Math Learning Through Inquiry

Why I teach the way I teach and why you won't see my students completing worksheets.

My first "blog" and I have to admit, I'm a bit shy.  I have read many great learning journeys by some fabulous teachers coast to coast to coast.  This year my professional focus is to make learning visible for my students and for my parents at home.  

Most of our learning in math takes place off of worksheets.  Worksheets only focus on one right answer.  What does it mean if you have the right answer and what does it mean if you don't?  Worksheets don't allow for students to extend their thinking or to enter into learning where they are developmentally in their thinking and knowledge.  

Last year my students were thinking of how they could sort the alphabet.  I sat down with one of my students who needed help to learn through guided questioning.  This was our conversation:

Me:  How can you sort these letters?

M:  Some are straight and some aren't

Me:  Which ones are straight?

She put all the straight upper case letters in one group

Me:  Which ones aren't?

She started to put the curvy ones like O, S in one group when she stopped.

Me:  What do you see?

M:  This one has both

Me:  Yes, this one has straight lines and curvy lines.  Let's stop here because I want to share your thinking with the rest of the class.  

The next day I re created M's problem for the class sharing her thinking and using her thoughts to highlight the learning.  The straight lines in one sorting circle and the curvy lines in the other sorting circle.  

"M noticed that some letters had curvy lines, and some had straight.   How can show that using these two circles?"

Responses:

Put them on top!

Put them underneath!

Would that work?  Then there was the silence.  There was a lot of silence.  And in teaching 10 seconds seems like an eternity.  But my class was great at letting the silence be just that.  Silence.  They knew that some students needed a lot of time to think.  

With this essential wait time came more ideas:

Put the hoops together! 

More wait time....

My one student who would turn out to guide us in very unexpected places took one hoop and placed it over the other hoop creating space in the over lap and .. and essentially a Venn Diagram.

The next moment is etched in my memory forever.  He jumped up, and lept around the room skipping and jumping and celebrating.  He knew that he had done it.  He knew that the space in between these two hoops meant that it shared characteristics from each side.  Whether it was somewhere back in his mind from the previous year, we'll never know.  

What I do know, is that he, and the rest of the class think that he discovered what we would then call a VENN DIAGRAM.  

This learning moment would have never been found in a worksheet.  This self-directed learning and student discovered knowledge will be planted like concrete in his brain.  I know.  I saw it all year.  Months later...and I mean at the end of the year, I took the two hoops and watched M talk about her "problem" and the rest of the class recreate this moment - step by step.  And yes the student once again lept around the classroom celebrating the learning......and the rest of the class followed him in his dance celebrating with him.

Teaching math through inquiry allows the opportunity to reach all learners.  Every student knows that it's not about the right answer.  It's about their thinking.  It doesn't matter if one student says 20 and one student says 3.  They know that their thinking is what is valued and cherished and wanted.  As my students have gone on in their learning these words have been used to describe them:

Brave       Creative           Collaborators       Thinkers

I hope that as they continue on in their learning journey they continue to be

Brave      Creative          Collaborators     and Thinkers.