Have individuals or teams look at an original primary source, interpret it, then discuss with the class, who all interpret something from a related source. Students put their heads together, discuss/debate and post some interesting original research to the Net.
Primary sources are way above the level of most college mathematics students, much less high school or younger students. Almost anything written in the last 50 years requires very advanced mathematical ideas, while anything written before that uses outdated notation which is very difficult to understand. Moreover, the primary sources for common ideas are often spread out over huge periods of refinements - going from a small idea to a general notion over the course of years, perhaps involving dozens of papers by multiple authors. One notable exception to this: Euler's papers. These might be readable by some students, yet when I see them presented in college courses, they are often presented by a secondary source for clarification.
The other thing I don't agree with is your use of the word "interpret." I don't think that it is common to find a mathematician who believes that mathematics is open to interpretation.
Lastly, original research in mathematics is hard. It's not the interpretation of previous ideas (although it is occasionally relating concepts previously thought to be unrelated - some consider this the most important type of mathematical result, but it is much harder to do than you might think), but the formulation of new ideas. Even to know if an idea is new requires a great deal of mathematical training.
Perhaps I'm wrong about this, but I think that for young mathematics students your ideas are unfeasible. Remember that the original sources for a lot of basic mathematics are hundreds of years old. Even Euler's famous writings on geometry (the exception that I said might be workable) were largely a rewriting of previous ideas into a coherent whole - basically a textbook - and could not really be considered an original source.
Edit: my apologies, I misunderstood. I did not realize that we were talking about teaching history, in which case I defer to someone of greater experience.
I wholeheartedly agree with the idea of primary sources, and of studying mathematics historically in general.
The Elements of Euclid is a model of clear, concise, beautiful mathematics which is easily accessible. Archimedes as well. Follow that up with Apollonius, Ptolemy, some Descartes, and then Newton, and you have a junior high and high school curriculum in mathematics that would give students a real advantage over the rote "here is what Disembodied Authority says you should know" learning.
Note -- I am not advocating the study of mathematical history in junior and high school, but rather the study of mathematics historically. It gives access to mathematics as a branch of the humanities, less focused on the answers, and much more focus on the questions and how some really smart people have addressed those questions in the past, which gives a good guide on how to address new problems that will come up in the future.
When it comes to history specifically, as the OP asked, I would still agree with going with some of the great works of history. Historiography can be left for college, but give the kids access to the letters and diaries and personal accounts of people who were at the scene of history, as well as the great works of history that have been written (Thucydides, Herodotus, all the way to Toynbee, Gibbon, and, hell, even Spengler). Drop the mundane and milquetoast textbooks.
I always missed the historical context in high school, especially with chemistry and to a lesser degree physics.
You always knew that the current model you were being taught was "kinda wrong" or not the current state of knowledge (Rutherford's atomic model, Bohr's atomic model, and so on), but you never heard anything about the motivations of the people developing it.
Primary sources can be rather dry/difficult reading. I'm fairly intelligent, but it's just not easy for me to grok older style language.
I have had some experience with reading primary sources though. I had an excellent history teacher in high school who had us read The Autobiography of Benjamin Franklin to prepare us for American History. Now, Benjamin Franklin is a fascinating person, and he did plenty of extremely interesting things, but I had a lot of trouble getting through the style it was written in. I love learning about the things he did, but the language and style of his autobiography just did not work well for me.
Primary sources are an option, but it doesn't work for everyone.
Strongly agree with that one. I've always hated history going through school. Then I took an american literature class in college where we read primary sources from the early colonies up to the founding of the US. I enjoyed every minute of it. I learned more about history in that one class than probably the last 14 years of education combined. History should all be taught this way.
primary sources is known to be one of the worst way to study any field, especially when you are not familiar with it, because you lack the context, and because they are rarely written for the profane. This is all the more true for maths: have you ever read a math books from the XIXth century ? This is almost impenetrable, if only because of the formulation
Have individuals or teams look at an original primary source, interpret it, then discuss with the class, who all interpret something from a related source. Students put their heads together, discuss/debate and post some interesting original research to the Net.