Welcome to "Teaching on a Tangent"

Welcome to my blog!  This is my first post and I want to take the opportunity to introduce myself.  My name is Rachel and I'm currently a teacher candidate in Ontario, Canada, and I'm navigating my first year of teacher education.  My goal is to become a high school math teacher (yes...math...I love math!).  One of my classes focuses specifically on teaching math.  In this blog, I will talk about my journey through this class; things I'm learning, things that may surprise me along the way, and just some general thoughts on math teaching that I want to share.  I hope to not cause any division (except long division, and, occasionally, synthetic division), but rather I hope to add to the general math community with my musings.

In this post, I want to focus on the name of my blog and why I chose it.  So, why "Teaching on a Tangent"?  Well, as you'll discover about me (and may have already guessed), I love math puns and math jokes, so, naturally, the title of my blog had to function well in this area. 

But there's more to it...

For one thing, I will literally be teaching on tangents at some point during my career.  The simple definition of a tangent in math is a line or plane that touches a curve but does not intersect it.  It's essentially a line that has only one point in common with a curve but does not cross over that curve; if you extend the tangent, it will never touch that curve again.  We generally speak of these curves as functions that are defined by equations (such as y = x²).  If we plug numbers into the "x", we can find the corresponding "y" points and plot the equation on a graph.  This visual representation will be the same every time you plot it - it doesn't change. There are, however, an infinite number of tangents (since there are an infinite number of points on the curve which a tangent can touch).

Here's a photo of a tangent (courtesy of http://study.com/academy/lesson/tangents-definition-properties-quiz.html):

This brings me to my next point.  I want to teach on a tangent.  Notice I didn't say "off on a tangent", I said ON a tangent.  I want to start with a concept and general method for teaching the concept, but I don't necessarily want to use the same method that's always been used simply because "that's the way we've always done it".  I want to see if it's necessary to deviate from that "equation" to make the lesson better.  That is, I want to find a starting point on the equation, and I want to ride the tangent; I want to find ways to make the lesson more interesting and more effective.  

However, keep in mind that any tangent does indeed have one point in common with the equation of the curve.  To me, that represents the fact that sometimes the classic way of teaching a concept is still the best way.  I'm not obligated to change lesson plans just for the sake of change; the change must make sense.

I hope I've been able to accurately communicate my reasoning behind the naming of my blog.  I do, however, realize I've talked a fair bit about graphs in this post.  And I know, graphs aren't necessarily everyone's favourite topic.  As far as I'm concerned, I love trigonometry, I love algebra, and I could do calculus all day.  But graphing...well - that's where I draw the line.