Why Does Math Instruction Consist of Just Doing Problems?

[kyphysics]

I start back at community college this coming Monday and have been reading reviews of professors at Rate My Professor. One common complaint that I see with so many math instructors on there is that they merely do practice problems on the board and that's all that math instruction consists of. People complain there is no explanation of why you're doing what you're doing (i.e., what's the logic behind these steps) and no connecting this stuff to real world problems. It's just rote problem-solving. And worst of all, on top of this method of teaching, I see so many reviewers complain that their teachers don't like students asking questions and frequently tell them they must just figure it out on their own.

Why is this? If we're just supposed to figure things out on our own, then why is the use of a teacher? What are they there for? Rote problem-solving to me is pointless instruction, because I could just do that on my own at home. But this seems to be typical math instruction (at least at my CC). Thoughts?

 

[johnqwertyful]

Rate my professor is okay, but you also must realize who is writing the reviews and the biases they have. Also, these questions have been asked by everyone who has taken a math class ever. I'm sure you can find good answers by searching.

"If we're just supposed to figure things out on our own, then why is the use of a teacher?"
There's literally nothing you don't learn by yourself. No one teaches you anything, ever. Everything you know now, you've learned yourself.

 

[jtbell]

One common complaint that I see with so many math instructors on there is that they merely do practice problems on the board and that's all that math instruction consists of.

I'm in physics myself, not math, but in my experience, no matter what balance a professor strikes between theory and examples, there are always some students who want more worked-out examples and less theory, and some students who want more theory and fewer examples.

 

[Devils]

Dan Meyer agrees with you.
https://www.ted.com/talks/dan_meyer_math_curriculum_makeover

I am a math & science teacher, and have qualifications in teaching English as a Second Langauge too. Math teaching is generally done badly, and there is lots of research on why it is so. its often presented in a boring manner too.

 

[analogdesign]

I think the real problem, that jtbell gets at, is that different people have preferred or more effective learning styles. Some people are conceptual and like to explore on their own, some people need to treat math like a sport and exercize, exercise, exercise!

I've always done best using an iterative approach. I first learn the mechanics about something, and then, when I read the theory again, it starts making sense.

I've had classes that are all theoretical (random signals and noise, for one) and when my classmates and I would sit down to solve problems we wouldn't even know where to start... so it was off to office hours to get examples from the professor.

I think the key is balance, and understanding not everyone learns the same way.

You can't please everyone...

 

[ActionPotential]

Kphysics:

People have provided some great replies but I thought I would add my thoughts as well.

Without having actually taken the courses yourself, it's difficult to gauge how accurate people's complaints are. When I first returned to CC, I spent the first two semesters heavily immersed in study groups and tutoring struggling classmates who needed more one-on-one time (almost all of which complained about the pace of the class, lack of 'good explanations' and 'bad professors'). In my mind I thought that if I could just give them a different perspective about a particular concept that it would suddenly click for them and they would be all set (keep in mind that I myself struggled through these courses at times but worked hard each day and stayed on top of the readings and problem sets -- the fact that I had to work hard to get a good grade made me feel like I could be a better mentor than someone who breezes through it).

However, as time went on I started getting irritated with certain people constantly complaining about how awful the teacher was (even though from my perspective I found the teacher to be quite good) and chalked it up to me just having a better foundation than they did (sort of like playing on a soccer or football team -- you see kids that have some talent but recognize they got a much later start on the basics and so their foundation is a bit weaker than yours and mentoring usually helps people catch up quicker).

Eventually, I really began to see the issues: almost all of the people that were constantly complaining, were the same people that didn't know what chapter we were on, didn't read the assigned pages, didn't work through all of the homework problems, didn't go to office hours, were on their phone every lecture and generally didn't put any real effort into the course until a quiz or test was coming up.

After those two semesters I stopped listening to people's reviews/opinions of teachers unless I personally knew they were hard working, diligent students

Of course, these are anecdotal experiences and in no way am I trying to generalize all situations in which one struggles as a case of poor preparation, lack of interest and poor study skills (obviously, bad teachers DO exist). However, I do think a portion of professor reviews are heavily skewed and biased accounts from people who simply do not put the required amount of effort into the course (based on reading a myriad bad reviews on a particular teacher only to find that I personally really enjoyed that teacher's course).

 

[symbolipoint]

ActionPotential has is right.

I have seen almost all three sides of this.


Anyway, "why...solving problems", is because mathematics has always developed through asking questions. To look for answers means solving problems. Find a process. Unscramble an equation; form an expression; cut things into parts.