Introduction

I have been experimenting with questions on how to organize undergraduate mathematics courses in this information age and what a typical course organization may look like in the next 5 to 10 years? I am not necssarily talking about online courses or distance learning. Rather, I am referring to the shape that our usual undergraduate courses may take in near future.

After extensive experimentation on these questions over several semesters, all my efforts took a concrete shape this past summer of 2000 and I realized what would be my model course organization at the undergraduate level, at this inoformation age. The model is based on, and implemented in, the way I organized the Elementary Statistics Course (Math 365) in Summer 2000. I am also currently using this model in my Topics in Mathematics (Math 105, Fall 00). Following are the main components of an undergraduate course in this model:

1. Supply Course Materials Online:
   1. The Online Lecture notes will take the place of the textbooks.
   2. Solutions to some of examples can be made available in the online lecture notes (audio visually, when suited).
   3. Give links to any online material available, or develop online materials, to which you would draw the attention of the students.
   4. Make a copy of one or more reference textbooks avaiable in the library for short-term borrowing.
2. Use of the in class time:
   1. Go through the material in a relaxed and casual pace.
   2. Work out as many exercises as possible at a slow and relaxed speed.
3. Give homework Online with instant feedback:
   1. Students will access and submit their homework online.
   2. On submition students will receive instant feedback on whether their answers are correct or false.
   3. They can resubmit their homework until the due date set by the instructor.
4. There will be in class tests and midterms and finals as usual.

1. Supply Online Course Materials

The online lecture notes may be prepared by the instructor or some ready online material may be used. I believe that in next 5 to 10 years the internet will be flooded with textbook like materials. I do not see how we will be able to justify imposing the cost of the textbooks on the students. As I used the word "flooded" in this context, I am afraid that there will be too many such notes and none may suit the instructor's taste. That is why I think it will be desirable for each instructor to develop or compile his/her own notes. The blessing is that once you start, you will be able to edit, update and improve your notes each semester you teach the course and eventually perfect your notes. In addition, with permission, we may be able to cut and paste some portions of some existing notes prepared by others.

I started developing my notes on the Elementary Statistics Course (Math 365) sometime before Spring 98. At that time I wrote them in Latex and the mathematics department distributed them at cost. Originally, these notes were not really perfect. I improved these notes whenever I taught this course (Math 365). In Spring 2000, I edited the same notes and developed a HTML version of these notes. In Summer 2000, these notes took the place of the textbook and notes were available online for the students.

I also developed my online lecture notes on the Discrete Mathematics course (Math 106) in Spring 99, while teaching the course. Currently, I am developing my online lecture notes for the Topics in Mathematics (Math 105) course, while teaching this course.

There is no reason why I would not continue to update and improve these notes whenever I teach these courses. Among the improvements I have in mind are to include more examples and add solutions to some more problems, audio visually when suited, and include more graphics.

Among the links I gave for this Elementary Statistics course (Math 365), are various sites on statistical tables and data. To win over those who still refuse to use calcualtors, I gave a link to a site about the Facit machines (with pictures) that used to be used for computations.

2. Use of the Contact Hours

Since lecture notes are available online, neither the students will have the need to spend the contact hours solely on taking notes nor the instructors will need to spend most of the contact hour "writing down" notes. This creates unprecedented opportunities to improve the quality of the contact hours or the face-time. I decided to use the face-time to cover the material in a relaxed pace, working out some of the examples in a slow easy manner, turning part of the face-time into a problem solving lab and getting them involved in discussions. To me the key here is that both the students and the instructor will be relaxed and there would be no appearence of rushing to finish something. This is how I used the face-time in Summer 2000 in my Elementary Statistics Class and currently doing so in my Topics in Mathematics (Math 105) class.

3. Give homework Online with instant feedback

I think that homework has always been the most important tool to teach and learn mathematics. Basically, we learn mathematics by solving problems. So, while thinking about organization of undergraduate mathematics courses in this information age, I gave considerable thoughts regarding homework. I decided to experiment with online homework.

So, I developed a software package to do homework online. Then I used this Online Homework Package in my Elementary Statistics Class (Math 365) in Summer 2000. Currently, I am using the package in my Topics in Mathematics Course (Math 105, Fall 00).

3.1 The Main Features of the Online Homework Package

The following are the main features of the Online Homework Software Package:

1. The instructor can create homework online.
2. The instructor can input the class roster online.
3. The students in the roster can access the homework, complete and submit it online.
4. The students answer is graded electronically and saved in the database.
5. The instructors and the students will have a userid and password for each course (i.e. line number) in a semester.
6. The students can change their password online.
7. Neither the instructor nor the students can change the database without the password.
8. The instructor can see the grades online.
9. The students can see his/her grades online.
10. The student gets immediate feedback about the correctness of the answers.
11. The students can resubmit the homework as many times as they want, before the midnight of the due date set by the instructor.
12. The instructor can give a maximum of 10 questions in a homework.
13. The instructor has a choice of three different types of answers :
    1. Answer by Checking the correct check-box,
    2. Answer by selecting the correct answer from a listbox,
    3. Answer by typing in the numerical answer.
14. The instructor will have to type in the questions, 5 choices of possible answers (in checkbox and listbox answer questions) and check the correct answer or type in the correct numerical answer, online, as always.
15. The instructor has the maximum flexibility, in the sense that he/she can edit it as many times as he/she wants (like extending the due date).
16. Students will not see the homework until the instructor makes it available to them.

3.2 Implementation of Online Homework

In my Elementary Statistics Courese (Math 365) in Summer 2000, (and currently in Topics in Mathematics (Math 105) class) I used my Homework package and gave 26 homework. Online homework has turned out to be an extraordinary teaching and learning tool, better than I anticipated. Students reactions and responses were extremely satisfactory. The following are some comments about student's reactions:

1. First of all there was only one drop/withdrawn in the whole semester out of about 35 enrollments.
2. Several students came and told me that they like it because of the instant feedback.
3. Students made comments like: " doing homework is like a video game, you want to try it because you want to win".

I also gave a survey about the online homework package at the end of the semester (Summer 00). Most noteworthy was the response to the following question:

1. "Do you think that you will receive a better grade because of the online homework than what you would have gotten otherwise?".
   

   Out of 21 respondents, 17 answered "YES" to this question. The following is the summary of the survey:
   

   
   

   The Spread Sheet of the Survey:

   Unless Obvious, Maximum possible is 10
   	Course : Semester	Math 365 : Summer 00		Math 105 : Fall 00		Math 365 : Fall 01		Math 105 : Spring 02
   	The Question	mean	st. Dev.	mean	st. Dev	mean	st. Dev	mean	st. Dev
   1	Student's Satisfaction Level	7.24	2.47	8.14	1.70	8.34	1.98	8.39	2.07
   2	Student's Comfort Level	7.43	2.13	7.96	2.00	8.20	2.20	8.39	2.06
   3	Student's Preference to Online Homework	7.55	2.22	9.18	1.32	8.44	2.28	8.47	2.00
   4	Will You Receive a Better Grade?	17 YES out of 21		44 YES out of 49		43 YES out of 50		296 YES out of 342
   5	Did Your Confidence Level in Math Improved?	6.62	2.75	7.61	2.44	7.34	2.68	7.88	2.43
   6	Spent More Time On Homework?	3.98	1.89	4.43	2.64	4.00	2.65	4.39	2.72
   7	Spent More Time for the Course?	4.52	2.06	3.88	2.02	3.8	2.28	3.77	2.24
   8	Recommend Online Homework as Standard Feature?	6.62	2.84	8.49	2.36	7.78	2.51	7.99	2.40
   9	Did You Have More Fun?	6.95	2.46	8.02	2.24	7.6	2.51	8.29	2.25
   10	Is Online Homework a Good Teaching/learning Tool?	7.10	2.43	8.43	1.67	8.4	1.92	8.26	2.12
   11	Overall Rating regarding Online homework?	7.33	2.46	8.61	1.43	8.42	2.12	8.53	2.17

   
   

Online homework "wins" because of the two features:

1. that the students get instant feedback and
2. that the students can try and resubmit homework as many times as they wish until the due date.

4. Assessment and Grading

I propose to base 75-80 percent of the grade on in-class tests, midterm and final examinations, and the remaining 20-25 percent of the grade on online homework. As I have already mentioned, homework - online or traditional - are the most important teaching and learning tools. To motivate the students to do the homework it is necessary that we give enough insentive. On the other hand, in-class tests become unavoidable because of questions about the credibility of the grading process.

In my Elementary Statistics course (Math 365) in Summer 2000, I gave 100 points for online homework and 400 points for four in-class tests.

5. Looking Toward the Future

It is widely believed that the information technology will have great influence in all spheres of life in the near and distant future, and teaching will be no exception. But I am not sure in exactly what way our job of teaching will change. I can think of a few scenarios:

1. It is possible that most undergraduate courses will be taught according to the model that I suggested or a variation of this model.
2. It is possible that a large part of undergraduate mathematics teaching will be through complete Online Courses. Although, we have to resolve the issue of grading. Perhaps, 5 years from now a laptop may cost only $300.00 and internet connections will be so abundant that we will be able to proctor online tests.
3. There may be an unprecedented surge in the number of nondegree seeking students because of the ever changing technology. Working people may need to take courses to update themselves continuously. The information technology makes it more feasible for them to do so through online courses, without upsetting their work schedule.

I do not want to make this list too long, but which ever way information technology influences teaching at the college level, it will be wise to be prepared.