## Aubrey Baxter and Dr. Hope Gerson, Math Education

Paul Fields in the statistics department was my first mentor. Together we tried to develop a new pedagogy for teaching statistics. This interested me because I may teach advanced placement statistics after I graduate from the Mathematics Education program. A position then came available to me as a research assistant for Dr. Hope Gerson. It was a better opportunity because it is in my field of study and it allowed me work with statistics and apply calculus. Together with Dr. Walter, Dr. Gerson taught an Honors Calculus 1 class for two semesters and an Honors Calculus 2 class for one semester. These classes used open-ended tasks in a collaborative environment. During these semesters and the summers between I took field notes in the class, videotaped the class and then transcribed these videos. While performing these tasks, I watched for things in which I was interested and which I could study further. The way in which students learn and understand mathematics concepts and statistical concepts still interested me and so, while transcribing these videos, I watched for these things. Because this class was a calculus class and not statistics, I can only try to relate the things I learn about the mathematics concepts to statistics.

One observation is that for each different type of mathematical concept the students confronted they used different tools that they collaboratively brought together to understand the concept. For example, while working on “The Cat Task”, most students used a tool they had learned in statistics, the Statplot program in their calculators, to reach conclusions. The Cat Task gives the students a series of photos of a cat in different positions. The students are then supposed to find a function for the position of the cat and ultimately the velocity of the cat. The data of the cat turns out to be neither strictly linear nor quadratic and so makes finding an equation challenging. Many students used the Statplot program in their calculators that they had learned about in Statistics 221. Overall it seemed that, when given a set of data or when the students collected a set of data, students used tools they had learned in statistics to generate the mathematical concept. I also found that students used physics and sometimes other scientific subjects to help them understand derivatives and integrals, and used life experiences to understand the meaning of graphs.

In the Spring Research Conference this year I presented my research and these findings. It was a frightening but rewarding experience for me to learn more about how to present and how to do this type of research, which is very different from research done in the rest of the College of Physical and Mathematical Sciences. I also learned a great deal about what other research has been done in my field, which I probably would not have otherwise sought out and studied.

My hypothesis is that this way of learning also applies to statistics. I believe that students take the prior knowledge they have from whatever they have done before and try to apply it to what they are now learning but that there are also specific “themes” to the knowledge they apply while learning each different concept. By doing this, the new information is more meaningful to them and they gain a deeper understanding of the information (although there is no way to actually show this that I know of). In the words of a friend of mine, “if you know it, you’ll use it”. And going a little bit further than that I would say that if you know why (a deeper understanding) to use it, you’ll use it.

I am continuing my research with Dr. Gerson and hope to help her further her research. It would be interesting to write tasks for classes I teach and to research exactly what makes a good task. The goal is that students internalize concepts instead of rote learning and that students find the subject more interesting and worth their time. By knowing what knowledge students generally apply, instructors can get them started in the right direction more effectively.