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I teach math at a community college. I've tried many times to teach my courses in such a way that understanding the concepts and thinking were the goals. Perh

I teach math at a community college. I've tried many times to teach my courses in such a way that understanding the concepts and thinking were the goals. Perhaps I'm jaded by the failures I encountered but students do not want to think. They want to see a set of problem types that need to be mimicked. In our lowest level course we teach beginning algebra. Almost everyone has an intuition that 2x + 3x should be 5x. It's very difficult to get them to understand that there is a rule for this that makes sense. And that it is the application of this rule that allows you to conclude that 2x + 3x is 5x. Furthermore, and here is the difficulty, that same rule is why 3x + a x is (3+a)x. I believe that for most people mathematics is just brainwashing via familiarity. Most people end up understanding math by collecting knowledge about problem types, tricks, and becoming situationally aware. Very few people actually discover a problem type on their own. Very few people are willing, or have been trained to be willing, to really contemplate a new problem type or situation. Math education in its practice has nothing to do with learning how to think. At least in my experience and as I understand what it means to learn how to think.

jaclaz 9y ago
I believe that your "failures" are not necessarily linked to "math", in the sense that other teachers probably experienced the same frustration for their own taught subject. Math is definitely "harder" in the common thinking of people, but I suspect that there is often a generic underlying issue. A number of students (I would say a large part) go to school or college not "to learn" but rather to "pass the exam" or to "get the degree", they are not interested in the subject but in what the consequences of having a good grade in that subject are or - sometimes - only do whatever is needed to get a passing grade. I don't blame the students, mind you it is not their fault, it is society in general that somehow has shifted the values, and culture is not anymore valued.
joe_the_user 9y ago
I've had the same experience - teaching math for a short time at a State University. I think the basic situation is that by the time students have reached the university level, the habit of looking for a set algorithm for completing a class is completely ingrained and moreover, the average student has little-to-no free time so they feel a panic concerning anything that will take an unpredictable amount of time.
jostylr 9y ago
A large part of the problem is that problems are presented to them, instead of coming from them. And then the solutions are presented. Humans just don't appreciate it. In a course I teach, I have students reading Guesstimation and doing two blogs: 1) A Guesstimation problem similar to that in the book, 2) Watch a TED Video and come up with a mathematically based skepticism with doing a guesstimate if possible to get a feeling for the skeptics answer. My students love that part of the course and it gives them way more value than the rest of the course covering standard mathematics. They start to incorporate the guesstimation ways into their work and slowly start to see the true fuzzy outlines of real math. Reading all their blogs and making appropriate comments is quite a bit of work.

jaclaz 9y ago

I believe that your "failures" are not necessarily linked to "math", in the sense that other teachers probably experienced the same frustration for their own taught subject. Math is definitely "harder" in the common thinking of people, but I suspect that there is often a generic underlying issue. A number of students (I would say a large part) go to school or college not "to learn" but rather to "pass the exam" or to "get the degree", they are not interested in the subject but in what the consequences of having a good grade in that subject are or - sometimes - only do whatever is needed to get a passing grade. I don't blame the students, mind you it is not their fault, it is society in general that somehow has shifted the values, and culture is not anymore valued.

joe_the_user 9y ago

I've had the same experience - teaching math for a short time at a State University. I think the basic situation is that by the time students have reached the university level, the habit of looking for a set algorithm for completing a class is completely ingrained and moreover, the average student has little-to-no free time so they feel a panic concerning anything that will take an unpredictable amount of time.

jostylr 9y ago

A large part of the problem is that problems are presented to them, instead of coming from them. And then the solutions are presented. Humans just don't appreciate it. In a course I teach, I have students reading Guesstimation and doing two blogs: 1) A Guesstimation problem similar to that in the book, 2) Watch a TED Video and come up with a mathematically based skepticism with doing a guesstimate if possible to get a feeling for the skeptics answer. My students love that part of the course and it gives them way more value than the rest of the course covering standard mathematics. They start to incorporate the guesstimation ways into their work and slowly start to see the true fuzzy outlines of real math. Reading all their blogs and making appropriate comments is quite a bit of work.