Are Geometry Proofs Still Needed?

My students wonder why they need to learn all those postulates, theorems, etc we normally teach in Geometry class.  Why write proofs using them if they can “see” why, then do they need to “prove” it. I ask them if they can explain why two triangles are congruent using the given information.  About 98 percent of the time, they can’t, so it proves they do need to learn it all.

I believe it is important because the theorems, etc, give us a much better grasp of geometry itself. I think half the problem is that many of us teach proofs the same way we learned them, in a very dry and straight forward manner.  We start with the given and go to the end, using the appropriate theorem, etc with the appropriate reason. We do not spend enough time helping them understand all the connections.

If you look on the internet or in app stores there is nothing that is set up to automatically do geometry proofs so students have to search each problem individually to find a proof for it.  In my search for this type of site, I discovered this site which has interactive proofs for a variety of problems.

By interactive, I mean it provides a problem with the given and prove part along with all the steps and reasons mixed up. You drag each step and reason into the correct location until all the spaces are filled. Once you are done, click the check button and it lets you know if your solution is correct. If it’s not, it simply says try again.

This makes it a great practice site because students do not have to figure out all the steps necessary. If a stun dent is incorrect the first time they try it, they can erase everything and start again.  The site allows access to certain proofs so you can assign them or you can create your own. In addition, students can hit a button to bring up a random proof.

As a teacher, you can copy and paste a link to a random problem that focuses on a proof you want them to practice.  If you do not find a proof you like, you have the ability to create your own interactive proof using the names of theorems you want. The great thing is that the site is free to signup for and use.

Tomorrow, I will share some great tips for teaching proofs so students end up with better notes and are easier to understand.  let me know what you think, I would love to hear.  Have a great day.