February 2010 Archives

Something that has only briefly been mentioned (if at all) is my role as a teaching assistant under the UTOP program. Unlike the responsibilities that math TAs are usually given as undergraduate student workers here at University of Minnesota Morris, which mostly includes grading homework and quizzes, I, as a UTOP TA, get to construct the homework and quizzes and lecture.

At the beginning of the semester Barry and I met to discuss what my responsibilities should be as a more involved TA. It was decided that I would be solely responsible for constructing the online homework (Webwork). I also help in the construction in both quizzes and tests. Since being a TA still means that grading is involved, I do grade the quizzes while Barry grades the tests. Being more involved means that I attend three of the four classes every week to assist in answering questions, however, the most exciting part of being a more involved TA is having the chance to actually lecture. At one or two points in the semester I will be responsible for presenting the material to the class in full-length 65-minute lectures. While this is a bit intimidating I have always enjoyed helping others in leaning mathematics, so the chance to lecture in a first-year calculus course is very exciting for me.

Indeed, my role as an undergraduate TA is well beyond that of a typical undergrad TA. In completing the online homework, students have every chance to email me directly about problems they are having, and answering these questions is something math TAs here a UMM don't get a chance to do. My more personal involvement in the class allows me to help Barry in teaching and assisting the students while experiencing what it takes to be a great teacher.

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.

    

Perhaps one of the first first things that should be discussed (it typically being the first thing students want to see) is the syllabus. I will describe what went into the syllabus for our section of Calculus I and why we choose to keep or loose certain parts of the initial proposed syllabus. I also want to compare what went into the syllabus with what should be in a syllabus (according to Thomas W. Rishel -- author of "Teaching First A Guide for New Mathematicians").

This being the first time I had to help construct and critique a syllabus for a first semester Calculus section, I had expectations of simply stating the crucial components of the class: grading scale, required texts, office hours, etc. As a student I mostly cared for grading scales and for the percentage of my final grade for which homework, tests, and quizzes counted. After reading Rishel's book I understood the need to have a more complete syllabus. Rishel describes the syllabus as a contract between the professor and the students. I very much agree with this! I, as a student have always looked at a syllabus as what was expected from me and from the professor. Rishel continues to describe a syllabus as something that should be more than just a summary of the course.

As for the syllabus created for Barry McQuarrie's Calculus class, much of what Rishel said should be in a syllabus was in the syllabus (and then some!). The syllabus that Barry and I decided on actually came from a past spring semester Calculus I course, and so most (if not all) of the necessary components were in place. This was nice, since that left us with mulling over whether or not we should do applied projects and in-class homework presentations. In retrospect, the completeness and thoroughness of the syllabus is far beyond what Rishel ever advised in his book (which makes sense since Rishel's audience is probably comprised of new first-time teachers). Rishel's recommendations for what should be in a syllabus merely scratches the surface of what is in the syllabus for our Calculus I course.

I planned on describing the syllabus, but instead I find it more useful to simply provide a link: syllabus.

The second week of class I found myself needing to look at the syllabus to remind a student (and myself) of the agreement dealing with late homework. Despite having read the syllabus several times over just a week before I felt the need to keep in mind my part of the "contract."
Having such a complete account of what is expected from both sides of the classroom is not only helpful to students, but also to TA's such as myself. While our syllabus is rather lengthy, it does not set an example of what should be in every course syllabus. Obviously each class varies from subject to subject and from teacher to teacher, and each syllabus should vary accordingly.