Like any good teacher, Shad fixes Jethro up with a fancy schmancy homemade map of the country, complete with important battle landmarks, railroads, rivers, and—most importantly—the Confederate line separating the country. All this is done to help Jethro understand why Forts Henry and Donelson are really nice feathers in the Union's cap, and Jethro feels "a great satisfaction" (4.105) when it all finally clicks. In this way, the map represents both Jethro's youth and naiveté, and how much he grows and learns over the course of the book.
In addition to being a great teaching tool though, Shad's map also represents a piece of Shad that he leaves behind with Jethro. Though originally used to educate Jethro on what the North will have to do to officially win the war, once Shad is gone, Jethro continues to use the map to track the progress of the war in combination with the information he receives from the papers and word of mouth. It's almost as if Shad is still there teaching him, and his map acts as a guide for Jethro. Which is not a surprise since, duh, it's a map and you're supposed to follow maps.
But Shad is also a map himself. We already know that Jethro adores Shadrach Yale, but consciously or not, Jeth also follows in Shad's footsteps. It's established pretty well early on that Jethro is a bright kid who enjoys learning (1.19), but the war kind of puts a hold on all of that once Shad joins up with the army.
During Shad's absence, Jethro takes responsibility for his own education. Good thing he has Shad's map—and all Shad's book that he left with Jethro—to help. Jethro even assumes the role of teacher himself, using the map to explain to Jenny, "it's just a little piece of river; once we take that, it's like Shad told me—the Confederacy will be cut in two" (8.3). Shad leaves some pretty big shoes to fill, but Jethro doesn't mind trying them on. In fact, he seems to kind of enjoy it.
While Shad is away at war, Jethro embarks on improving his speech with the help of Ross Milton. You know who else speaks properly? Yup—Shad. Shocking, we know. By the time the war is nearing its end, Jethro is writing and speaking like a respectable young gentleman—or at least he's trying to, and trying is half the battle.
Even Matt Creighton acknowledges the good influence that Shad has on Jethro, allowing his son to ditch school after Jeth makes a compelling argument that includes, "'I get more out of staying home and reading the newspapers—the way Shad told me to do'" (10.33). Even from afar, Shad is an ace in Jethro's pocket. But while this argument works for Jethro, we don't recommend trying this angle at home.
You know how Shad is literally a map for Jethro? Well he picks right up where he left off when he returns home with Jenny and tells Jethro that he will officially follow in Shad's footsteps by getting a good education while living with Shad and Jenny. Shad also informs Jethro that "[John] wants you to get an education and then later to help his own boys along the same road" (12.102), so it looks like the long-term plan is for Jethro to become a teacher… just like Shad. Now that's a map worth following.