Main Area

Reflections and Thinking

Posted on September 29th, 2012

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:

Polynomial functions all have the same domain- all real numbers, or (-infinity, infinity). This is what makes them continuous. They reach across all values of x on a graph without breaks or interruptions.

What makes them have soft edges, at turning points, instead of sharp or corners?- is this the exponential effect? What functions have sharp corners, only those with absolute value in them?


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:


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


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

This is really a specific case example, but I hope it answers your question without confusing everyone.


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?


Student Driven Education

Posted on September 1st, 2012

This tweet:

got a reaction out of me. My own children are self motivated students who are becoming wide read and very intelligent young adults. Part of this is because they take demanding courses where teachers are dictating what they will learn. Left to their own choices, they would not know what to read and what to study. They would stay inside their own interests and not be exposed to a more expansive world. This is analogous to their preschool days where they had to try foods different from what they ate at home.

I agree that once people gain a base from which to grow, formal education holds little interest and can be limiting. However I am a firm believer that US secondary education needs a canon to follow. Will the CCSS achieve this? Maybe. It depends on how the system is implemented. Teachers in my SU spent a couple of days formally looking at the content area standards during the before school inservice days. What I walked away from this with is that it will require a lot of time, resources and collaboration.

Looking at the content area standards and then following Keith Devlin’s posts about the MOOC he is running this fall I’m seeing that even the CCSS isn’t going to be the fix. He writes that the paradigm shift from HS mathematics to mathematics students have to do at the university level is really wide. I’m going to participate in his MOOC just to see what he is talking about. I’m hoping I can get a couple of my HS students to also work through the course. I know this is a choice and not a dictated path my students must follow, but Prof Devlin thinks the transition is necessary.

I guess I’m talked out. If anyone reads this, I’m sorry for the disjointed rant.