of the area he quoted me and charged me for. I nicely inquired about the discrepancy, and he hemmed a bit and said he'd made a mistake, and adjusted the bill accordingly.
Of course, we both knew he tried to cheat me, quite egregiously. I figure he did this regularly and got away with it with his math challenged customers.
I recall a documentary about a famous entrepreneur who made a lot of money in high school by gambling with other teens who did not comprehend the odds.
Sure, finance doesn't interest a 6 year old. But I've never heard of a teen who didn't want to have money in their pocket, and who looked forward to being taken advantage of. Even the unruly ones.
I don't agree that finances are bullshit reasons for learning math.
P.S. In high school, I joined a poker game with some peers who I knew had engaged in fencing stolen goods. They cleaned me out. I knew enough about poker odds to realize they were card cheats, but I didn't see how they were doing the cheat. It was a cheap lesson for me :-/ The most effective scams are the ones where the mark doesn't realize he was cheated, and will come back for more. I didn't return to poker.
I just talked about this with a friend of mine who related a story about a teacher friend of his in a low-income school. Lots of gang violence, standard rough neighborhood. A kid asked the usual "why do I need to learn algebra?" question. The teacher replied "If you want to stay poor, you don't have to." The kid got the message.
I had these "though talking" teachers, and to be honest they didn't impress anybody. The best teachers I ever met all had a burning enthusiasm for their subject and managed to spark interest in their students as well. So much so that nobody ever had to ask them why a thing was needed. It was obvious that it was either needed or the lesson was so interesting that nobody gave a damn whether there was any use to it. I mean people watch documentaries about aliens and pyramids all day — teenagers don't need things to be useful to be motivated, but they need to be motivated to learn things that turn out to be useful.
There are studies on whether negative or positive drivers are more effective at getting people to learn. I won't spoil the findings, but you can probably guess by my line of reasoning already.
According to the teacher, he did. Even if he didn't change his behavior, he now knew there was indeed a reason.
I started my first small business when I was 8, and was able to do the accounting for it (not that there was much to it). I never thought about the connection between math and business at the time, because it just seemed natural and obvious. I did several businesses, earning enough that I could buy a car by the time I was 16.
I bet you knew kids during school who had small enterprises on the side.
The eternal problem with this idea the some people are smarter than others is that never finishes the statement *smarter at what?*
An overly simplistic view of intelligence and human capabilities seems to think that you’re just “smart” or at least smarter than those around you in general and that’s it, you’ve won the lottery. When in reality, people have aptitudes and gifts across spectrum of endeavors and where you may not seem smart in maths, you can be an incredibly smart engineer or artist or communicator.
It’s hard especially to have this conversation with traditionally “smart” people because you find very quickly that their entire identity is wound up in this idea of being universally intellectually superior than others through no effort of your own. Gods own gift. You challenge that, and the teeth come right out.
I'd argue this is an overly pedantic way of looking at the situation. Yes, everyone has different aptitudes and things they're good at. That fundamentally doesn't matter to the core of my argument, which is that some people are just worse at everything.
> many refuse to accept is that some people are, in fact, smarter than others.
... I'll caveat that "some students are smarter than others _at the same age_."
It's bizarre and frustrating because we already have the solution, we just need a way to assign students to a grade level that's based on how smart they are, rather than how old they are.
yah, I can't see any issues that will evolve from having a wide range of physical development level of approximately the same mental prowess in a classroom... I mean I certainly never got into any mutual violence situations with any of my classmates, nor did we ever choose each other as sexual partners.. (I can keep going with sarcastically listing things that definitely routinely happened in my k-12 classrooms that you almost certainly don't want happening between people more than a couple years apart that your policy choice would heavily facilitate).
There are valid social(ization) reasons to keep kids approximately the same age in a classroom. The lucky thing is, if you live in a city you usually have a big enough cohort of kids that you can do some of this sorting within grade, although I am personally skeptical of that as a solution. I remember ~10% of the kids being highly disruptive and it would have been nice to have them gone but there was this huge, probably majority of the class, that was dumber than me but trying hard to get ahead and keep up that I think was probably beneficial to society keeping there because they got pulled ahead more than I got held back.
>There are valid social(ization) reasons to keep kids approximately the same age in a classroom
Fair enough. I'm already of the opinion that k-12 is primarily a daycare and that smart kids will prevail no matter the education model.
> I think was probably beneficial to society..
Yes, there will always be a tension between what is best for the individual and what is best for society. A difference of opinion likely stems from a difference of personal philosophy.
While it's hard to say what's best, I think most would agree that there is a lot of room for improvement in the current education system.
