But I think that a lot of students don't have what it takes to learn the mathematics curriculum they signed up for, no matter how you teach them.
This part is simply untrue. The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. This is amplified by the fact that most math teachers tend to be frightened by the subject [1]. That fear tends to be passed on from generation to generation despite its irrationality. Thus it persists memetically. Add to this the fact that education has been trending towards standardized testing, and most incentives to create engaging ways of expressing these concepts are actively discouraged if not futile (within the system).
Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. With this being stated, there is an important aside that must be made. People tend to focus on the relationship between the student and the teacher and the failure of communication there. However, there is an equally important chasm that remains hidden in plain sight—the relationship between educators and the academy itself. Mathematicians tend to take pride in performing their research for its own sake without concern for pragmatic applications. While there is merit to performing research without having to immediately justify its utility, that lack of justification should stop at practical applications to feed whatever social machinery is en vogue for the time period. It absolutely is not an excuse to put no effort into communicating what is being worked on in terms that others can understand. Thus we see a lack of empathy and communication from the genesis of mathematical ideas to the ones who find/create[2] those ideas to the ones who must pass that knowledge along to the ones who must absorb and apply this knowledge as students in order to expand their horizons or to simply find food, shelter, and partners for procreation.
[1] Calling Mathematics a subject is actually disingenuous since it encompasses so many different ways of thinking, conceptualizing, and expressing.
[2] Depending on your point of view, either concepts are “discovered” by the mathematician or they are “created” and did not exist before the creation.
>The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it.
I'm sure if you spend enough resources on teaching a student to do something then almost every student will eventually get it, but at what point does the amount of resources spent become too much? Just the fact that math classes have 25-40 students each already means the resources we spend are limited and within those constraints it might very well be likely that those kids can't be taught this. It's not like we're suddenly going to get a massive surge in math teachers.
>Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives.
It might be pervasive, but most people could go through their life without learning half the mathematics that they do in school. I think studying mathematics is important to learn ways of thinking, but I also recognize that, in practice, most people have little need for most mathematics they learn.
This part is simply untrue. The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. This is amplified by the fact that most math teachers tend to be frightened by the subject [1]. That fear tends to be passed on from generation to generation despite its irrationality. Thus it persists memetically. Add to this the fact that education has been trending towards standardized testing, and most incentives to create engaging ways of expressing these concepts are actively discouraged if not futile (within the system).
Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. With this being stated, there is an important aside that must be made. People tend to focus on the relationship between the student and the teacher and the failure of communication there. However, there is an equally important chasm that remains hidden in plain sight—the relationship between educators and the academy itself. Mathematicians tend to take pride in performing their research for its own sake without concern for pragmatic applications. While there is merit to performing research without having to immediately justify its utility, that lack of justification should stop at practical applications to feed whatever social machinery is en vogue for the time period. It absolutely is not an excuse to put no effort into communicating what is being worked on in terms that others can understand. Thus we see a lack of empathy and communication from the genesis of mathematical ideas to the ones who find/create[2] those ideas to the ones who must pass that knowledge along to the ones who must absorb and apply this knowledge as students in order to expand their horizons or to simply find food, shelter, and partners for procreation.
[1] Calling Mathematics a subject is actually disingenuous since it encompasses so many different ways of thinking, conceptualizing, and expressing.
[2] Depending on your point of view, either concepts are “discovered” by the mathematician or they are “created” and did not exist before the creation.