HP Prime too complicated

[Claudio L.]

(07-12-2018 02:39 PM)sasa Wrote:  One particular part where CAS may choose longer path may be following:

Find determinant of:

Code:


1 2 3
4 5 6
7 8 9

While student may have idea to transform by simply subtracting it to:

Code:


1 2 3
3 3 3
3 3 3

... and then easily apply rule that determinant is zero if two columns or rows are equal (or proportional), CAS may run into LU decomposition complexity or standardized path of elimination, which certainly would not be a benefit for a Joe which should learn some shortcuts/tricks (which actually comes from basic rules) in order to perform the task with pencil and paper better and faster than calculator, especially with any larger similar singular matrix, actually making it to develop affection to math, not to blindly use calculator and use to its abilities or flaws.

I do not have any CAS capable calculator to claim upper, however I would be supprised that any calculator can calculate upper determinant with only one described step.

The beauty behind solving some problems is that solution is easy and fast accomplished by spark of an idea, avoiding all complexity standardize approaches may involve.

I think it all depends on context. If that matrix was given to a student that is learning matrices and determinants, you are 100% correct: they are better off learning "old-fashioned" way.
However, in more advanced courses, that matrix might come as part of a system of equations to solve a physics problem. In that case, I much rather prefer the student's mind focused on the physics than on row-reduction, and it helps to be able to get that determinant with a single keystroke. The student does need to know that getting a zero determinant means his formulation of the physics problem was either incorrect or simply has infinite solutions, and his mind needs to go back at the physics model and equations that gave origin to the matrix to see what went wrong (bad model, or if you are designing something, perhaps an accurate model of a bad design). In this context, the procedure to get that determinant is a mere "distraction" from the actual problem.
In the end, you need to have a calculator that is capable of doing it all, it's up to the user to use that power wisely in each context.
That context will change dramatically over the life of that student, so it's important to keep an open mind, people can't expect to limit the capabilities of a product based on the limited scope of its own context at one point in time.