Teaching to the Top
I am starting to hear feedback about my teaching and have hit an ideological question. Should you teach to the top, middle, or bottom of the class? A student in my class was talking about her struggle to understand the concepts this quarter. She's doing okay, but feels much less certain about the material than she did last quarter. She described what the instructor did last quarter. He had the class work on worksheets, which were shorter versions of HW problems. His exams were very similar to worksheets. I would consider this teaching to the middle. He is teaching students how to perform concepts in exactly the same way that they are presented in the text, but he is not encouraging them to grow beyond the text to to recognize problems in new situations that can be solved with the same tools.
Turns out I have been teaching to the top. I have been really encouraging my students to stretch and reach to that synthesis phase of learning (never thought I'd use that Bloom's taxonomy stuff but there it is). I want my students to understand the material deeply so that they can see how the principles and equations that they learn are applicable to other problems and to daily life.
The problem with teaching to the top is this. Students at the top feel pretty good. It is a little hard, but they get it. This is about the top 15% of the class. The middle students (25-85%) have trouble getting it. They are used to understanding and feeling comfortable with concepts and for what may be the first time thing aren't coming easy to them. Because of this, they lose confidence in their abilities which can negatively impact their grade. I have seen students who are doing well in general make simple mistakes because they don't feel "sure" about a problem. Several studies examining the classroom environment for women and minorities have shown that confidence in one's abilities (perceived or actual) can influence performance. So perhaps teaching to the top undermines the abilities of the middle section of class, which is most students. Meanwhile the bottom part of the class (last 25%) really doesn't get it. If a student would normally have trouble getting a concept as written in the book, they will have a great deal of time stretching that limited understanding to new classes of problems.
So the question is: which is better to teach to the bottom or the middle or the top?... and if I teach to the middle or bottom, how can I be sure that the top students are still challenged? How can I encourage students to develop a synthesis level of understanding without undermining confidence in their abilities.