After making a few changes on their own cadets are able to predict what the plot will look like before it is generated.
Directional Derivatives: Another area where experimentation is very useful is the directional derivative. Cadets quickly learn how to compute the directional derivative, . Very few understand what the numerical answer represents, the rate of change in the direction of motion. Armed with a Mathcad worksheet they can change a starting location or direction and immediately see the impact.
Again, after experimenting with the worksheet cadets are able to predict what the answer should be before it is computed. They can also experiment and discover the maximum directional derivative is achieved when we travel in the direction of the gradient.
These are just a few examples of how technology can help students better understand Multivariable Calculus. I do not know if USMA should issue every cadet a laptop. I do know there are advantages to having a laptop in the classroom. But we can also realize some of these advantages with the technology we currently have. What we all must understand is technology does not replace learning; it should enhance it. I believe that is what we have accomplished.
I have taught composition in computer labs both at civilian universities and at the USMA and am convinced that the introduction of laptop computers can help develop cadets' writing competence. But that is only if the instructional methodology is appropriate. The use of technology can (and should) change both what and how we teach. Having taught for the past two semester in a classroom where cadets used laptop computers, and for several years with students at desktops in computer labs, I can testify to both the advantages and the problems that instructors should be aware of in working with laptops in teaching writing.
The machine is not a magic wand. It is the appropriate use of the computer (i.e., effective instructional strategies that complement the computer) that makes the difference. Conventional wisdom suggests that the use of word processing makes students better writers, but that is a typicallyl wrongheaded idea of technology. The word processor is a tool; writing is a complex cognitive act. Unless the writer uses the tool appropriately, it is of no value in "improving" writing. When I began teaching students via word processing, my hypothesis was that although the computer replicates the essentially recursive process of human composition, thereby making the writing task itself much less arduous with ease of correction and revision, the writer without a well-established personal writing process does not benefit much from the machine. The use of a computer for writing in and of itself has little value in developing student writing. One personal analogy might illustrate this point. My father was a skilled craftsman, a cabinet maker. He had superb tools for his craft, but had I inherited them, I would have been unable to produce anything even vaguely resembling the custom furniture he made. Such tools do great work only when plied by a craftsman. Similarly, college freshmen who arrive with limited writing experience, and even less formal feedback on their writing from their teachers, will be no more able to write effective college essays with their computers than they would be with their Bics.
Research conducted on student writing has confirmed this. What the average undergraduate will produce is neat copy (the laser printer does a terrific job) that is essentially free association of ideas rather than a structured essay. Since the writer can only see a portion of the text on the screen at a time, it is essential that he or she have a firm sense of the organization of the entire essay and have planned carefully. Because the computer is a fluid medium, both planning and organizing can be done on the machine itself, but the key is instruction. Knowing that awareness of planning and organizing strategies is essential for writing effectively with a word processor, those skills should be the baseline of any college composition course. Unless students are taught effective writing strategies for writing with word processing, the technology would have little value in improving their writing.
When I was taught to teach writing many years ago (well before the advent of the computer), I was introduced to the cognitive process approach that stipulated a workshop environment in the writing classroom. In the early seventies, composition specialists already knew what higher education in general has only recently discovered--for students to learn to write well, they benefit from actually writing rather than listening to lectures about writing. In the workshop environment, the student is central and the student's writing is the basic text of the course. As a graduate teaching assistant, I was thoroughly schooled in this approach and thought I conducted effective writing workshop classes. But the first time I taught in a computer lab, I realized how far I was from my ideal! The student at the computer instantly decentralizes the classroom and places the instructor in the role of "guide on the side" rather than "sage on the stage." This was my experience, and it has been affirmed in research studies.
Although I welcomed this arrangement in facilitating the workshop classroom, many of my colleagues at West Virginia University could not adjust and refused to teach in the computer room. However, it's important to note that while it's not easy to eliminate the presence of desktops, instructors can easily ignore the laptop in the classroom if they find it impinging on their implicit sense of their central role. So the first thing to consider in terms of teaching composition with laptops is the nature of the learning environment and the instructor's role in that environment. The laptop will not magically produce a workshop environment if the instructor is not attuned to its desirability.
Writing an essay is a problem-solving process, and the inept writer has not yet solved the problem. Just as solving math problems in class under the guidance of an instructor is helpful, solving the problem of writing a paper in a collaborative workshop atmosphere under the guidance of an instructor helps foster student competence. However, one of my less happy discoveries is the high degree of classroom management skills needed to keep students on task when working with computers. I had always thought I had good classroom management skills (the parochial school teacher in me is never well hidden), but I was amazed at how much I had to ratchet up those skills in a computing environment. The machine is a great distracter, and unlike other classroom distractions, it's malleable, responsive to the student's manipulation and therefore more enticing. Any instructor working with students at computers needs to have a very clear plan for the class worked out in advance in great detail. Although the atmosphere of the writing workshop classroom should seem relaxed, the instructor has to be in firm control at all times. This need for good classroom management should not be underestimated, nor should the faculty's ability to achieve this be overestimated. Both attitudes are common, in my experience.
However, in addition to firm control, the instructor working with students who are at laptops needs to be flexible and have contingency plans. There are many more problems with laptops than with desktops in a computer lab--mainly because the latter are under our control while the former will be subject to the cadets' care. I've had laptops "die" because the cadet had not correctly charged the battery, and I've had machines "freeze" on some cadets in the middle of an important lesson. Part of lesson planning has to be developing contingency plans in the event of computer malfunction.
In the writing workshop environment, the instructor's major tasks are in the planning and the subsequent response to student writing. One of the great advantages of working with computers is the ease of student submission and instructor response. In the beginning I worked with disks but eventually created a shared drive so that students could save texts, and I could retrieve them at my desktop. In responding to writing on the computer, I am able to provide much quicker feedback. My cadets don't have to wait for the next class session; I e-mail corrected copy as soon as possible after it's been submitted. In addition, I've taken advantage of student interest in technology to encourage revision by "publishing" their writing on the web. Twice I tried having the cadets create their own writing portfolios on the web, but I found that since EN101 is a plebe course, the uneven ability of the cadets to manage this task in the first semester was a problem, but more of a problem was the fact that the more expert cadets got very involved with the graphics and design of their pages and lost the intended focus on editing their writing for publication. This semester I seem to be having more success with posting the cadets' writing myself on our class web site.