More on Geometric Proofs.

When I went through the teachers program, the focus was on starting at the beginning to the end but it was not necessary to have students fully understand why.  In fact, I got through high school without writing a single proof so I never learned to do any until I started teaching.





In the past few years I’ve been looking for better ways to teach students how to write proofs.  It needs to be done so students understand why you do things in a specific order.  I tend to have students draw a flow chart to determine the order of steps in a proof before they actually begin the proof.


I also have students create two lists of theorems, postulates, etc. one list has the names of them while the other list has the same list with what it is used to prove or support.  The first list is on the left hand page while the second list is on the right side.  It is important to know what each theorem etc is used to prove in a proof.

Another thing is to work on having students fill in the given information before they do anything else.   My students had so much trouble understanding they needed to start with the givens.  I finally explained it as the givens are what ingredients you have to make a cake with.  The prove is the type of cake and the in between is where you get the rest of the ingredients, mix them in the right order, and bake it.

One way to make the process a bit easier is to begin with a fully done proof and cut the lines of statement and reason into pieces, mix them up before having students reassemble them into the
correct order.The next step is to begin removing reasons so students fill the reasons, then take out some statements and reasons but not for the same step.

I like having students use colored pencils to highlight the parts of the diagram and then write the statement and reason in a matching color so students “see” what they’ve done.  It is important to mark up the proof with arrow etc so students see how the steps relate to each other.

All of these things make it easier for students to understand the process of writing a successful geometric proof.  Let me know what you think, I’d love to hear.  Have a great day.