Activities in Functional Notation

One of the first topics we covered in our Calculus class was functional notation. Since understanding the definition of the derivative requires the understanding of functional notation, Barry and I tried to make it clear that functional notation is important and will come up again and again as the course progresses. We quickly learned that the students were not understanding how to work with functional notation and one day in Barry's office we came up with a little in-class group activity which is the topic of this entry.

In an attempt to resolve the issues students were having with functional notation, Barry and I worked on a short in-class activity that was meant for students to understand the algebraic and graphical aspects of functional notation. Our hope was to witness a class-wide epiphany! This never actually happened the way we visualized it happening when we were constructing the activity in Barry's office. However, despite the lack of large scale epiphany, a reasonable number of students walked away with at least an inkling of what they had previously been doing wrong with functional notation. A few more students completely understood the point of the activity. While we may have not made our point clear to every student, it is our hope that students will help each other outside of class.

While working on this activity I've learned that just rephrasing something does not make it clear for everyone. Sometimes when we as teacher/tutors/TAs work with a group of students who struggle with the same problem we hope that what we have to say is understandable and clear. However, being so accustomed to concepts in mathematics sometime gets in the way of conveying the math and other means of explanation are sought out.