Thursday, June 12, 2014

Giants and Mermaids and Fairies! Oh My!

I have been following the hashtag #tmwyk and browsing Christopher Danielson's amazing blog and website Talking Math With Your Kids. It's got me looking for opportunities to talk math with my own 6 year old and 3 year old daughters.

At dinner a few nights ago, my oldest daughter offers this bit of wisdom:

S (6 years old):  Daddy, if there was a giant here, his little finger would be as big as you. 
Me:  Wow, that's big! How big do you think his foot would be? 
S:  As big as the table! 
Me:  Can I ask you another question? 
S:  (with big wide eyes in anticipation... or suspicion) OK.
Me:  If there was a fairy here, how big would her little finger be? 
S:  (after some thought) As big as my finger nail. 

L (3 years old):  Ask me one, Daddy! 
Me:  OK, How long is a mermaid's tale? 
L:  (thinking, thinking... grabs a fork) This long! 

At this point I'm a little confused. L loves mermaids and has a good idea what they look like and how big they are. I'm not sure why she has chosen a small fork to represent her tail.

Then some magic happens! She pulls her milk cup over and explains:

L:  If this (cup) is the mermaid, then this (fork) would be her tail.

She has created her own scale model using her place setting. And S (never to be outdone) has her own frame of reference:

S:  If the mermaid was 6 years old, her tail would be as long as my legs.

I thought that was a good place to stop. I was wrong.

L (my wife, ___ years old):  How come I don't get a question? 
Me:  If there was a dragon...

Wednesday, May 14, 2014

Don't Ever, Ever, Ever Take the Pen Out of the Student's Hand!

One of my favourite things to do when students are whiteboarding problems (or designing labs, or playing with manipulatives) is to point at something that is correct and ask "Can you please explain this to me?"

The students' instinct to immediately grab an eraser under the assumption that something must be wrong because the teacher asked about it is incredibly strong and must be squashed.

I want my students to be able to talk to me about physics (or math) even when their answers are correct. Correct mathematical answers do not necessarily correlate to deep conceptual understanding. I want to know what they know. And I want them to be able to explain it to me with confidence.

Of course, I then point out something that is incorrect and ask again "Can you please explain this to me?"

The teachers' instinct to immediately grab the pen (or pencil, marker, crayon, manipulative, mouse, iPad - hereafter all referred to as the "pen") out of the students' hand to "show" them the correct way is incredibly strong and must be squashed.

Don't ever, ever, ever, EVER take the pen out of a student's hand.

Why? These are some of my thoughts:
  • It turns a problem or inquiry activity into a lecture.
  • It makes the teacher an integral part of the conversation (not a good thing).
  • It makes the student a spectator rather than a participant or leader in their learning.
  • It makes the student a listener rather than an explainer.
  • It removes responsibility from the student to explain their thinking and reason through the problem.
  • It negates any opportunity for a student to self-correct by discovering the flaw in their reasoning.
So, I resist the urge to grab the pen. Instead, I continue the conversation something like this:

Me: Can you please explain this to me?
Student 1: We are calculating the coefficient of friction. We know that the force of friction is equal to the applied force.
Me:  How do you know?
Student 1: Because the forces are balanced.
Me: How do you know?
Student 1: Because of Newton's 1st Law.
Me: How do you know 1st Law applies here?
Student 1: Because it is moving at a constant speed.
Student 2: Wait. It's not moving at a constant speed, it's accelerating.
Student 1: What?
Student 3: Ya, see the position graph is curved so there is a change in velocity.
Student 2:  So there must be an unbalanced net force.
Student 1: Oh, I see. So the friction force is not equal to the applied force.
Student 3: But how do we figure out the friction force then?

The entire conversation is student driven. They supply all the arguments and reasoning. The only thing I say is "How do you know?" This forces them to get to their fundamental assumption, the bedrock of their reasoning which is Newton's 1st Law. Once there, the error in their assumption becomes obvious. They self-correct and move on to the next problem, determining the friction force.

Notice how the teacher becomes unnecessary at some point. In fact, I probably walked away around the time that Student 2 jumps in. And I am no where to be found when they start asking what to do next. I am not needed.

And the pen is where it belongs, in the hands of the students.