How to Teach Proofs in Geometry

Teach your students the art of proof writing.

Through the composition of geometry proofs students can demonstrate their understanding of geometry rules and facts. Many students struggle when it comes to learning the proper proof form as the process differs so significantly from other math activities they have completed in the past. By working patiently with your students to explore the process of proof composition you can enable them to successfully demonstrate their geometry understanding.

Instructions

1. Educate students on geometric math facts. To successfully solve proofs, students must be well versed in an array of geometry rules. Before beginning to tackle proofs, spend time learning some of these rules that students can use as evidence once they begin the composition of these wordy math solutions.

2. Teach the two-column proof method. The two-column method is a systematic approach to proof solution and, as such, is a great place to start. To compose proofs of this type with your students, have them draw a two column chart. On the left side of the chart, instruct students to write their statements of fact regarding the math problem they are exploring. In the right column, ask them to write their proof, making reference to the facts that they have learned about geometry laws.

3. Practice with simple proofs. Before giving students proofs that may actually prove challenging, allow them to practice their basic proof writing skills through the composition of easy proofs, such as ones that ask to to prove that two angles are equal.

4. Demonstrate how to transfer the two-column proof to a paragraph form proof. Ask each student to select a two-column proof and re-write the proof in paragraph form, using sentences to explain the proof instead of relying upon this set form.

5. Encourage students to avoid worrying about wording. Many students become frustrated when they over-think their word choice. Remind students that proof writing is not like composing an English essay and that it's the meaning of the words that matters, not how elaborate or simple each term may be.

6. Challenge students with increasingly complex proofs regularly. Instead of inundating your students with a pile of proofs, start each day with one of these puzzles. Increase the difficulty of the proofs you present gradually as your students' skills improve.

References

• TheMathLab: How to Write a Good Proof
• MathForum: FAQ About Proofs