They avoid the issue on many other things too. For example (this is just the first thing I thought of…I’m sure there are others), they will never ask students to evaluate the indefinite integral (some say this diverges, some say this is 0–the Cauchy Principal Value of the integral) but they WILL have students evaluate the indefinite integral because by all accounts, this diverges. They just want to avoid the nuance of this conversation entirely, which I completely understand.

]]>Can you clarify?

]]>With only one set of sides being parallel. Your argument is overbuilt to the simplicity of rhe concept. There needn’t be any further eloquent description. Occams Razor- the simplest solution is most often the best solution. ]]>

It’s the same as with number e. What is special about it? Why do we use it for powers and not the simpler 2^x or 10^x, or as basis for the logarithms? Because is the exponential whose derivative is the same function.

]]>My vision, shared by most math teachers, I would hope, is that proof would be a central part of every math course. Mathematics is different than other disciplines and the thing that makes it different is that mathematics is a *sense-making* discipline. It’s only in math class that you don’t have to answer to authorities–you can verify results yourself. And, in a truly ideal world, a student would encounter *no* unjustified statement in math class.

If math class isn’t logical and doesn’t make sense, what exactly *is* math class offering? This is our entire business, I say.