Seeing Through the Eyes of your Students

During my coursework at Ohio State, I read a powerful article that made me think more deeply about what questions we might ask students.  The article was written by Shelly Harkness who is currently a professor of mathematics education at University of Cincinnati.  Entitled "Social constructivism and the Believing Game: a mathematics teacher's practice and its implications', the article examined how teachers responded to students when the teacher took the position that what the student said was correct - regardless of the accuracy of the student's statement.  You can access the full article here: http://bit.ly/1rgRAEY

Harkness writes of a student who responds "false" to the statement that All triangles have three sides.  The student is asked to come to the board and draw a figure to represent what she sees.  She draws the following:

The teacher responded, "No.  That's not a triangle.  It's not flat.  The answer must be true."  The conversation ended and the class moved on.

Harkness writes that the drawing above made her reconsider her own thinking about the mathematics.  She wondered if Kayla looked at each side individually, thinking each of the four sides was flat.  What questions might you ask Kayla to explore three-dimensional space? What discussion might you have about sides and faces?  Or about geometric language?

What does Kayla know about triangles?  How might this knowledge be influencing her interpretation of the question?

As we begin this new school year, I encourage you to assume all answers your students give are correct.  At least from their point of view.  Children do not intentionally give incorrect answers - the answer they give has validity from their point of view.  Working to understand why they believe they are correct is the first step to uncovering their misconceptions and working to build their understanding.  This school year, work to build meaning together WITH your students.