## Teaching with Technology Portfolio:

Reflections on Technology in Teaching

It is stereotypical that we, as mathematicians, favor traditional chalkboard lectures as opposed to flashy presentations with all the latest technology. However, as I have grown as an instructor I have learned that we can strike a balance between the old and the new. Technology, when used thoughtfully, can significantly enhance the learning experience for our students.

One of the pitfalls of technology that I have experienced as a student involves the dreaded PowerPoint presentation. All too often I have endured lectures based on slides filed to the brim with a jumble of words that the instructor would speed through without a hope of having enough time to copy down even half of the information presented. Lecturing in this way may allow the instructor to get though more information in a shorter period of time, but at what cost? If the students gain nothing more from their time spent in class than what they could have achieved by reading the textbook, the use of technology is not effective. I have found that the greatest hurdle for many of my students to overcome is their self-proclaimed "math anxiety." For them, simply breezing through the terminology and quickly moving through examples in the lecture notes or on a PowerPoint presentation is not going to help them truly learn. I used PowerPoint presentations when I taught Math 034 (Mathematics of Money) and online lecture notes/handouts for many of my courses to expedite the process of covering new material. When PowerPoint slides or handouts can be used instead of forcing students to copy down lengthy word problems, I believe it is a good use of technology in the classroom. However, when I started using PowerPoint presentations, I had to be careful not to move too quickly. By asking my students for feedback, I was able to modify my use of PowerPoint slides. Instead of simply explaining the process in words and projecting the solution on the screen, I would stop and give my students a couple minutes to work through the example (either on their own or in groups). As I've learned through my own experiences as a student it's one thing to sit in class and think you understand the examples as the instructor goes through them in class, but it's another thing entirely when you try to work through them yourself with no external guidance. Taking the time to work through the examples in class allows the students to realize what their questions are while I'm there to answer them.

Technology has been extremely useful for me when I want to include complicated images in my classroom examples. When teaching Math 251 (Ordinary and Partial Differential Equations), it is difficult and time consuming to draw direction fields on the chalkboard in order to discuss linear stability. The image to the left (created using Mathematica) can be projected on the screen and students can instantly see the arrows leaving the origin indicating an unstable spiral point. This use of technology allows us to focus on the important concepts (what it means for a point to be stable or unstable) instead of wasting time drawing arrows on a chalkboard.

I've had the privilege of experiencing a different type of "teaching with technology" - teaching multiple online courses. When your classroom is virtual, you can't escape using technology in your teaching. However, that does not mean you should use technology just because it's there. I feel very lucky that I have been able to teach Math 036WEB (Insights of Mathematics Online) for five consecutive semesters (including a 10-week summer session and a 6-week summer session). Teaching the same course for so long has allowed me the ability to hone my teaching of the material, though it will always be an ongoing process. My first iteration of teaching Math 036WEB looks much different than it does today. True, the same basic structure remains - the students listen to pre-recorded lectures, submit homework assignments, and take exams - but my use of technology has changed. When I started teaching online, I used Piazza both as a discussion forum and as a place to post course announcements. While this seemed to work well, I learned that the dual purpose of Piazza was confusing to my students. Were they supposed to log on to Piazza to read course announcements (that I was already sending them via ANGEL email) or use it as a place to post questions? Taking this into consideration, I now use Piazza solely as a discussion forum where students can ask/answer questions and talk about real world applications of the course material.

When teaching online, live lectures and office hours are as close as it gets to having a "traditional classroom experience." As such, I would like for as many students as possible to be able to attend. When I first started, I would simply set the live lecture time (normally at night, hoping that it would be more convenient for students who worked during the day). However, I didn't really know if I was picking a convenient time or not. Now, I use Doodle polls to give the students a choice of dates/times for the live lectures. It isn't a perfect solution (there are always some students who cannot make the live lecture and must simply watch the recording instead), but this simple bit of technology has increased the number of students who attend the live lectures.

My goal is to always be growing and improving as an instructor and I believe the thoughtful use of technology in the classroom is part of that process.

One of the pitfalls of technology that I have experienced as a student involves the dreaded PowerPoint presentation. All too often I have endured lectures based on slides filed to the brim with a jumble of words that the instructor would speed through without a hope of having enough time to copy down even half of the information presented. Lecturing in this way may allow the instructor to get though more information in a shorter period of time, but at what cost? If the students gain nothing more from their time spent in class than what they could have achieved by reading the textbook, the use of technology is not effective. I have found that the greatest hurdle for many of my students to overcome is their self-proclaimed "math anxiety." For them, simply breezing through the terminology and quickly moving through examples in the lecture notes or on a PowerPoint presentation is not going to help them truly learn. I used PowerPoint presentations when I taught Math 034 (Mathematics of Money) and online lecture notes/handouts for many of my courses to expedite the process of covering new material. When PowerPoint slides or handouts can be used instead of forcing students to copy down lengthy word problems, I believe it is a good use of technology in the classroom. However, when I started using PowerPoint presentations, I had to be careful not to move too quickly. By asking my students for feedback, I was able to modify my use of PowerPoint slides. Instead of simply explaining the process in words and projecting the solution on the screen, I would stop and give my students a couple minutes to work through the example (either on their own or in groups). As I've learned through my own experiences as a student it's one thing to sit in class and think you understand the examples as the instructor goes through them in class, but it's another thing entirely when you try to work through them yourself with no external guidance. Taking the time to work through the examples in class allows the students to realize what their questions are while I'm there to answer them.

Technology has been extremely useful for me when I want to include complicated images in my classroom examples. When teaching Math 251 (Ordinary and Partial Differential Equations), it is difficult and time consuming to draw direction fields on the chalkboard in order to discuss linear stability. The image to the left (created using Mathematica) can be projected on the screen and students can instantly see the arrows leaving the origin indicating an unstable spiral point. This use of technology allows us to focus on the important concepts (what it means for a point to be stable or unstable) instead of wasting time drawing arrows on a chalkboard.

I've had the privilege of experiencing a different type of "teaching with technology" - teaching multiple online courses. When your classroom is virtual, you can't escape using technology in your teaching. However, that does not mean you should use technology just because it's there. I feel very lucky that I have been able to teach Math 036WEB (Insights of Mathematics Online) for five consecutive semesters (including a 10-week summer session and a 6-week summer session). Teaching the same course for so long has allowed me the ability to hone my teaching of the material, though it will always be an ongoing process. My first iteration of teaching Math 036WEB looks much different than it does today. True, the same basic structure remains - the students listen to pre-recorded lectures, submit homework assignments, and take exams - but my use of technology has changed. When I started teaching online, I used Piazza both as a discussion forum and as a place to post course announcements. While this seemed to work well, I learned that the dual purpose of Piazza was confusing to my students. Were they supposed to log on to Piazza to read course announcements (that I was already sending them via ANGEL email) or use it as a place to post questions? Taking this into consideration, I now use Piazza solely as a discussion forum where students can ask/answer questions and talk about real world applications of the course material.

When teaching online, live lectures and office hours are as close as it gets to having a "traditional classroom experience." As such, I would like for as many students as possible to be able to attend. When I first started, I would simply set the live lecture time (normally at night, hoping that it would be more convenient for students who worked during the day). However, I didn't really know if I was picking a convenient time or not. Now, I use Doodle polls to give the students a choice of dates/times for the live lectures. It isn't a perfect solution (there are always some students who cannot make the live lecture and must simply watch the recording instead), but this simple bit of technology has increased the number of students who attend the live lectures.

My goal is to always be growing and improving as an instructor and I believe the thoughtful use of technology in the classroom is part of that process.