Young was an undergraduate at the beginning of the computer age and had many experiences with the experimental introduction of technology in undergraduate education. Later, Young was a graduate TA at the Georgia Institute of Technology at the time when math professors were first experimenting with the use of Mathematica for teaching. That experiment was going very badly, so Young developed and implemented his own approach. As a postdoc at Northwestern University, Young took part in the introduction of Maple into the calculus sequence. Based on these experiences he is writing a book ``Computers in Undergraduate Math - A Simple Approach". In the book, Young promotes the use of CS in carefully designed homework assignments. Here are a few of the key points from the book:
Widespread availability and widespread use are crucial. The obvious advantage of widespread availability is that students can use the software when and where they choose. This eliminates problems like crowding of specific computer labs when a project is due. Widespread availability also allows the students to make use of the software as a tool not only for math classes, but allows the software to become part of mathematics usage across the campus. The introduction of computers in the dorms is a great step, but, for students to get the full benefit from the computers, they must have access to good software.
Another clear advantage of widespread availability and use is that in subsequent Math classes and in math-using courses, professors are able to assume knowledge of the software. This leads to a type of snowball effect: widespread use encourages more widespread use.
A less obvious benefit of widespread use is that a culture or collective knowledge about the software develops. When this happens, the need for technical advise plummets, because students are able to obtain immediate help from classmates, friends and neighbors.
Others have observed the wisdom of widespread availability and use. According to Krantz [5],
We have had catastrophic experience, at my own university, trying to introduce MAPLE or MATHEMATICA or some other software into isolated courses. Students are not stupid. They catch on right away to the fact that this software is specific to the particular course, and as soon as the semester is over they are unlikely to see it again. They resent having to learn a whole new language .... If we are going to introduce serious software into the lower-division curriculum then we should do it globally instead of locally. ...It makes sense to tell students from day one that their entire lower-division mathematics curriculum will depend on MAPLE ...and that they will need to master it right away. Having understood this dictum, they will comply ...and the software will become part of their lingua franca. They will (we hope) carry it (or the analytical skills attendant to it) on to the rest of their education, and their lives.
Assignments should focus on the principals needed to use the software well. Assignments in Young's approach are primarily aimed at training the students to understand the differences between numerical and symbolic computations and the underlying mathematics needed to use each effectively.
Use of the software can and should be simple for students. An instructor of an introductory math course should be careful to not unduly burden students with technology, as has often happened in experimental introduction of technology. It is an undeniable fact that math courses are difficult in themselves. Further, these courses are major career events for students interested in the Sciences and Engineering. To overburden students in these courses with additional difficulties borders on irresponsibility. Widespread availability and use are two keys to making assignments simple for students. Other steps which are important for this purpose in Young's approach include: 1. Use simple, basic calculations to demonstrate important principles, 2. Give very clear assignments, and, 3. Give very clear technical information.
Using the software can and should be easy for instructors. Many previous attempts (at other Universities) to incorporate software in math classes have required extensive time commitments on the part of instructors. This use of time is not only impractical for professors with other time demands, but it is unnecessary. Widespread availability and use of the software, and a clear, simple approach to assignments, make demands on professors minimal. Also important is that professors can make good use of the software without direct in-class use. Experience has shown that in-class use of software is not a good model for many professors. The simple homework approach can give students significant experience in using the software without burdening the faculty.
Writing should be incorporated in the assignments. There is a growing body of research which indicates that writing in the context of mathematics helps students to form and solidify abstract mathematical concepts [1] [7]. Writing is also an important skill in and of itself and should be encouraged whenever possible. Each homework assignment contains essay type questions where students are asked to describe and analyze results of the computations. It is emphasized that quality of writing will be an important part of the grade on the assignments.