The
official publication of the New Mathwright Library
and Café:
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1] Education Planet Award
2] A New WorkBook for the Free Player 2.1
We were very pleasantly surprised last month when the Internet Resource Magazine
for teachers, Education Planet,
named us "Top Math Site of the week" (01/29/01). The wording of the award
was as follows:
"This site has been awarded the Education Planet "Math Top Site Award" by our teacher/reviewers for its quality content and usefulness to Math educators and students."
We
prize this singular acknowledgement by our peers, and of course, we hope to
continue to live up to their review of the Library and Café:
"The New Mathwright Library and Cafe - One problem in learning upper secondary and college mathematics is that of getting the math to leap off the page and become real, i.e. to become the vehicle by which parts of the world can be understood. Students often become buried in the details of the various calculations and fail to realize the utility of the math. The Mathwright authoring program allows math and science based lessons to be covered in an interactive manner with many applications and examples. This Library includes over 150 workbooks for download after purchase of a very inexpensive annual subscription. Topics covered include Pre-Calculus, Calculus and College Algebra in addition to a variety of secondary and college level mathematics topics. For 3D simulations, there is now a new program called Mindscapes."
Thank you.
We
have received some useful feedback from you, our readers, in our first month
as The New Mathwright Library and Café. One of the comments frequently made
was that the six WorkBooks that we provide on the Free
Stuff page generally deal with rather esoteric topics, rather than demonstrating
how the Library can address the common concerns of students in the mathematics
curriculum.
Of
course, it does require an entire Library to begin to address those common concerns,
but we have added a seventh WorkBook to the list of WorkBooks on the Free Stuff
page that you can read with the Free Player 2.1. That WorkBook is called: Derivatives
and the Graphs of Functions
It
should give a sense of how the Mathwright Library WorkBooks can cause "math
to leap off the page and become real" as the Education Planet Teacher/Reviewers
put it. First of all, the WorkBook is a free-form function grapher that allows
you to define and graph functions, to choose their domains, and to zoom in or
out at will. In that sense, the WorkBook can be a tool that can help students
visualize the graphs of functions by experimenting with your own examples.
But
Derivatives and the Graphs of Functions is much more than a grapher.
The WorkBook tells a story about how the derivative can give information about
the shape of the graph. It discusses how the sign of the derivative determines
where the graph is rising or falling, and how the local extrema (maxima or minima)
are related to zeros of the derivative - the places where the derivative generally
changes sign.
The
WorkBook goes on to apply this analysis to the derivative itself, showing how
the sign of the derivative of the derivative (that is, the sign of the second
derivative) is related to upward and downward concavity of the graph of the
function. The "critical points" of the original function are generally associated
with the vanishing of the derivative, and the "inflection points" of that function,
the critical points of its derivative, are associated with the vanishing of
the second derivative in this beautiful tower of ideas.
It
is easy to get lost in the words. But that is where the WorkBook shines. All
of these themes are illustrated with 15 built-in example functions that you
can step through. The functions are graphed, along with their derivative and
second derivatives. And the various regions of monotonicity (rising or falling
behavior) as well as critical points and inflections are illustrated for you.
And
when you grow tired of our built-in examples, you may modify them in any way
you like, or, better, supply your own examples! In this way, you can experiment
with the functions that make sense to you. Those examples will teach you the
concepts better than any examples that I, or any other teacher could dream up.
You
do not have to join the Library to read and use this WorkBook. It works fine
with the Library Player 2.1. But of course, we would like to convince you to
join the Library, and to discover the joy of interactive learning as you build
up your own Mathwright Library on your own computer.
James E.
White, Ph.D.
Library
Director