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Welcome Kostya! The mapping view is definitely important, but I don't think it's supreme. For me here's how I think about it. There are three ways to think about (basic) linear algebra: As a theory of ...

One angle you could look at is molecular geometry. Not really my subject area but a couple of examples: Organic molecules can have different chiralities. That means that while one is the mirror image ...

Since no one's posted an answer I will get things started with some general advice. Calculus 3 is my favorite course to teach, but it can be a bear to wrestle with the first few times. Some more ...

I feel like the question you are interested in is whether there is a "kind of person that can produce mathematics" and a "kind of person that can't." I don't know of any conclusive ...

To add to Namaste's answer above, two of the thing we're trying to teach in math is literacy and competency with the algorithms used to solve problems and the ability to solve problems for which you ...

The MAA has quite a long guide for new TA's, it's a little too much to take in at once but as a supplement it's very good, it's got a section on everything you could hope for: I agree with Brendan ...

Use them for what they're best at testing, like conceptual understanding questions. One way to do this is by having students evaluate statements they would never be expected to come up with on their ...

(1). It's going to depend on level to a huge degree. In my experience, up into advanced undergraduate you could expect definitions to be named sensibly and an instructor to explain how a sensible name ...

Economics has a ton of applications since they are interested in relationships between variables, not functions per se. Two simplish ones that come to mind are Price elasticity of demand: Supply ...

I had a couple but one in particular sticks out: years ago I was teaching a summer program for middle school students, one of the other instructors suggested I show my students the youtube video "...

Math With Bad Drawing has some images that approach an info-graph (and in general is just a great website for math education), for example: https://mathwithbaddrawings.com/2015/07/01/infinity-plus-...

To use set builder notation you need to carefully state to which set every element you want to discuss belongs. In general it goes \$P = \{x\in\text{some set} : x\text{ satisfies some truth evaluable ...

One theoretical framework for designing actives and assessments is ETS's Evidence Centered Design framework, although it requires long term analysis of a task or series of tasks in conjunction with ...

You might just want to use a game buzzer app. There are tons of them for jeopardy like games/pub quizes that you can find online. Students have to sign up but they don’t have to use their real names. ...

Interesting question, here are some ideas just off the top of my head: Direct product groups act on Cartesian products, so the symmetry group of two two squares rotating independently (you could then ...

I'm not a tenured faculty member so take this with a grain of salt: No one is going to care, your reputation in the field and job prospects will almost certainly be based on your PhD work. Many people ...

We're on Blackboard as well, here's some workflow's we've been experimenting with to do everything through that interface: Lectures: Blackboard Collaborate Ultra works pretty well here. Just remember ...

There are already several "yes" answers so I'll give you a qualified "no": What you do in class is what your students learn, so it depends on what you want to teach them. They should of course be ...

I don't know of a good problem book but I found D.H. Collingwood, K.D. Prince and M. M. Conroy's OER precalculus book to be a quite good source of well thought out word problems.

Kevin Arlin already gave my "best" answer in All of Statistics. That said, statistics is a large topic. If you're looking specifically at inference and statistical learning and want a ...