I am passionate about Maple because as an academic with
theoretical physics training and a love for mathematics. I see it as a terrific
tool for making math come alive and empowering students to carry their
mathematics to a new level instead of seeing it just as a test taking exercise
disconnected from real applications. Most of the students in these courses need
to learn how to think mathematically to solve physical problems. If they can
only “get the answer” to artificial math problems, they cannot transfer their
knowledge to applications in science and engineering. “Getting the answer” is a
syndrome encouraged by our secondary school emphasis on standardized tests where
mathematical notation and terminology is irrelevant, as is also clearly documenting
how one “gets the answer”. Graphing calculators facilitate this same mentality.
Push a lot of buttons and get an answer. A computer algebra system instead
creates naturally an organized document of a sequence of steps towards a result,
expressed in standard mathematical notation (reinforcing the use of the proper
symbols), which can be commented as well to provide clear mathematical
discussion. This should also be encouraged in hand work since many students have
trouble with mathematics because they are disorganized in the way they perform
mathematical calculations. This is especially important for math majors.
Here is a statement I wrote years ago on our Math dept
website:
Why MAPLE?
One no longer has to “teach” Maple as in the old days---because
of the context sensitive menus and palettes to build mathematical notation,
something that comes quicker to younger generations who grew up in such an
environment, it
is enough to guide students in using it as part of their normal homework like
they use graphing calculators. Watch this 3 minute video about clickable
calculus:
http://www.maplesoft.com/products/maple/demo/player/ClickableMath.aspx
Providing an frequent example as an instructor is also essential in getting them
to take it seriously, as is assigning some ordinary homework problems to do or
check in Maple.
The most important part about calculus and its follow up (DEwithLinAlg) is the understanding of the steps needed to solve a problem and how the concepts lead to these steps. Often the actual mechanical steps (do the derivative, simplify, do the integral, solve, etc) are the least important thing about such calculations and if we were in a more progressive environment, we might try to aim higher with our expectations of what students are capable of, and use a tool like Maple in a more serious way. For now even I keep it light and low key so I don’t stand out too far as an outlier in our department.
Because I believe in Maple and want to share my experience, I
long ago created and have
maintained 4 worksheets that show what Maple has to offer for each of these four
courses, for instructors to be aware of how Maple can be used in various
contexts in these courses. They are not meant to imply that every part must be
used in the course of teaching, but show what Maple has to offer any particular
teaching style on the key topics of those courses.
Maple tips and hints
[for instructors]
http://www.maplesoft.com/demo/streaming/M18_Training_EducatorsResearchers.aspx
The first 40 minutes are probably enough, but the end of the hour points out the
short training videos which show how to use Maple in teaching certain concepts:
http://www.maplesoft.com/TeacherResource/
Of course Maple is very powerful and can seem overwhelming to a beginner who looks at its power through an hour long video, but we all have to begin with baby steps like our students, and we can certainly be happy if they can begin doing the most elementary calculations to support their homework environment. If the use of Maple is not seen as connected to the everyday course material, it will fail.
I am happy to help anyone who wishes to learn 1 on 1 with me, and will certainly do some workshops for those interested, but I will not push anyone to do what I do, although everything I do is fully documented on my website for every course I teach, for anyone's amusement. Since I am the course coordinator for MAT2705, I wrote some brief Maple advice [MAT2705 syllabus] for that course. For both MAT2705 and MAT2500, one can look at my daily homework assignments to see how I incorporate Maple into them, and the help I offer students in terms of templates and examples. I allow them to check all work on quizzes and tests with Maple, which means I don't just ask questions which can be responded to by a technology device readoff. [All my quizzes and tests including PDF hand answer keys and the Maple worksheet solutions are online for all of the courses I have taught this century.]
In these courses, I grade a collection of HW problem worksheets from each chapter done in groups of 2 or 3 with flexible deadlines due after the completion of each chapter, and allow them to resubmit to correct their errors from my feedback in those worksheets, until they get maximum credit if they want it. I offer to help any student fix problems they still do not understand how to fix, and allow them to fix worksheets till the end of exam period. I only count the total Maple homework as 10 percent of the final grade. It is an easy 10 percent.
--- dr bob jantzen updated 23-apr-2015 (then 1-apr-2022)