# Faculty Experiences - Hector Fattorini

*HECTOR FATTORINI*

#### Mathematics

Interview TopicsWhat matters most to you in your teaching? How are you using technology as a tool to achieve your teaching goals? How have your students responded to your use of technology? What new goals do you have for using technology in teaching? How could the University better facilitate the use of technology in instruction? | PedagogyThinking like a researcher Critical thinking Test & critique theories Immediate feedback Student creativity | TechnologyAlgebra software |

## Increasing Efficiency in Computation and Enhancing Comprehension

My objective in teaching is to introduce my students to the tools
they will need in their professional life, in particular to give them a picture as
accurate as possible of what it means to do research, either of the "pure" kind or
of the kind you do in industry.

**What matters most to you in your teaching?**

My objective in teaching is to introduce my students to the tools they will need in their professional life, in particular

**to give them a picture as accurate as possible of what it means to do research**, either of the "pure" kind or of the kind you do in industry.

For many years now it has become clear that research, be it of the pure or applied kind needs the computer as an essential tool. The solution of some of the "purest" problems -- the four-color problem, the classification of simple groups to mention only two – requires essential use of the computer. I can see the truth of this statement in my own research; the writing of many of my recent research papers began with computer experiments, although my research is not particularly in the field of applied mathematics.

A student who exits our undergraduate program without being conversant in computing will not be adequately prepared to do research or to work in industry.

Until the 1980s computing had to be performed using the classical languages (Basic, Pascal, Fortran...). The simplest operations (finding roots of polynomials or matrix eigenvalues) required considerable programming, which sometimes got in the way of the mathematics. After 1980 this situation changed radically;

**computer algebra systems**such as Maple, Matlab, Mathematica came into existence. These high level programming languages require only one-line commands to find polynomial roots and matrix eigenvalues. Programming is eliminated or kept to a minimum. Finally, computer algebra systems do symbolic (not only numeric) computation, which extends their usefulness in an essential way. I teach my students how to use computer algebra systems to save them from drudgery computation, thereby allowing them to use their time

**to think about the theoretical concepts and the mathematics problems**.

**How are you using technology as a tool to achieve your teaching goals?**

All my undergraduate courses use a computer algebra system, available in various labs on campus.

Homework contains the traditional pencil and paper problems plus computer problems (about 50% each). The boundary between the two categories is not sharp, the students can use the computer to check the answers of their pencil and paper problems.

However, my use of the computer is not limited to furnishing the students with a useful tool. It is also used to enhance comprehension.

**To give the definition of, and prove theorems on a given mathematical concept**(for example, matrix eigenvalues) is only the middle stage in a triad in a student’s learning process. The first stage is motivation and the last stage is application. After having learned the concept of eigenvalue in the comprehension stage, the students see its applications in the analysis of large oscillating structures. This analysis (which is impossible without the computer) makes eigenvalues "come to life" as descriptors of oscillating characteristics. Students can analyze changes in these characteristics as a consequence of changes in the design of the system. At this point eigenvalues become an indelible reality in the student's mind, rather than a mere dogmatic abstraction.

As to the actual use of technology in my courses, my approach is conservative. I communicate with students using a

**class e-mail list**. This is a fast way of class contact by means of which I pass to the class handouts, homework solutions, last minute corrections, etc. I answer e-mail from students at various set times during the day, which

**achieves almost "real time" contact between the students and myself**. Questions on the software are the easiest to answer, since commands are text-alone.

**How have your students responded to your use of technology?**

Students respond to the use of technology favorably. Our undergraduates seem to be very computer aware and seem to have a clear idea of the importance of computing in their future careers.

The most important effect of my use of computing on students has been stimulating their critical thinking and

**creativity**. Frequently, after doing a computer problem students see the possibility of proving a theorem. This kind of "computer evidence" sometimes leads students to an actual result but sometimes it can also mislead them. In either case, this process leads students to develop a strategy to plan computer experiments and to interpret their results.

**What new goals do you have for using technology in teaching?**

My goals at present are mostly technical. One is to further improve communication with students with broadband Internet. I would like to achieve a "real time" communication where a student who is stuck with a problem could get help almost immediately.

*E-mail Interview, May 2005*