Are You Smarter Than a 1st Grader?

12.10.10 By Aira Jackson-Sams

So….last Wednesday at the BPS Math Facilitators Meeting (a monthly meeting for schools to meet with the BPS Math Department) our entree into discussing squares and rectangles was an activity in which we (teachers) were asked to sort different shapes: quadrilaterals [a quadrilateral is a shape that has four straight sides, four angles, four corners, four vertices (love that word); think rectangle, rhombus, trapezoid] and curved shapes.  My partners and I easily sorted the shapes until we got to the Chevron (imagine a shape similiar to that of the Star Trek logo, but the corners are not curved) and at first I said, “no, it is not a quadrilateral,” and then my partner said “maybe…”.  I was so confused and felt incredibly self-conscious - it was not like any of the quadrilaterals I had encountered while teaching my 1st graders.  But my partners were very generous and explained how it was a quadrilateral and pointed out the attributes. As we ended our activity, we moved into a discussion about what we had just done and if there was any confusion.  I of course raised my hand and shared what had just occurred for me.  And I boldly stated that though the Chevron fit the quadrilateral attributes, I did not think my 1st graders would agree or recognize it as a quadrilateral because I had not taught it, nor did we have it among the manipulatives we had just used for the past month.  Maybe as they got older and learned more, but at the moment they woulldn’t know what kind of shape it is…

As I drove home after the meeting, I started thinking… did I really know what my students knew about quadrilaterals?  There was only one way to find out!  Thursday afternoon, I started a discussion with my students about quadrilaterals; we reviewed the meaning, talked about their attributes, and gave examples.  I then presented my students with a drawn image of a Chevron with the question, “Am I a Quadrilateral?”; next to the image was a “Yes” and a “No” sign. 

I asked each table to come up and look at the shape and to write their name under the opinion they agreed with.  Once everyone signed their name, I explained to my students what had happened the previous night, and how confused I was about the shape.  Then I started asking different students to explain why they thought the Cheveron was or was not a quadrilateral.  Throughout the discussion, I kept telling my students there was no right or wrong answer and that we were talking about this shape to have a better understanding of math. 

Finally, when the comments slowed down, I told them the Chevron was a quadrilateral and explained why.  I introduced the word “concave” and gave a very rudimentary explaination of right angles and degrees.  Our conversation continued, but now it was peppered with lots of questions about the middle point and how it really was one of the four vertices.  We used our hands (imagine the church steeple) to display that regardless of what direction the point is facing it is stil a point, vertice, and or angle.  It was an awesome learning moment!!!

I felt that this conversation deepened my students’ (and my own) understanding of quadrilaterals, because it took them beyond our classroom shapes/manipulatives and let them talk and explain their understanding of shapes.  Now not every one of my students may have been convinced that the Chevron is a quadrilateral, but when my students get to fourth grade and are looking at irregular shapes - they may just remember this conversation.

Oh, and most of my students did think it was a quadrilateral…see for yourself!