We searched long and hard and did a couple of years of research before settling on the Trivium method. Yes, the boys learn Latin as part of their schooling, and it's far from "backward-looking." Not only do they study how the Greco-Roman society influenced our Founding Fathers; they also recognize the root of many English words, which helps them decipher meaning based on the Latin they already know. (Example: one of this week's spelling words for my 5th grader is "culpable." He already knows that in Latin culpa means "fault." Easy as pie.)
For people looking into home schooling I'd highly recommend, "A Well Trained Mind," (Jessie Wise and Susan Wise Bauer). It lays out the Trivium method in a very concise, well thought out format.
I second that recommendation. For those investigating homeschooling and especially the Trivium, they lay out not only theory but also specific suggestions for study and curriculum.
We don't follow any specific curriculum but have instead built our own based on what we deemed to be the best in each area. Our kids are thriving, brilliant, fun, funny, well-behaved, personable, and great people to be around. I love homeschooling.
(Aside: We visited a church last week and the boys sat quietly and mannerly through the entire service...the other children left for children's church, but as we were just visiting, they wanted to stay with us. They were the only kids left in the service. An hour later, literally dozens of people came up and shook their hands and told them how unusually well-behaved they were. One of the crowd asked where they were going to school, since we just moved to this town. They answered, "We homeschool." One lady said, "Well, that explains everything.")