To conduct a middle ages Socratic discussion would I need to buy the Introductory Teacher and Student Instructional DVD AND the Take a Stand! Medieval Civilizations or just one of them?
It depends how much you have already conducted Socratic discussions. I can't assess exactly what you need, since I am not sure how much you have taught and how comfortable you are in leading a discussion. The DVDs show students learning the tools of the historian, and your child and you can learn these tools along with the DVD lesson. The DVD also shows Socratic Discussions based on the Ancient and Medieval World curriculum.
Teaching with the Take a Stand! series helps me get to know my children and students better and it helps them how to think critically, form historical judgement, and express themselves in speech and in writing.