Thursday, 25 April 2013

Thinking Out Quiet

Someone recently posted a tweet that said something like "Just because we teach it, doesn't mean they learn it."  I read it quickly, went "huh" and moved on.  But it has stuck with me.  It is so true and yet seems to go against what we, as teachers, do every day.  We teach, we question, we guide to help our students learn.  But some of them don't, despite our best efforts.

I have been thinking about one student in particular.  C is a good student.  She pays attention in class, participates, answers questions, asks when she doesn't understand, comes in for extra help but still doesn't seem to be learning what I'm trying to teach her.  And I'm sure she is not the only on.

Perhaps in my 19th year of teaching it should not be a revelation to me that my students aren't all understanding the material.  It's not really, I have always known that.  But something about that statement has really struck me.  Why is it that some students just don't get it?  And how can I change that?  How do I explain finding the equation of a line in a different way that will make that light bulb go on?  I ask a lot of questions, take kids back to where they understood and walk them through the next steps to get where we need to be.  But then the next day, they are back where they were so they clearly did not truly understand it.

I guess there are two parts to this.  The first is knowing who doesn't understand.  Enter formative assessment, which I value greatly.  But then after spending 1-on-1 time with a student and having them say "I get it", sometimes they still don't.  Then what?  I try again, but I feel like I'm the one who is missing something.

I'm pretty sure there is no magic answer here.  But I will keep reflecting and trying new strategies.  'Cause I certainly never stop learning - every day the "finish line" moves further ahead!

About the title of this post... My introverted nature means that I don't tend to "think out loud" - thinking quietly to myself is what I do.  A lot.  But I am trying to share, as you see, although I push publish and then assume that no one will read this. 

Sunday, 21 April 2013

Parabolic Art

For many years my grade 10 academic students have created parabolic art - a picture created using only parabolas.  Students usually like this assignment as it gives them freedom to choose their design and allows those who might not be the most mathematically-inclined to shine.  My perspective is that they cannot complete it without having a solid understanding of the transformation of quadratics.

After seeing some examples, they start by sketching their design on paper. Then they have to figure out the equations of each parabola. Most choose to use vertex form (y = a(x - h)^2 + k) and I tell them to estimate the 'a' value - (positive or negative?  more or less than the previous equation?).  I tell them that at least 95% of their equations will change along the way but they need a starting point for the next step.

Enter This marvelous, free on-line graphing software allows students to quickly and easily see graphs of their equations.  They can find the intersection points of two parabolas and use that information to restrict the domains.

Here is the handout I give them.  And here are some of this year's submissions.  You will see that some students went a little crazy with a LOT of equations and some coloured in the final drawing too.  My students are fantastic!