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.
That was a very thorough summary! I have to say though, I would have enjoyed reading the summary more if it wasn't simply a list but you got the point across which was good.
ReplyDeleteI am also wondering, are we supposed to refer to proofs as proof, singularly? It seems weird to me but I have seen it in other articles too... hmmm?
This was a great summery of the article. I really like the topic and the detail you put into the summery. I really want to read this article now. I think the structure was great. How successful was this style of teaching proofs? did she get any feedback from other teachers?
ReplyDeleteI really like that you included in your summary who the article was written for. This article seems like a very interesting topic as proofs are very essential in the process of student's learning, especially as they get into higher math classes. I'm just curious if you think there are any negatives to proofs, as we all know students don't tend to like them very much.
ReplyDeleteI felt that the first paragraph could have had a clearer topic sentence, but you did a nice job summarizing.
ReplyDeleteI thought the third sentence of your last paragraph was the topic sentence. You did a very nice job giving reasons why this article is helpful for new, and old, teachers.