The author of this article is really addressing her paper to new mathematics teachers. She gets this idea to write about how to teach proof when watching a new student teacher struggling at teaching proofs. She comes up with ten ways to think about proofs to make teaching proofs more effective. First, students should have sufficient understanding of the lower level mathematics needed for proof. Second, have the students think about proofs as a problem solving activity. This is more engaging. Third, make doing proofs a central part of the classroom and not a rare occasion. Fourth, be sure the students understand that proofs are used to explain why something works. Fifth, talk about the necessity of using assumptions and other rules of proofs. Sixth, make sure you as a teacher are fluent and ready to teach proofs. Seventh, she recommends using flow proofs rather then two column proofs because flow proofs are easier to understand and see. Eighth, provide enough wait time for students to think about proofs on their own before interjecting and solving the proof for them. Ninth, students should be making informed guesses before they ever try and prove anything. Tenth, and lastly, she suggests to teach proofs not theorems. By teaching proofs the teacher can show where theorems came from.
Teaching proofs can be a daunting task. It can seem very overwhelming, especially to a new teacher. This article is a great resource for beginning teachers to draw from. Just having guidelines is helpful for a student teacher who is overwhelmed with teaching. It is a source of comfort and suggestion. Just knowing that another teacher has struggled with teaching proof is nice to know. Its nice to know that it is common and normal to struggle with teaching proof. These are great guidelines written by someone with more then 20 years experience teaching. Teaching proof and having students understand is an accomplishable goal if done with great care and premeditation.