Sunday, September 28, 2014

Is a Square a Rectangle and Other Questions to Ponder

Is a square a rectangle?  Is a rectangle a square?  This is such a fun conversation to have with learners!  For you see, a square is most definitely a rectangle.  Don't believe me?   Neither do the kids!  Let's take a look at the conversation that ensues.

What is a Rectangle:   a closed figure with...                                    
  • four vertices                                    
  • four right angles
  • 2 pair of parallel lines
  • four sides  
          

Does a Square Have...
  • four vertices...yes!
  • four right angles...yes!
  • 2 pair of parallel lines...yes!
  • four sides...yes!            
         

Does a square meet all the criteria for being classified as a rectangle?  Yes!

Conclusion?

All squares are also rectangles.

This is where the fun starts, for now that I have the learners fully convinced that a square is indeed a rectangle, it's time for the next phase of the conversation.  I begin with another question.  This time I want to know, "Is a rectangle a square?"  Now, fifteen minutes earlier, every child in the room would have absolutely sworn that no, a rectangle is definitely not a square...it's a rectangle!  A rectangle is a rectangle and a square is a square, and by the way Ms. Malone, what's wrong with you today!?!?!? 

But remember, I just spent fifteen minutes convincing every one of them that a square is, in fact, a rectangle, so for these learners, it naturally follows that a rectangle is also a square.   Unfortunately, they couldn't be more wrong.  (Are you beginning to see why I have so much fun with this conversation?) 

Let's take another look at the criteria.

Square: a closed figure with...

          
  • four vertices
  • four right angles
  • 2 pair of parallel lines
and...
  • four congruent sides

Rectangle: a closed figure with...
  • four vertices
  • four right angles
  • 2 pair of parallel lines
and...
  • four sides
but... those sides are not necessarily congruent!

            

Conclusion?  

All squares are indeed rectangles, but not all rectangles are squares.

Okay, fun conversation...but what's the point?  

Well, some might say the point is to help kids to understand the difference between a rectangle and a square...nope!  

Maybe it's to give kids a chance to talk to each other using mathematical language?  Important, but... nope!

Learn more about squares?  Nope!

Learn more about rectangles?  Nope!

Show them the teacher is always right?  Ha..tempting, but most definitely...NOPE!

Here's the point.  Through this conversation...and others like it...kids learn to evaluate ideas, concepts, decisions, etc...through the lens of the criteria that define them.  

Ahhh..cool!  But as we say in the classroom...So what?  Now what?

Well, this same line of questioning can be applied to any number of topics in any number of ways. For example...
  • in a family...a dad is always a father...but not all fathers are "dads."
  • at the grocery store...an carrot is always a vegetable...but not all vegetables are carrots.
  • in your neighorhood...a home is always (or usually) in a house...but not every house is a home.
  • in the world of construction...all buildings have a foundation...but not everything with a foundation is a building.
and...
  • in the Schoolwide Enrichment Model...all enrichment experiences are enjoyable for the participants...but not every experience that a learner enjoys is enrichment.













Whoa...what?  I thought the Schoolwide Enrichment Model was all about student interest...passion based teaching...learner driven instruction?   

YES!

And that it involved providing enrichment experiences for all learners based on those interests?

YES!  

And if learners are interested in something, they will enjoy experiences centered around that interest?

YES!

So therefore enjoyment = enrichment?

Ummmm...no!





















Let's go back to the criteria.  

What is Enrichment?  
  • learner driven
  • no pre-determined lesson plans
  • interest based
and...
  • authentic tools / methods
  • advanced content
  • real world problem solving













What is Enjoyment?
  • learner driven
  • no pre-determined lesson plans
  • interest based
  • fun!
but...
  • may...or may not...include authentic tools / methods
  • may...or may not...include advanced content
  • may...or may not...include real world problem solving









Conclusion(s)?

All enrichment is enjoyable...but not all that is enjoyable is enrichment!  

Click on the link below for more information about how the Schoolwide Enrichment Model is changing the face of learning @Austin Elementary!