I'm not sure if I have made mention of the differences in mathematical maturity between students who take calculus I in the fall as opposed to those who take it in the spring, but in order to give some direction to this blog I will say that students who take calc in the fall are typically stronger than those who take it in the spring (at least this is true here at UMM). Since our calculus class is taking place in the spring, I have had the chance to witness and experience some of the difficulties that some of the students in a spring semester of calculus face. While a large part of the students can succeed, success is somewhat contingent on the presentation of the material. Barry was well aware that he need to treat our spring semester class just slightly different (with respect to how he presented the material) and he made sure I understood this. While I was aware of the students abilities, I did not quite catch on to how Barry has managed to polish his teaching style so that these students could improve in such a way that would prepare most of them to succeed in a section of calculus II.
I believe the way that this happens begins with how Barry lectures. For example, when I presented the material on u substitution I hurried through some of the tedious algebraic steps, believing that the students would follow what I was doing. And for some of the students did follow, and I feel that most who didn't follow right away could have followed if I had quickly jotted down the of the rule of exponents that we made use of. This may have taken just 10 seconds and would have ensured that all the students knew what I was doing. While Barry felt strongly about my presentation on u substitution, he made note of the fact that I should have made quick mention of the rule of exponents that I was using. While this is just a small detail that would have made my lecture more self contained, such details would benefit some of the students in our calculus I course.
For the most part much of the feedback that I received from Barry pertained to small details that, as Barry said, "Come with experience." It is my impression that Improving on these small yet important parts of my recent lectures would greatly improve the clarity and allow students to better grasp the material presented.