I was observed today. Normally on observation days, teachers whip out their very best interactive lessons. I however decided not to create an artificial lesson and to teach the lesson I planned to teach all along. This lesson covered the properties of isosceles triangles (and using them to find missing angles and sides) and area of a triangle.

My block 3 class (observation class) ran smoothly, as is typical of that group. I wonder if the students would have better understood/learned the material had I included "real-world" examples. But are there "real-world" examples of the properties of isosceles triangles? In what context would you use congruent angles to tell you the sides are congruent?

I can see some artificial contexts for area of a triangle. You could propose that a room is trianglular--but really, how many of us have ever seen a room shaped as a triangle? Is it better to just cover the material with basic examples or create artificial context?

I propose this question in light of what has been discussed recently on other math teacher blogs. I get the feeling that artificial context doesn't really help students learn the material.