The Clarity of the Venn

What did I learn?

I learned the benefit of using Venn diagrams this week.  They are very helpful when showing the relationships among quadrilaterals.  This visual helped me “see” the relationships among parallelograms, rectangles, squares and rhombuses.    When I learned the properties of quadrilaterals, years ago in geometry class, we made grids similar to those passed out in class on Wednesday……which are very helpful, but the “picture” of a Venn diagram was even more helpful, at least to me.  The “family tree” of quadrilaterals was also a visual representation that helped me understand the relationships among these shapes.  Both are useful tools when teaching math.  

What do I have questions about?

When introducing new material to a class, how does a teacher know (when they see puzzling looks on the faces of their students) when they should stop for a question to clarify a point or to continue the lesson without interruptions (hoping that, by the end, the questions of those who didn’t understand are now answered)?  One of my favorite teachers in high school taught geometry.  She always did a complete lesson on the overhead (I’m dating myself) before taking any questions.  She would methodically go through a problem and ask us to write it in our notebooks, and then she’d work through lots of problems and let us ask questions.  This method worked well for me but I know I’m not representative of all students and that sometimes, if a student is “lost,” they just “stop listening”.

What are the implications for classroom practice?

The implications for our classrooms are clear.  In class on Wednesday, as I was struggling to learn the different properties of quadrilaterals, I realized that the Venn diagram really helped me “see” the relationship among the shapes we were studying.  The importance of presenting a lesson in multiple ways, to appeal to the many different learning styles of my future students, was again demonstrated.