# Reflection of using Geo-Gebra app in Linear Algebra course

Last semester I had the chance to explore how would using Geo-Gebra in my Linear Algebra course affect student’s learning experience. My initial goal was to find out whether using it would improve student’s engagement in the class. I had taught this course for a few times by then, and one observation I made was how quiet the lectures were, compared with my other sections. In fact many students who took Linear Algebra last semester with me also took my other math course: Intro to Math Proof and we were discussing this interesting finding. They agreed that our Linear Algebra lectures were too quiet.  They told me that Linear Algebra classes were not as engaging, and interesting as the other course even though my teaching style didn’t change. I had to do something.

I managed to secure a small funding from my university and did the following experiments. Once every two weeks, I will have four TAs going in to my lecture and sit among students. We will do one Geo-Gebra activity that helps students visualize and understand a new concept. For example, when we were learning the topic of eigen-value and eigen-vectors, students were asked to go here: Exploring Eigenvectors and Eigenvalues Visually and follow the steps:

1. Set the matrix M to be (1 0 ; 0 2)
2. Drag the point u until you see the vector u and Mu are on the same line. Record the value of lambda. How many times do you see u and Mu lying on the same line when u travel through the whole circle? Why?
3. Based on your observation, what can we say about the eigenvalue and eigenvector of M?
4. Set the matrix M to be (3 5; 1 -1) and repeat what you did above.
5. Check your lecture notes about the eigenvalues and eigenvectors of this matrix. Are the results consistent with what you observe?

TAs will be walking around the lecture hall and answer any questions students have. Some are about the applet itself, some are about the mathematics involved. By the end of the activity, a majority of students feel more comfortable about the two new concepts.

We did similar activities for a few other topics, and in general they helped students in understanding the abstract math ideas better. However, the interactions between students were not improved much. Most of them were working alone, and the class for most part was still pretty quiet. I’m in the middle of getting the data in place and measure whether the engagement level has improved or not, but my guess is there probably isn’t a significance improvement. Next semester if I’m to do these activities again, I will add at least one step: share your work with your neighbor and exchange what you have found with each other. And I will invite volunteers to talk about the questions, instead of me explaining them.

I will come back to this post once there are new findings.