There are many differing views in the math teaching world about this, ranging from "proofs are a waste of time" to "proofs are absolutely essential," and everything in between.
While proofs have their value and are used in the professional math world, students do not write formal proofs in my course. Throughout the course, I teach students to use logic and the rules, definitions, theorems, and postulates of geometry to work problems, but we do not write formal traditional proofs. There are several reasons for this.
1) When writing a proof, there is no "one answer" for the proof. If a proof differs from the answer key, it needs to be closely examined. Often, I find students will take a different, unexpected, or less direct route to a correctly written proof, but rarely discover this by just comparing to an answer key. This can be very discouraging for students, causing them to hate geometry or to unnecessarily lose self confidence in their math ability.
2) Formal proof writing is never used anywhere in any math courses going forward, nor is it tested on standardized tests. This was not my main reason for excluding formal proof writing, but it did play a part in my decision.
Having said all of this, I am not anti-proof, and it does have value. But for a typical homeschool geometry student (the audience for this course), I have found proof-writing to be very counter-productive.
In 20+ years of teaching math (11 of them in public school), I did not see any positive difference in student performance in the years I taught heavy proof writing vs. the years I taught little to no proof writing (I experimented both ways). In fact, proof writing actually tended to have negative effects on the students (they pretty much universally hate writing proofs, which makes them hate geometry and sometimes math altogether).
There are excellent teachers on every point along the traditional geometry proof spectrum, but this is the reasoning behind excluding them from my courses.
HS.
