We Need to Keep Learning

Every spring semester I get to write the last blog post for Math 371, Technology for STEM Educators. I always title it, "What I Learned This Semester," but this year I want to be more specific about why educators need to keep learning. 

If we don't continue to learn, how can we ask our students to learn? As a teacher educator, I have always felt that modeling what I want our future teachers to do is the most important aspect of my job. How can we say one thing and do another? So I try to model good teaching, fair assessment practices, and being a lifelong learner. 

Last semester I did an action research project with collaborators from Georgia Southern University and the University of New Hampshire. We used a two-column proof software in our Geometry for Teachers courses at our respective institutions. We collected data through student surveys and the software. When it came to analyzing the survey data, I initially used a Chi-square Test of Independence on the pre-and post-responses to our Likert-scale questions. Our results weren't great, but we did have some low p-values. As I began to read more about statistics, I decided that a different test should be used because my sample sizes were too small for the Chi-square test to be accurate. So I kept searching for an appropriate statistical test and kept asking questions of my awesome colleague, Dr. Gary Hatfield. He even took my data to his class on nonparametric statistics and had them look at it to see if they could conclude anything from the data.

As I kept reading more about statistics, I found several tests that wouldn't work because they only worked for categorical variables that had 2 categories. My Likert scale had 4 categories, with 29 samples in the pre-survey and 20 in the post-survey. I finally converted the data from categorical to numerical, and then as I was reading some forum, someone mentioned a partially overlapping test. Then I Googled a partially overlapping sample and found a dissertation from Ben Derrick from 2020, where he created a new statistical test that seemed to fit exactly what I needed. He even created R code and I was able to perform the new test. We then got more results with low p-values. In addition, I did a paired t-test and Wilcoxon rank-sum test on the paired data, but these only resulted in low p-values for questions that already had low p-values from the new test.

This semester I went far outside my comfort zone and learned a new statistical test out of necessity for my research. I had to learn how to do some coding in R. And the best part of this experience was that one of my statistics colleagues asked me to send him the information on this partially overlapping samples test. He just got some data that he plans to use it on. My learning led to something that helped a Statistics colleague! Usually, the Math faculty are asking the Stats faculty for help, not the other way around.

How does this experience translate to help my future teachers? Well, I have shared this experience with them as they are required to do action research projects in their second semester of student teaching. They were able to see my first-hand account of my action research project--that the data you get doesn't always give the results you want, that you need to figure out how to analyze the data, and that a portion of the data doesn't give the whole picture.