Let me add some details about the front lines on which I am fighting -- I mean, teaching.

First, I am an old-timer who is most comfortable with my fingers on the keys. I can type. It slows me down to use the mouse or to use multi-key command sequences.

While I admit to being an old-timer, I do not admit to be an old Doug who can't learn any new tricks.

Second, it's not about me. All calculus students at the University of South Carolina spend one hour each week in the computer lab. I oversee the lab coordinators, who give detailed guidance to the TAs who actually meet the students. Most TAs have very limited (if any) prior exposure to Maple (or any mathematical software). So, we have to give the TAs simple, easy-to-learn skills and techniques that they can feel comfortable teaching to students less than one week after they first see them.

I readily admit that document mode and 2D math input are more attractive than worksheets and Maple notation. The problems with document mode and 2D math input can be summarized with two statements:

• actions and options can be very sensitive to the state from which they are initiated
  
• there is no clear trace of exactly what was done to obtain a specific action.

Students do not have the mathematical sophistication to understand how small changes in the selection can lead to such large differences in the context menus produced.

Students cannot see the instructor's hands and keyboard to know exactly what was done to enter something that leaves no trace. And, their attention is diverted from the presentation whenever they try something on their own - as they are instructed to do. Miss the wrong step in an interface-based construction and there is no hope of catching up!

To me, the interface issues are not solved by creating more tutors and templates. While there is a place for tutors and templates, in the end they boil down to the equivalent of a button on a calculator -- they teach nothing about the mathematics. I want students to learn to use Maple as a powerful tool for solving problems. I want students to get a better understanding of the structure of the mathematics. I want students to have to formulate a sequence of steps that allows them to move (logically) from the given information to a solution.

For all the stump speeches I've given lately you might think I had some political aspirations. (:-))

Doug

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Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

that's because I, like you, prefer simple rules. The rule of using * for multiplication is simple; the rules for when it can be omitted are not.

Note that part of the problem is that Maple is dynamically typed. If Maple were statically typed, then it would be possible to overload space/juxtaposition to mean both application and multiplication, because then there would always be enough context to clarify which it has to be. In fact, even more overloading is possible. And that is how mathematicians do it too - they know, in advance, what type their "objects" are, so there is no confusion caused by their notational overloading. The real mistake in the design of the interface rules for implicit multiplication is the hope that this can be done context-free.