russelpolk

Using the method described will also avoid the isolating of geometry to its own little world, not explored until many years down the road.

Perhaps. In one of his presentations Dr. Perrin said that academic performance is a side benefit, or a secondary gain of classical education. You may be right: While a sports program may raise academic performance, that is secondary to the point of whether to have a sports program. So, someone proposes starting a football team. To support his proposal he presents his data about the correlation between sports participation and academic performance. It's effect on academic performance is irrelevant since academic performance is a secondary objective. Had he touted the idea that a sports program would somehow help develop Truth, Goodness or Beauty, would that have been relevant?

When does an Irrelevant Thesis change to a supporting point or secondary gain? In example 1 the speaker says they should have a football program because there is data that shows that students who participate in sports programs perform better academically. Let's take as a given that the data the speaker possesses is accurate. If the goal of the school is to have students do well academically and a sports program helps accomplish that, where is the fallacy? Perhaps in being to specific as to the sport?

I like Ms. Floyd's statement that, "A fallacy is an error in part of the reasoning that renders the conclusion invalid." Metaphorically, it is the one piece in the Jenga tower that, when removed, causes the entire structure to collapse. Having gone through 14 of the lessons in this book I can see where 40 fallacies in one semester would be rigorous in the extreme for middle-schoolers. As you noted, it would give them little "time to practice and contemplate the concepts and skills". Twenty-eight fallacies on the other hand obviously dials it back a bit to an appropriate number for a semester. Plus the book is entertaining enough for students through the artwork and mock conversations to make it enjoyable. It seems like twenty-eight, is manageable considering the discussion and homework needed.

There is a "depth of knowledge" necessary to teach math, but what depth at what level? I can see the necessity in the Upper School levels, but in the Grammar school, it would seem to be more necessary to know the chants and "jingles" well. Perhaps alternatives if a student doesn't understand something when taught in a particular manner, but that takes more flexibility in method rather than depth of knowledge.