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Effectiveness of Teaching Mathematics Online

by Sloan-C

I. Introduction

Online education is becoming more and more popular but its effectiveness is still questioned. In this paper we will describe an online mathematics course at Pace University. The topics we will discuss include communication with students, student help, and testing. We will then compare the success rate for this online course to the success rate for similar traditional courses at Pace University.

The use of the Internet as an educational tool is becoming more and more common at universities worldwide. Today, many universities and colleges offer a wide variety of online courses in a variety of different areas. One major benefit of online courses is that they can reach people in different areas of the world who could not get to a particular campus where the course they wanted is being offered. One other advantage of taking online courses is that they tend to be asynchronous which allows the student to learn according to their own schedule. This type of freedom allows people with tight schedules to continue learning. Still, others say "there is nothing like being in a classroom face to face with the professor." There are many differences in these two education styles and some question the effectiveness of online education. In this paper we will address this issue. We will analyze success rates of Pace University's online Mat-125 (technical mathematics) and compare these rates to the success rates to similar traditional classroom courses at Pace University and test for significant differences.

II. BACKGROUND

Mat 125 is an online mathematics course developed to fulfill a requirement for students enrolled in the Nactel program at Pace University. The students in the Nactel program need the mathematics covered in Mat-125 as a prerequisite to the courses that they must complete for their degree in telecommunications. Mat-125 has been offered in the spring of 1999, the fall of 1999 and the spring of 2000. The data we will use is from these three semesters.

The students who take Mat-125 usually have a wide range of mathematical skills. Some students breeze through the course, while it seems impossible for others. Communication is done mostly through e-mail. If a student is stuck on a homework problem, he or she can e-mail it to the professor and get a solution e-mailed back. For the more complicated problems, handwritten solutions can be faxed to a student.

Another form of communication or student help is the chat room. Chat room hours are usually held every week. This is a very useful tool for helping students. Students in the chat room can ask a question and see the solution written out step by step on the whiteboard. In the chat room, students see problems worked out as if they were in a classroom. The professor uses the mouse as a piece of chalk.

The last form of communication is the telephone. Students can call the professor and have a problem explained over the phone or even call while they are in the chat room for a better explanation. These types of interaction may make this combined form of education effective.

Having different methods of communication make it easy for the students to be in contact with the professor and each other. These students get more than just a few e-mails a week. They see problems done at the white-board, they get handwritten solutions faxed to them, and even talk through problems on the phone. This abundance of communication and feedback adds a "classroom" type atmosphere to the online experience.

Mat-125 covers a variety of precalculus topics including algebra and trigonometry. The course content closely resembles the material covered in traditional classroom-based algebra and precalculus. This study compares the success rates of Mat-125 to Mat-130 (precalculus at Pace University) and Mat-103 (college algebra at Pace University).

III. METHOD

The first thing we will show is that there no statistical difference in the success rates of Mat-103 and Mat-130. This strengthens the case for using the combined success rate of Mat-103 and Mat-130 to test against the success rate of Mat-125.

Since we are discussing success rates, we should also comment about the testing. In any online course security is a major issue. To deal with the issue of security, we have installed test proctoring into our program. It works like this. Every student who enrolls in the program signs up with a proctor. This proctor is a person who meets certain criteria and who will be able to administer the exams to the student. For example, a local librarian or teacher could be a proctor for a student. At the same time we do not allow a student's parent to be the proctor. The proctor is issued a password that lets him or her have access to the exam. Without the proctor the student can not access the exam. The proctor then prints out the exam, administers the exam to the student and sits with the student while they take the exam. When the student finishes the exam, it is given to the proctor and then the proctor mails the exam to the professor. The professor then grades the exam and posts the grades online. This process makes test taking and grading quite a bit more secure.

The test we will use to analyze this data is a standard hypothesis test for the difference of proportions (large samples). We will first test for significant difference in the success rates of Mat-130 and Mat-103 and show that there is no statistical difference in these rates. We will then test for difference in the combined success rate of Mat-130 and Mat-103 against Mat-125. By "success rate" we mean the proportion or percent of students that finish the course with a passing grade to all students that finish the course.

IV Results

First we will test for differences in Mat - 130 and Mat - 103, using a z test of differences of proportions for independent samples (Mann, Prem S. Statistics for Business and Economics, pp527-529. New York: John Wiley & Sons, Inc). Over these three semesters, spring 1999, fall 1999, and spring 2000, the number of students taking Mat-130 is N1= 92 and the number of students that passed is r1= 69 which yields the success rate of p1=.75. The corresponding numbers for Mat-103 are N2=114, r2=90, and p2=.7894. We will test the claim that there is no statistical difference in these proportions. One should note that this will be a two-sided hypothesis test with the following setup.

Ho : p1 - p2 = 0
Ha : p1 - p2 ¹ 0

The numbers above yield the test statistic,

Z=-.68

This means we cannot reject Ho with an alpha level of a=.05. Failing to reject Ho means there is no significant difference in the success rate of Mat-130 and Mat-103 against Mat-125.


We now get to the main purpose of the paper. We will test for differences in the combined success rate of Mat-130 and Mat-103 against Mat-125. Using the information above,
The number of students who took Mat-130 or Mat-103 is N1= 206 and the number of students that passed is r1= 159 which yields the success rate of p1=.7718. The corresponding numbers for Mat-125 are N2= 178, r2= 151, and p2=. 8483. Testing the same claim as before we have the setup,

Ho : p1 - p2 = 0
Ha : p1 - p2 ¹ 0

Which gives the test statistic,

Z=-1.86

Once again we fail to reject Ho with an alpha level of a=.05. Failure to reject Ho shows there is no statistical difference in the combined success rate of Mat-130 and Mat-103 and the success rate of Mat-125.

V. CONCLUSION

We first discussed several factors including an abundance of feedback and communication for the students, as well as test proctoring. These factors may add to the quality and effectiveness of the online education. We then showed that although Mat-103 and Mat-130 are different courses, there is no significant difference in their success rates. This justifies combining their success rates to test against Mat-125. We next showed that there was no statistical difference in the combined success rate of Mat-130 and Mat-103 against the success rate of Mat-125. We used a two-sided hypothesis test, since either the online or the classroom course could be better.

These results on the success rates support the claim that online teaching is a legitimate and reliable method of education.

VI. ABOUT THE AUTHOR

Augustine B. Mascuilli is an assistant professor of mathematics at Pace University. He teaches both online and in the classroom. Dr. Mascuilli's research interests lie in real and complex analysis. He received his Ph.D. in mathematics in 1996 from the State University of New York at Albany and since that time he has been with Pace University.