If anyone associated with my HS job reads this, I’m only talking about a few of you kids. Most of you are doing the right thing! Keep it up! It is what makes that job fun and why I come into work every day to be with you. If you are my Principal or the AP, I’m coming to talk to you Monday about my concerns.

In a couple of my HS classes, I’m a bit discouraged because there seems to be a lot of outside school behavior that is getting in the way of several students learning. (I’m not going into depth because I still want that job ) This behavior seems more wide spread than it has been in the past. Maybe it is just the mix of students I have this year? It is depressing because they are bright people making poor decisions.

How is this related to what follows? Well in the midst of despair there is always a glimmer of joy:

In my online cc Precalculus course, I have student’s respond to some discussion type questions from the text. This morning I found the following, which I thought I’d share:

A student responded and asked:

Wow that made me take a step back and ask myself how should I answer this without getting into how a function might not be differentiable?

Here was my response:

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A great question Stu Dent. You’ve really made me consider how to answer it.

In calculus you’ll learn that as a function changes from an increasing function to a decreasing, the slope of the function changes from a positive value to a negative value, momentarily having 0 slope at the maximum point.

This is reversed when the function changes for a decreasing function to an increasing function.

For functions like

f(x)=|x|

there is not a gradual change in the slope. It takes a sharp corner.

How did I do answering without getting too in depth?

It is nice to work with people who are thinking and not distracting themselves. Isn’t this why we do this job?