On the teaching side, I could see how remote teaching can eliminate many of the inefficiencies that were present pre-pandemic. For instance, why do we need to give three identical lectures on Calculus ...

Many of the geometric figures are so elementary that they are deeply rooted in daily language, and there seems to be no great solution. I agree with you here, and I think this is the key point. To me ...

Example: $(x+1)(x−1)=x^2+2x+1$ is an linear equation. I agree with all above answers. I wouldn't say that it is a linear equation, but it reduces to, or it is solved by or any other phrase you want ...

One of the things I'm currently testing is the addition of "find the error" based problems, and possible variations. For example (related but not the same topic) last semester I taught ...

I don't know if your idea has a name, but it feels weird when you try to apply it to something like 10-4: \begin{array}{r} & 1 & 0\\ -\!\!\!\!\!\!& \! & 4 \\ \hline & & -4 \\ +\...

Without being rigourous, the equation $F(x,y)=0$ defines a relation between $y$ and $x$. To promote this relation to a function, some restrictions in the $(x,y)$-plane has to be imposed. Assuming that ...