Hi Joel,

     Thanks for the great questions.  Before I answer let me contextualize my comments a little bit.  I really do enjoy teaching math and science from the primary source documents.  And I'm looking to find others that share my passion, so let's keep in touch if you're interested in this.  My classes end up reading around 100 pages of primary source material or more per class because I believe it really grounds them in the discussion, the observations made, the manner of thinking by the greats, and the narrative of discovery.  I've also found that the students can go further conceptually by referencing primary source material then one would expect.  In my senior calc and physics class we do some very advanced work when reading Einstein's papers on relativity theory.  It involves not just tough physics, but elements of calculus 3 that the students learn while reading James Clerk Maxwell.  So even though I teach through AP Physics Electricity and Magnetism and AP Calculus BC the students, by tracing the primary sources go much further than the syllabus requires.

On the other hand, it would be very difficult to teach everything I do and prepare the students for the AP exams without using any textbooks (tertiary sources) and secondary sources.  When we work in the textbooks I want the students to master the problems with all the rigor that any other AP math or science teacher would expect.  The students will in fact not understand Maxwell and Einstein if they don't have some facility with the concepts. Textbooks emphasize the application of the concept learned to solving problems.  In contemporary math and science education, the correct application of the rule (for example the quadratic formula or Faraday's Law) is taken as proof of knowledge of the rule.  But for the ancients the derivation of the rule would have been taken as proof of knowledge.  Here I think we are wise to walk a middle road.  The contemporary emphasis on application and problem solving does help the students understand the idea and moreover it is crucial to their future success in college classes.  On the other hand, I do not feel the students are adequately taught unless they can demonstrate the "why of a thing" as Aristotle would desire.  So my call for rigor is to highlight that while teaching the "why of the thing" and the narrative of ideas, our students must be fluent with both the justification or proof of the concept as well as its application.  These proofs and the  application to problem solving are both rigorous, demanding, and require exactitude.

I have begun calling this approach "mediating the conversation".  We must get the students reading the primary sources like Ptolemy, Kepler, Galileo, Newton, and Einstein.  But they can not just read the Principia Mathematica cover to cover without interpretation.  The teacher will of course provide much of the interpretation, but other secondary sources can do that too.  In addition, the textbooks will often then give many helpful diagrams and resources to further dig into a concept.  This is the approach I take in my Precal, Calc BC, and Physics with Calculus classes.

Regarding Euclid, I don't teach geometry but am interested in it. And because of that I have always been big on Euclid, but I have not been in contact with anyone that has had great success with using Euclid's Elements alone as their sole textbook.  If you have been successful with Euclid, I would love to talk with you more.  But it was partly for this reason, that I urged caution for teachers that have never used primary sources before.  I suggest that they try them out in small doses lest they fall flat, get a black eye, and then have to backpedal. I have found that it takes a lot of work to contextualize the primary sources that I use and still get the students ready for the kinds of objectivist exams that characterize math and science education.  I would hate for crit