Using Sage to replace lectures altogether....
sebe...@spawar.navy.mil
teaching???
"Why (and how) I teach without long lectures"
http://cm.math.uiuc.edu/where
I like many of his ideas. It seems something similar could obviously
be done with Sage.
I wonder what others think on this list.
Chris
kcrisman
On Mar 13, 6:44 pm, "seber...@spawar.navy.mil"
> Anyone familiar with Jerry Uhl's "Calculus & Mathematica" method of
> teaching???
>
> "Why (and how) I teach without long lectures"http://cm.math.uiuc.edu/where
>
> I like many of his ideas. It seems something similar could obviously
> be done with Sage.
suppose you could do it without technology at all; the resistance to
forcing students to really grapple with it ahead of time (which
demands much more up front) might be very difficult, of course. Some
places already do teach largely with a lab method; see also
http://www.math.duke.edu/education/calculustext/, which is being tried
out at Hood College in what is more of a lab environment and
relatively little lecture (but still regular class sessions).
Sage wouldn't be any better or worse in that regard, though TinyMCE
helps; however, some of the Sage/Moodle or other system integration
ideas would make it much easier. Sometime in the not-to-distant
future one should be able to have Sage embedded in a system which
enables chat, virtual chalkboard, comments on HW, automatic grading of
routine exercises, etc. - sort of Sage notebook+WeBWorK+Moodle+more.
So, as they say, implement it and send in a patch :) Just kidding.
But if you try this in an experimental section, let us know, and
definitely help brainstorm what notebook functionality might be useful
in attempting such a venture.
- kcrisman
Rob Beezer
> Anyone familiar with Jerry Uhl's "Calculus & Mathematica" method of
> teaching???
and it was a great experience. The essay at the link is classic JJ.
In 1992 I taught integral calculus to a small group of first-term
freshman using the Calculus & Mathematica materials. We met one day a
week in a classroom and then three days a week in a lab setting. I
had an undergraduate TA to help with lab sessions. I chose to do a
lot of grading of the electronically submitted worksheets. Here's
another +1 for TinyMCE - the ability to insert legible comments in
student work to be returned to the students.
I thought it was a good experience for the students. It gave them
competency in different ways than a traditional class. I wouldn't say
they learned *more*, but they became adapt at certain things (such as
visualizing global/local behavior of functions, applications of
definite integrals, convergence of power series) while not reinforcing
other skills (algebraic manipulation, techniques of integration,
calculation). Folks on this list would probably say that was an
improvement.
The course was an experiment and in a small department we didn't have
the luxury of continuing to run it in parallel with our regular
courses, and there wasn't sufficient enthusiasm to cutover to this
style en masse.
However, I continue to borrow ideas to use in my own courses from this
experience. Which explains *some* of my enthusiasm for Sage. For
example, I may try to do a better job of motivating series in a weeks'
time by first "playing around" in Sage with some power series obtained
by any tricks possible (algebra, polynomial division) other than the
traditional Taylor polynomial via derivatives. I'm hoping it will
motivate students to ask about questions of convergence/divergence
*before* being told about it. I'll probably post separately about
this in the next couple of days.
Rob
Offray Vladimir Luna Cárdenas
Rob Beezer escribió:
[...]
> In 1992 I taught integral calculus to a small group of first-term
> freshman using the Calculus & Mathematica materials. We met one day a
> week in a classroom and then three days a week in a lab setting. I
> had an undergraduate TA to help with lab sessions. I chose to do a
> lot of grading of the electronically submitted worksheets. Here's
> another +1 for TinyMCE - the ability to insert legible comments in
> student work to be returned to the students.
>
>
[...]
> The course was an experiment and in a small department we didn't have
> the luxury of continuing to run it in parallel with our regular
> courses, and there wasn't sufficient enthusiasm to cutover to this
> style en masse.
>
>
[...]
Talking about small experiments with digital technology and mathematical
education and the possibility of continuity, there is an article about
how can be the educative system changed in a larger scale:
Models of growth — towards fundamental change in learning environments: http://www.media.mit.edu/publications/bttj/Paper11Pages96-112.pdf
In some part of the article Cavallo and his coworkers ask them selves
about the contexts for changes and how that positive changes can be
spread. There is also the segregation model of Thomas Schelling. One of
the most important things is that small local behavior can create global
behavior. This is stated as microchanges create macro behavior. For me
this statement has a "hope corollary":
To change the world you don't need to change it all, just change
something/someone that changes something/someone, keep that way, and
iterate.
That ideas make thing about how this small experiments that we're making
with Sage on mathematical education can be keep local and contextual and
still create something in a broader scale. For me the key is thinking
small but connected (moodle + Sage is "too big" for me). So one
experiment in that line of action is to use microblogs (twitter alike)
to make students publish "solved exercises powered by Sage" and talk
about them. This is the place where is happening (in Spanish and may be
the server is down :-/ ):
http://uvikuo.presentlyapp.com/
The idea is to use tag clouds and feedback to give more coherence and
structure to the system (may be next semester) but now that I'm trying
to catch up the community after long silence, posting this in this
thread, even if is a experience in early stages, seems fine.
Cheers,
Offray