0 What do you think it is?

As the school year was wrapping up and my students were working on their final projects of the year, I found myself asking a certain question a lot.  I don't know why I never thought to take advantage of this question before.  But, the results were enlightening.

Since my students had already been tested a crazy amount, I elected to give them a project in lieu of a semester exam.  Seriously, they took their EOI which is our state standardized test.  Then, I gave them a practice Common Core test as a requirement of the OGAP Program I am involved in.  Then, our school was randomly selected to test out field test questions for next year's Common Core test.  So, my students spent another day in the computer lab.  There was no way I was going to subject my students to another test!

I pulled out the Road Trip Project (Part 1  / Part 2 and 3) I designed while student teaching to give to all six of my classes - Algebra 1, Algebra 2, and Statistics.  The project was originally designed for 8th graders to emphasize proportional reasoning.  Proportions are something that are no longer covered by high school standards, but my students still struggle with them.  So, this was the perfect refresher/learning opportunity for my students.  Plus, it shows them how math is used in real life.

After revisiting this project two years after creating it, I've got some ideas of changes I would like to make.  Be on the lookout for a post regarding those changes soon!  (And, by soon, I mean hopefully within the next year.  I'm so behind on blogging!)

As students worked on planning their road trips, they were continually raising their hands to ask me questions like "What is the state abbreviation for Maine?"  Instead of telling them, I responded to their question with a question.

Our conversations went like this:

What is the state abbreviation for Maine?
What do you think it is?
MA?
Nope.  That's Massachusetts.
MI?
That's Michigan.
MN?
That would be Minnesota.
ME?
Yes!
Oh, so the abbreviation of a state is always the first and last letter of the state?
What's the abbreviation for Oklahoma?
OK
So, does that follow that rule?
No.  That would make our abbreviation OA.

Other times:

What is the abbreviation for Colorado?
What do you think it is?
CO?
Yes!

Asking "What do you think it is?" gives my students a chance to be successful when they don't quite believe in themselves.  If they get it right, they are proud of themselves for figuring it out on their own.  If they get it wrong, it gives me insight into their thinking processes.  And, I can better guide them in the future.

I started asking that question anytime I could.

What does MPG mean?
What do you think it means?
Miles Per Gauge?
It's miles per something, but it's not miles per gauge.  Try again.
Miles Per Gallon?
Yes!

One of my goals for next year is to teach my students how to ask good questions.  To ask good questions, I need to get them thinking more.  Perhaps the way to achieve both of these is to start answering more questions with questions.  When I just give my students the answer, I'm cheating us both.

Detail: What do you think it is?

0 Asking Why

Can you guess what our lesson was a few weeks ago in children's church?

Wise Man / Foolish Man Object Lesson

Yep.  We studied the story of the wise man and the foolish man.  The wise man built his house upon the rock.  The foolish man built his house upon the sand.  When the wind blew and the storms of life came up, the wise man's house stood firm on it's foundation, but the foolish man's house was demolished.

Storms of Life

My mom found a template online to print off tiny lessons for an object lesson.  Each house was taped together and weighted down with a small rock inside.  It was my job to tell the story and pour on the storms of life.

It was rather nerve-wracking because we did not practice this beforehand.  I spent a lot of time asking the children what they thought was going to happen and why.  What will happen when I pour the water on?  Why will the house on the sand fall over?  Why?  Why will the house on the rock stay standing?  Why?  Why is the foundation important?  What is the foundation made of?  What is the foundation adhered to?  Why would it be important to build your house right the first time?  Which house would you want to spend a warm sunny day at?  Why?  Which house would you want to spend a stormy, tempestuous day at?  Why?

Anticipation was building.  The kids were expecting the house on the sand to fall and the house on the rock to stand.  But, wouldn't the stream of water from my milk jug knock over both houses?  One girl thought that they were both going to fall over.  Others were convinced only the house built on the sand would fall.

Nervously, I started with the house on the sand.  A few moments after the water hit, the sand was soggy and the house was laying in the water.  So far, so good.  Now, the house on the rock.  I tried my hardest to pour the water directly on the roof of the house.  Amazingly, the house stood firm.  I continued pouring the water, clearly shocked that the illustration had worked.  My hands must not be the steadiest because eventually the house started sliding across the rock.  But, it remained standing, and I quickly stopped pouring the water to avoid messing up my illustration.

So, what's my takeaway from this?  I need to ask my students "Why?" more often in math class.  Why do you think that?  Why will that happen?  First, I need to start asking my students to make more predictions.  What do you think will happen if we do this?  Why?  My students will be more engaged and learn more if they see cause and effect in action.  Desmos will be perfect for this.  What will happen if I change the sign of this number in the equation?  Why?  Demonstrate.  Did it do what you expected?  If yes, yay!  Let's explore what happens if we change something else.  If not, why not?  What would we have to do to the equation to bring about the change that you originally predicted?

I need to ask more questions.  I need to have my students do more of the thinking.  I need to have my students do all of the thinking.  I get so caught up in trying to "cover" everything that they never grasp a full understanding of the basics.  I do the thinking for them ahead of time and give them the cliffnotes version.  But, they don't get to experience the math for themselves.  They don't get to get their hands messy with math.

Next year, my students will explore more.  Next year, my students will experience more.  I just ordered Max Ray's book on noticing and wondering, and I can't wait for it to get here.  This isn't the way I was taught, and it's going to take some getting used to.  But, I'm excited about the changes that are to come in my classroom.    

Detail: Asking Why