# Analysis

#### W. Ted Mahavier, Fall 2011 - Spring 2012, Lamar University

**FAQ**'s

**Q.**
How do you get students to go to the board?

**A.**
By sending students to the board on the first day in a relaxed setting, students are put at ease so that presentations are not viewed as something to be feared, even though presentations constitute a significant portion of student grades in every course I teach. The diary and commentary for the first day, 8.22.11 show just how I do this. The key moment, about half way through the class, is the moment when I toss the marker to Amber and the class laughs. Some cheese company once advertised that, "happy cows make good cheese." Well, it turns out that happy students make good mathematics. Motivational talks throughout the course (some aimed at engineers, some at teachers), such as the one on 2.3.12 highlight both why I teach this way and the potential benefits to students as a potential employees some day. Later in the course, I pass out articles to students during these introductory chats which are directed at double majors such as engineers where workers in industry speak to the importance of forcing students to work independently to create good employees. The point here is that if the students believe that *you* believe that what you are doing is in their best interests, then at best they will tackle the work with a good attitude and at worst, they will not be mad at you for making them work!

**Q.**
What do I do when students have nothing to present?

**A.**
Read the diary and subsequent commentary for 9.21.11 where I offer two techniques that I use.

**Q.**
Do Moore Method instructors lecture?

**A.**
Yes, although lectures are not the focus of the course. My lectures tend to fall into four overlapping categories: reactive, motivational, intuitive and supplementary. Reactive lectures are the most common and follow student presentations. They are brief and intended to clarify or expand on the presentation, potentially foreshadowing upcoming problems or showing connections between this problem and previously resolved problems. These lectures show the forest, as the students have been working on the trees. Motivational lectures are very common at the beginning of classes since I come in five minutes early. These motivate the students to work, or motiviate why I teach as I do. Intuitive lectures are those used to provide intuition for an upcoming definition or theorem. Supplementary lectures address material not included in the notes on the rare days (two days this past year) when students do not have sufficient material to present. I consider these treats to the students for their progress and often am quite animated when students are working hard, and many are close to success, but none have anything to present. I'll say, "you mean *I* get to go to the board today?! Oh boy, let's talk about countability!" And I'll spring into an interactive discussion on some topic that I want them to have a big picture of by the end of the semester.

**-** The diary and commentary for 10.28.11 and 11.11.11 show lectures where I react and expand on what a student has already presented.

**-** The diary and commentary for 10.31.11 show a lecture where I attempt to provide intuition for a definition in response to a student question about continuity.

**-** The diary and commentary for 11.28.11 demonstrate a full day lecture on a day when students did not have material ready to present.

**Q.**
Is there competition in a Moore Method course?

**A.**
There is a healthy competition, in the sense that certain students will want to resolve a certain problem before another student resolves it. Certainly that was the case when I took such courses and I see this occasionally in my courses. There has never been any evidence of unhealthy or demorailzing competition in my classes. The students are very supportive of one another at the board (sometimes too supportive) and are especially supportive of weaker students. The diary and commentary on 10.31.11 show a nice example of this. Multiple students are working to show that the sum of the limits of two sequences is the limit of the sums of the two sequences. Two students take different approaches. We are able to see the presentations of both approaches and it turns out that it requires the totality of both approaches to resolve the problem. Katie is an education major and Jacob is a double majoring in mathematics and electrical engineering.

**Q.**
What to do if the class is not progressing at the rate you hope for?

**A.**
In many classes I have taught, this has never been an issue and students have forged forward completely of their own accord. As described in Observations this was anything but a normal class due to the large number of student life issues, and I had just this problem in both the first and the second semesters. To see how I resolved this in the first semester, view the diary and commentary for 9.21.11, 10.7.11 and 11.28.11. To see how I resolved it in the second semester, read Item 3 on the resources page and view the diary and commentary for 2.20.12.