I first started teaching Geometry last year and have taken over "Informal Geometry" this year. As the name of the second class implies, the idea of formal proof is strongly de-emphasized; this class is for kids who really struggle with mathematical concepts and computation. However, even in our formal geometry and honors geometry classes, we still tend to largely ignore the "two-column" proof.
By the time I'd left the 9th grade, I could do 2-column proofs in my sleep. Unfortunately, this sort of proof isn't just busy work for the kids. It's an important lesson in logic that translates directly into programming and computing skills, as well as mathematical and scientific problem solving.
The trend in education is to avoid these proofs in favor of narrative descriptions and prose about how we relate geometrical concepts. While writing is an invaluable skill and should certainly be emphasized across the curriculum, an entire generation of students is missing a tool that leads directly into computer science and algorithmic studies.
I gave my students an extremely simple proof to complete on a test yesterday. In fact, they were given a bank of reasons, the statements were filled in (in order), and students merely had to fill in the blank. All but one of 28 students failed this portion of the test.
While it's true that these students will probably not be the next Alan Turing, this problem points to a general lack of problem-solving skills. As we fall further behind in technology education and more software development is off-shored, something as fundamental as rigorous logic studies in math can't be ignored. Talk back below and let us know how you get through to your proofless students and ensure that they can walk out of high school with a set of reasoning skills.