In the sections which follow I will highlight a few examples of the various resources I employ to make course content more engaging. A few representative examples are provided below, but a more exhaustive list of work can be found in the Appendix: Teaching section of the portfolio.
Course Blogs
When the course blog system was made available beginning in the Fall 2009, I was excited at the opportunity to use the blog as a content hosting site, LMS, and to help facilitate class discussion. To date, I have created and maintained 17 separate course blogs for students across all courses I teach. I have provided links to a few of them below for you convenience.
LaTeX Lecture Slides
Effective and efficient mathematical typesetting remains a problem even today. When new products like iBooks Author release without any usable means of typesetting involved mathematical constructs it is disappointing to say the least and frustrating for users at best. To expect students to suffer through content in a mathematics class without top notch mathematical notation, documents, etc… is equally frustrating. Since graduate school I have worked hard on improving my overall competence with using the LaTeX document preparation system to write lecture notes and slides for my students. LaTeX is the industry standard for mathematical and scientific publication. Because of this I try to expose my students to its use at multiple levels within a course. In the past I have assigned projects to be completed in LaTeX, and all content in the course is produced using LaTeX or LaTeX Beamer. I have provided a few examples of course notes rendered in LaTeX for your convenience. The examples are presented in chronological order to demonstrate my personal growth in using the software over time. Please click on each image to view the full set of lecture notes.
More examples of in-class content can be found in the Appendix: Teaching section and in the course blogs linked above. In any given semester I produce around 30 lectures similar to those above per class.
Creative Course Projects
I have created a variety of creative projects for students in my courses over the last five years. I will briefly describe two of the more effective projects I have developed.
MATH 361: Screen Casting Project
In MATH 361, Ordinary Differential Equations, students are tasked with completing a screencast of their solution to a problem after each unit which utilizes Maple, the specific models of that unit, and an explanation of the techniques processes involved. Students are organized into groups and part of their grade includes a peer review process and screening of the video with class feedback. In addition students have created posters using LaTeX for the course as they would do for any undergraduate conference. This project was developed in conjunction with the Learning Studio and students are expected to work with the studio resources to produce their podcast. A few of the project materials and an example of student work are provided below for your convenience.
Student Screencast Example
http://www.youtube.com/watch?v=RKhkjr79wN4&list=37D7A52B748CFEAC
MATH 227: Proof through Original Texts Project
The discrete mathematics course is a math major’s first introduction to concepts of narrative proof in mathematics. This course is a struggle for many students and much time is spent engaging students in the idea of what it means to write as a mathematician. To this end, I thought it would be interesting to provide students with original sources of some of the great mathematicians and ask them to explain the works using modern notations and syntax. Additionally, students were asked to complete their papers using LaTeX and so the project served as an introduction to the typesetting program for many of the students as well. An example of one of the prompts is provided below.
MATH 120: Integration of Faith and Learning
One of the units we discuss in the quantitative reasoning course deals with personal finance including things like IRA, loan amortization, interest, and mortgages. After each of the three units: probability, statistics, and finance I assign students a short reflection paper dealing with looking at each of these topics through the lenses of the students’ faith. The students tend to enjoy these prompts, in particular the finance one, and we take a day during each unit to watch a video related to the prompt and have class discussions related to the talk. I have included a few materials below for your convenience and a really excellent example of a video I use to spur discussion on the probability topic “Reasoning With Uncertainty”.
Reasoning With Uncertainty Prompt
[youtube kLmzxmRcUTo]
Screen Casts
Not only do I ask my students to create screencasts of their work, but I have on multiple occasions created my own screencast tutorial videos on a variety of topics. I began by mostly making calculator tutorial videos, but have since expanded to homework videos, Maple tutorials, LaTeX tutorials, and lecture topic videos. All videos are made available to students through the ACU course blog system, Xythos, or on my personal website. A couple of sample videos are provided below for you convenience. All videos are formatted for optimum viewing on iOS devices. The more recent videos are also available in 720p HD format.
http://www.youtube.com/watch?v=IFEVUYkAFy0
http://www.youtube.com/watch?v=njI4IuEUvgA
http://www.youtube.com/watch?v=2XbJvgxmohc
http://www.youtube.com/watch?v=kmHSoECyVfM
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