# Tag Info

### Why do we teach even and odd functions?

One of the major themes of precalculus is what I call “connecting geometry to algebra”. Being able to translate between an algebraic statement like $f(x)= f(-x)$, and the geometric statement that the ...

### What deficiencies are present in Precalculus curricula that causes so many students to fail Calculus I?

A blanket problem I've observed over-and-over is that the deficits that scuttle calculus students are even more fundamental than what is discussed in (typical) pre-calculus courses. Specifically, kids,...

### Why do we teach that every line is a linear function?

The usage you object to is, in fact, the original meaning of "linear". "Linear" means "having to do with lines". The notion of "linear" in the sense of "linear transformation" is a more modern, ...

### How to help new students accept function notation

You might remind them that $y$ is just a name for a number. When they draw a plot, they draw a bunch of points: maybe $y=3$ here, $y=5$ there, and $y=-2$ over there. But at some point (no pun ...

### How to help new students accept function notation

Start by talking about functions in general, not only about functions that can be expressed by a simple formula in x and y. Examples: The function that maps every non-empty list to its first element. ...
Accepted

### Examples (for beginners) of real functions which are not given by elementary formulae

How about $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = y$ where $y$ is the unique solution to $y^5+x^2y+5=0$? This does not have an elementary formula, but students can understand that for any ...

### Enlighten younger students about the concept of "procedural justice" in mathematics?

On the contrary, many seem surprisingly impatient when being asked to prove 1+1=4/2, whose proof (with properly delimited deepness) involves nothing beyond and possibly well below most people's ...

### What holds your students back in Calculus?

My impression (as a former private tutor/current university employee and from my mind as a former student) is that mainly equation solving is a big problem for poor (sometimes also for advanced) ...