Monday, June 05, 2006

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 problems with 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.


Anonymous Johnny - Oh said...

I'm uncertain as to exactly why I'm interested in this thing... but dangit I AM! Keep 'em coming.

10:31 PM  
Blogger MathCogIdiocy said...

I'll do that and let you all know when a new post is up.

6:36 PM  
Anonymous Teresa said...

I've got an interesting book by Eugene Volokh - of the Volokh Conspiracy blog fame - on writing law review articles. It's an excellent book (which I got because he is an excellent writer) and has some great insight into backtracking on research.

If you want a copy - I've got 2 of them. Short book. The company publishing it, put me on a list and when the book had a second release with updates, I ended up with another copy... sheesh. I was too lazy to send it back. *grin*

1:23 PM  
Blogger MathCogIdiocy said...

Teresa - I'd be interested in reading the book although research in terms of law if somewhat different. I did find the studies done within linquistics (the book claimed 20 years of research), it's just that there have been very few studies specifically applied to mathematical cognition with the exception of those addressing number sense and numerosity (about 10 years worth). Swear to god, that's all the psychologists look at.

There's a post over at the new Mixing Memory site where he talks about psych books - not widly impressed with because the authors can make claims without the supporting evidence. He suggests what I've learned to do in the past few years - use the books as a starting point, but go back to the source material and published studies. This is one of the reasons I spend so much time on research with relatively little to show for it other than piles of journal articles and CDs full of pdf files. *grin*

2:21 PM  
Anonymous Teresa said...

Ah but at least you aren't simply making claims with nothing to back them up. That makes you a true researcher. It seems to be a lost art lately.

I'll see about getting the book out to you.

6:58 PM  
Blogger MathCogIdiocy said...

I can't get away with making claims with nothing to back them up. The professors always want the sources. I'd say that it's easier to make a claim in math, but if you can't provide a viable proof...

At least I'm a true something. *grin* If we ever get that lunch thing scheduled, I could get the book from you then.

7:24 PM  

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