## Empowering Students in the Mathematics Classroom

## USA

#### USA008

## Résumé, summary

Having graduated from college in 1965, I can say that I learned mathematics the "old" way, where we had to do everything by hand or, occasionally, with the aid of a slide rule. It was in graduate school that I first had the opportunity to write the code to tell a computer to carry out an algorithm and come up with an approximate answer to a problem that I needed to solve. Since then, I have eagerly watched the power of the computer expand, and it was the computer language Logo that made the first dramatic impression on me. Realizing the allure that Logo had with children of all ages, twelve years ago, I developed a Logo class for elementary education majors. In teaching mathematics classes, I used a variety of programs, including spreadsheets and graphing packages, but the turning point in my teaching mathematics came when I discovered Mathematica.
In January of 1990, I had the opportunity to attend the first International Mathematica Conference. Never before had I imagined that a computer program could do such things! I knew that Mathematica would change forever both what we teach in the mathematics classroom and how we teach it. If we were to provide our students with the very best education possible, I knew that we had to bring this type of software into our classrooms. However, there was one major hurdle: our college did not have the funds to buy either the computers capable of running the software or the software itself. I decided that the only way we could provide our students with what I deemed as essential was to write grants asking for the necessary funds. In that endeavor, I have been very successful, having received two sizeable grants for such equipment.
My zeal in this endeavor spread outside the confines of my college. I wrote several successful grants to bring nationally recognized individuals in the field of utilizing computer software in the teaching of mathematics to our campus, and we hosted state- wide meetings for mathematics educators at the secondary and college levels throughout Montana. I have also worked with mathematics teachers who are involved in a systemic initiative to rewrite the high school mathematics curriculum.
At Carroll College, the computers and software have allowed us to restructure our undergraduate curriculum for mathematics and engineering majors and also to upgrade the courses we teach for students not entering the field of mathematics or engineering. On the national level, we are working with a group of seven other colleges throughout the country on COMAP's (Consortium for Mathematics and Its Applications) Curriculum for a New Century Project and have also been invited to West Point to study their Seven- into-Four curriculum. Without our own access to powerful computers, we could not be seriously considering these innovative programs, each with a strong technology component.
Throughout all these activities, one of the most difficult challenges is convincing others that we cannot keep doing things as we have done them in the past. We have to be risk takers if computers are to significantly alter the way we teach, and we need to invest long hard hours of our own to make it work. When I watch my differential equations students in the computer laboratory, there is no doubt in my mind that all my efforts are paying off. And when I observe what our seniors in mathematics are doing with Mathematica in writing their theses, it is a particular delight. This year, one of my students, an undergraduate, has had a paper accepted to present at the International Mathematica Conference in England.
My nonmath major students in my statistics classes are analyzing large sets of data, including AIDS data, with the assistance of the powerful SPSS for Windows. The insight they gain into the problems they are analyzing by using such software is truly remarkable. My business students are doing linear programming and network problems, critical path methods, decision analysis, forecasting and queuing problems with the aid of the computer. We could not solve these problems without it.
At the age of fifty-one, when some people are looking forward to their retirement, I am having more fun with my career than ever before. It is a great time to be teaching mathematics!

## Discipline, subject :

mathématiques
Mathematik
mathematics
matematica
## Public :

formation d'adultes
Erwachsenenbildung
adult education
formazione degli adulti
enseignement spécialisé
Sonderschulen
specialized training
insegnamento speziale
## Contacts :

Vanisko, Marie

Carroll College, Department of Mathematics

USA-59625

HELENA
Tel : 406-447-4451

Mail :

Fax : 406-447-4533

## Pédagogie, pedagogy :

The utilization of computers in the mathematics classroom has brought about a fundamental rethinking of both what we teach and how we teach it. Cooperative learning is a natural companion to computer projects. These projects usually involve the exploration of meaningful problems, unable to be solved by hand. Many of our mathematics courses now have a formal laboratory component.
Learning Aspects:
Students spend less time doing tedious calculations which used to be required if one were to gain insight into a problem. Now, students and teachers together can ask and seek answers to the "What if..." questions.

## Apprentissage, learning :

Students spend less time doing tedious calculations which used to be required if one were to gain insight into a problem. Now, students and teachers together can ask and seek answers to the "What if..." questions.

## Enseignement, teaching :

The teacher does far less lecturing and far more working one-on-one with the students. However, class preparations take more time and textbooks that have problems other than those that can be solved by hand are just now becoming available.

## Technique :

The primary software program that I use is Mathematica, a combination symbol manipulator, graphics and numerics package, and programming language. I also utilize SPSS for Windows and Quantitative Systems for Busines

## Société, society :

Students experience what it is like to be a team member in solving problems. They also profit from orally presenting results of group projects.

## Culture :

At Carroll, we have a number of International students and it is interesting to see their perspective in solving certain problems, as compared to our traditional students. I also feel that computers put students on a more even footing with one another. Students who are typically unsuccessful in mathematics classes, frequently do very well when they discover the power that the computer gives them.

## Institution :

Through grants I have written, we have been able to provide our students with both computers and software in a laboratory setting. Our newest laboratory is equipped with Pentiums and provides the setting for the laboratory segments of our classes. The computer laboratory is opened to students seven days a week and every evening except Saturday.

## Logistique :

Teachers need to reassess what they are teaching and how the students can better learn, now that they have such a powerful tool in their possession. By their use of technology, teachers must model what they expect the students to do. In other words, we need to "practice what we preach."

## Remarques, remarks :

Having graduated from college in 1965, I can say that I learned mathematics the "old" way, where we had to do everything by hand or, occasionally, with the aid of a slide rule. It was in graduate school that I first had the opportunity to write the code to tell a computer to carry out an algorithm and come up with an approximate answer to a problem that I needed to solve. Since then, I have eagerly watched the power of the computer expand, and it was the computer language Logo that made the first dramatic impression on me. Realizing the allure that Logo had with children of all ages, twelve years ago, I developed a Logo class for elementary education majors. In teaching mathematics classes, I used a variety of programs, including spreadsheets and graphing packages, but the turning point in my teaching mathematics came when I discovered Mathematica.
In January of 1990, I had the opportunity to attend the first International Mathematica Conference. Never before had I imagined that a computer program could do such things! I knew that Mathematica would change forever both what we teach in the mathematics classroom and how we teach it. If we were to provide our students with the very best education possible, I knew that we had to bring this type of software into our classrooms. However, there was one major hurdle: our college did not have the funds to buy either the computers capable of running the software or the software itself. I decided that the only way we could provide our students with what I deemed as essential was to write grants asking for the necessary funds. In that endeavor, I have been very successful, having received two sizeable grants for such equipment.
My zeal in this endeavor spread outside the confines of my college. I wrote several successful grants to bring nationally recognized individuals in the field of utilizing computer software in the teaching of mathematics to our campus, and we hosted state- wide meetings for mathematics educators at the secondary and college levels throughout Montana. I have also worked with mathematics teachers who are involved in a systemic initiative to rewrite the high school mathematics curriculum.
At Carroll College, the computers and software have allowed us to restructure our undergraduate curriculum for mathematics and engineering majors and also to upgrade the courses we teach for students not entering the field of mathematics or engineering. On the national level, we are working with a group of seven other colleges throughout the country on COMAP's (Consortium for Mathematics and Its Applications) Curriculum for a New Century Project and have also been invited to West Point to study their Seven- into-Four curriculum. Without our own access to powerful computers, we could not be seriously considering these innovative programs, each with a strong technology component.
Throughout all these activities, one of the most difficult challenges is convincing others that we cannot keep doing things as we have done them in the past. We have to be risk takers if computers are to significantly alter the way we teach, and we need to invest long hard hours of our own to make it work. When I watch my differential equations students in the computer laboratory, there is no doubt in my mind that all my efforts are paying off. And when I observe what our seniors in mathematics are doing with Mathematica in writing their theses, it is a particular delight. This year, one of my students, an undergraduate, has had a paper accepted to present at the International Mathematica Conference in England.
My nonmath major students in my statistics classes are analyzing large sets of data, including AIDS data, with the assistance of the powerful SPSS for Windows. The insight they gain into the problems they are analyzing by using such software is truly remarkable. My business students are doing linear programming and network problems, critical path methods, decision analysis, forecasting and queuing problems with the aid of the computer. We could not solve these problems without it.
At the age of fifty-one, when some people are looking forward to their retirement, I am having more fun with my career than ever before. It is a great time to be teaching mathematics!