words and math?

Mathy type math questions can be fun! Pure mathematics studies many esoteric mathematical ideas. This is serious stuff. I enjoy it myself, going off on a tangent playing with some problem that has no conceivable application (although sometimes these come later when least expected).

However, applied mathematics is a tool for those of us who want to learn various aspects of the how the world around us works or use that knowledge to create stuff. This is the world of science and engineering. And to interface with that world, we need words that can be translated into mathematics. Calculus is the language that world speaks. Solving calculus problems that imagine some relatively simple idealized situation in the real world through wordy math problems are the baby steps we need to take in learning how to actually use calculus outside of a math class. We have to connect the cryptic efficient mathematical notation to a context which gives meaning to it apart from the collection of mathematical symbols we use to create expressions and equations.

dr bob has training in theoretical physics, and so thinks of mathematics as a tool that must also be useable in confronting STEM ideas where artificial math tests or standardized test problems are useless without more understanding of context for the ideas which for practice you do mathy problems where you are given an expression or equation or whatever and do some one or two step manipulation of it without the need for many words. Word problems are closer to how we use mathematics in applications, but even in mathy problems, delivering results in proper notation in a clear sequence is key to actually understanding how to use these tools. One should distinguish between general equations or functions, and specific values of those objects. If you are using a function, first state what the function is. In a new equation state a value of the function first before plugging in argument values:

f(x,y) = ...

f(1,2) = ...

etc.

Don't run these equations together.