And when the student went on with her explanation of why the two triangles were similar well, I was blown off my feet. Because on the tests she never showed any understanding. SAT's and standardized tests concentrate on memorization of math. The bottom line is children learn in different ways. There is more than one way to pass on information to students.
Memorization does play a part in all of learning.
When you are involved in, lets say, a Math Trail project, many times problems that are created come from what a child remembers from a topic that you have covered. It is key to remember that to do well on any examination students must be empowered. Empowerment comes from their ability to understand. You know students understand when they write and speak about what they have learned. A project like the Math Trail allows students to show off what they really have gained an understanding of.