Today my family visited some long time friends. They are actually my husbands' super nerd friends (think computer programmer/ security types who play role playing games). The host is an adjunct professor who teaches intro. to programming at a local university. We had a GREAT conversation about math, problem solving and computer programming. We also talked about Moby Dick and the Count of Monte Cristo - NERDS!
This was his first full year of teaching and I am so inspired by his desire to help his students learn. As all of them were talking, they agreed that geometry was the last math class they really enjoyed and the one that probably helped them the most in computer programming and other later logic courses. The logical proofs taught them to break things down, work step by step and find the fewest steps to solve a problem. It taught them the essentials of problem solving.
He said that his intro. classes were difficult to teach because most of his students don't understand the basics of logic and problem solving in math. They knew some formulas sure, but didn't see math as a set of tools for problem solving. Without this fundamental piece it made programming, in a different language no less, very difficult. He is now searching for ways to help fill in that gap for his students.
So, maybe a good understanding of geometric proofs (after students have played with geometric figures a lot - as Boole recommends) could prepare your students to be computer programmers! It seems that Math Mammoth has a series of four geometry books for elementary students that focus on construction and playing with concepts. Really, some simple manipulatives like tangrams, constructive triangles, angles and lines, geometric solids (for younger kids and older kids), pi and circles (check out way #3), and geoboards are fun ways to play with these ideas. Here are some geometry/ montessori pinterest boards, page 1, page 2 with even more ideas, lesson plans and Montessori geometry printables. Maybe these are worth playing with over the summer and letting kids spend more time with them than we normally might.
Honestly, although my friend didn't understand my argument, I think that Latin could accomplish some of the same goals. It is very logical, it teaches you that different languages require a different syntax and there is an exactness to Latin.
Another pet project is finding one of the simplest but most useful programming languages to teach his students. Currently, they learn Java and the nerds discussed other potential program options. He said that one of the best uses of minecraft might be to learn how to program new modules - when I got home there was a program that teaches just how to do that in Java (it is currently on sale at educents.com). If I had received the email yesterday, I wouldn't have known what it meant! Today, I am educated!
Basically, I was very encouraged that focusing on math (especially geometry, which my son really enjoys) and Latin might produce some "real world" skills indirectly. These are subjects worthy of study in and of themselves, but sometimes it is helpful to explain to people why dead languages and obscure math (like Euclid in his original form) are worth our time.