An Introduction or maybe an explanation
In my last semester of the math degree I took a child and adolescent psychology course to complete my general education requirements. The first half of the semester consisted of lectures from the professor. The second half of the semester was a series of presentations by the students. We were supposed to work in groups of 3 or 4, research a topic (approved by the professor), and do a 1 hour presentation. I really really really did not want to work with a group of students on this. I already had a class where every week I had to meet with a different group of students to prepare and do a presentation on the week's topic and a math class where I was working with another student on a presentation. Yet another student group presentation was straining my patience and my schedule - work so gets in the way sometimes. *grin* And, to be perfectly honest, the topics the kids in the psych class wanted to talk about bored me to tears. It's not that eating disorders, body image, and sports aren't important, but ...
So I talked the professor into letting me do the research and the presentation on my own and got him to approve "mathematical thinking" as the topic. I had a blast and no trouble whatever talking for an hour on the topic. Unfortunately for the world at large, a new "passion" was awoken. The semester ended, I graduated, and I kept on researching. However, a small problem arose - I was reading stuff I didn't always understand. I decided to fix that by going back to school for a degree in psychology. And whenever possible I used the research I was doing on my own in assigned papers. The honors research project grew out of that.
The project started with a book I read for the original presentation. The book is Where Mathematics Comes From by Lakoff and Nunez (2000).
As time went on, I ended up with a few problemswith this book. I felt like the authors had jumped past a few basics by going to more advanced mathematics. Why weren't they talking about the maths, like Euclidean geometry, that are the oldest and most basic? I was starting to feel as if the act of communicating math was being confused with the act of doing math. And finally, after a lot of reading, I was feeling as if one of the authors was trying to be all things to all areas of psychology. On top of all of this, the authors said that there were studies proving their claims, but I wasn't finding the studies. At least not specifically in relation to mathematics.
So when it came time to present a proposal for a study, I decided to choose one of the ideas from this book and see if I could "prove" it. Because I love Cantor's transfinite sets, I chose a piece of their ideas on how we conceptualize sets.
And that's my story. Next time I'll explain the ideas behind sets a la Lakoff and Nunez.