Technology use for pedagogical innovation:
 Class communication: mail list, Angel discussion board, quick polls
I believe that communicating with the class is as important as knowing the subject you're teaching. Students tend to learn best when they are in good contact with an instructor, so that they can share their concerns, aren't afraid to ask questions and know whom to turn to when they need help. I encourage my students to talk to me whenever they have questions, either during class or after class, during office hours or via email. Every semester I create a class email distribution list and use it for class correspondence. This semester I integrated Angel mail and discussion board into my Math250 course. It definitely breathed some life into our communication, since now students can post messages to me as well as their classmates and discuss homework questions on the message board.
Here are a couple of screen captures from Angel:
For the students who wish to leave their comments anonymous, I always include an Anonymous feedback form on every course web page. Students sometimes leave really valuable comments if they know they won't be judged by their contents.
 Online surveys: Angel Quick Polls
Another Angel feature that proved to be of use to me is the Quick Poll located in the "In Touch" Tab of the website. This is how it works: I give one quick poll every 23 weeks and ask questions like "Which topic you found to be the most difficult so far?", "Do you think class pace is appropriate so far?" or "Do you think you might need extra help with partial fractions?". In contrast with the Online Survey implemented in Angel, Quick Poll makes it possible to provide users with a short list of answers. The answers should not necessarily be multiple choice, there is a way to include multiple select or even openended questions, so that students can express their opinion in writing if they feel like it. I've benefited a lot from the feedback I got in these quick polls. Due to their quickandeasy format, I was able to detect problems right when they started and modify course pace according to the audience.
 Online assessment: Angel quizzes
Last semester I started using online quizzes. As every other instructional tool, it has its advantages as well as weaknesses. This is a really great tool if you have no time to assess students' knowledge in class and want to save time on grading. It also has really nice features, e.g. you can specify whether or not to provide an answer key to students, how many attempts they have, start and end time of the quiz etc. I usually give students 2 attempts, so that if they made mistake they can go back and find it, which forces them to take material more seriously and use accuracy when answering test questions. There are of course drawbacks in that one has to go through a lot of steps in order to include a formula in an online quiz (it can only be done by uploading formula as a picture). Another obvious weakness is a necessity to use multiple choice answers, which sometimes doesn't assess the actual knowledge of a student. The approach I usually take is a compromise: I do small in class quizzes every other week, alternating with more substantial online quizzes. This way I reduce my grading workload and get to test students on the material. The students seem to like it too since they feel less stress and can take as much time as they need to think problems over.
 Collaboration: team projects
This is a relatively new experience for me, since I only started using group assignments this semester. This innovation resulted from my participation in the Course of College Teaching given by the Schreyer Institute of Teaching Excellence this semester. We talked about different teaching strategies and I realized I might be missing something by neglecting collaborative learning. I decided to compile 3 team projects and give them out to students a couple of weeks before each of the exams. Students could work in groups of up to 4 people and submit one report per group. Solution sets were made available on the course web page after each assignment got submitted. Although the projects are completely voluntary, I've had a great return on this assignment. 9 groups have been formed and I was pleased to see that those people who worked together on these assignments continued to help each other with the material and showed more participation in class than others. One explanation I can offer is that students feel much more comfortable and confident when they know their peers and consider themselves not just as individuals but as part of the group. I think I will continue using this method in the future in order to foster learning atmosphere in my classroom.
 Use of commercially developed software
As it was noted in other parts of this Portfolio, most of my class preparation is in one way or another related to the use of computer software. Here are some of the ways in which various software aids me in achieving my goals:
 I use TeX (mostly AmSTeX and MiKTeX) to create homework solution sets;
 I use Microsoft Word and Adobe Acrobat to make in class and online quizzes;
 I use MATLAB and Java applets to create pictures of direction fields and various other pictures and graphs;
 I use Adobe Photoshop to optimize graphics for the web
 Finally as I already mentioned I use the Course Management System (ANGEL) which is integrated in many different areas of the course.
 Selfconstructed instructional tools: tutorials, lecture notes developed by the TA
To help students install and run MATLAB scripts producing direction fields, I made a small tutorial with stepbystep instructions and screen captures. The tutorial put an end to constant flow of letters I've been getting on the matter, since a lot of people were using a wrong installation procedure and couldn't get the program to run.
I also made the set of lecture notes for my students that I already discussed in previous section of the Portfolio, so here is one more sample file from that series: Math250chap1.pdf(152KB)
 Electronic data or research resources
I make use of an extensive list of web resources in any course I teach. I already mentioned some of them (e.g., Java applets) in the Digital resources section of this Portfolio. Another form of resources I utilize is the collection of online tutorials and class notes. There is a huge number of personal and professional mathematical websites online, some of which are specifically dedicated to providing help to students in different areas of the subject. Although they sometimes present the material from a different perspective or use other notations, I still think that selected resources can provide a useful exercise for students in my classes, so I make sure they are exposed to them. Here are some of the web electronic resources I gathered to provide student with some extra help:
R U Ready for ODEs?  a set of webbased quizzes from U. Arizona
S.O.S. Math ODE course online  nice short introduction to ODE with sample quizzes and exams
Integration Tutorial from MathsDirect
Besides strictly technical publications, I try to give students some additional motivation by including links of general interest related to the field of study. For example, in my Math231 Multivariable Calculus class, I showed beautiful graphs from this
Curve repository which seemed to trigger students' interest in studying polar coordinates.
The complete collection of links can be found by scrolling to the Links section of my current course webpage.
