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MW - Education Today - Reviews
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: MW - Education Today - Reviews
*From*: smh at matilda.vut.edu.au (Stephen Hunt)
*Date*: Mon, 13 Jun 94 21:52:22 EST
Below are short reiews of articles in Mathematica World - Education Today.
Analysis of Planar Mechanisms - Carol Rubin - Constrained 2-D mechanism
simulation and analysis tools for an introductory kinematics of mechanisms
course. The goal is to produce a helpful demonstration for a lecture. As well
as enhancing the students' appreciation and understanding, the use of
Mathematica as a tool in lectures is seeen as motivating its use in student
project work.
Animating Calculus - Ed Packel & Stan Wagon - More than just calculus
animations, this book and electronic materials explores calculus using many
helpful graphics, but also using a range of other interactions to develop
student understanding. Although the notebooks are intended to be integrated
into a existing course, they are largely self-contained. Many interesting and
useful animations have been designed, but it is the narrative, interactive
evaluations, and exercises throughout each lab that take center stage. The
inclusion of background material and additional exercises, in parallel with the
main exploration, offers students with a range of abilities the opportunity of
making their own independent way through each lab.
Calculus & Mathematica - Bill Davis, Horacio Porta, Jery Uhl - Not just a
course, more a way of life, Calculus & Mathematica introduces an educational
philosophy which challenges the traditional teaching methods. The basic
difference between its use of Mathematica as a tool for developing knowledge,
and more traditional approaches is its direct engagement of the student in their
own learning. How do they attempt to accomplish this? In Mathematica they find
a tool that enables them to present discovery based methods which tackle
problems of relevance to students through an interface that stimulates and
inspires an ongoing interest in the material at hand. Three sample problems
with their student responses are presented, so you can get the feel for how this
develops practically.
Computational Physics - Paul Abbott - A third year undergraduate laboratory
style course consisting of 9 x 2 hour lab sessions. These laboratories provide
students with an opportunity to do things. In the example labs: verify the
orthogonality integrals, and explore the natural frequencies and normal modes of
a system of coupled oscillators. They do not so much attempt to introduce the
student to new material, as aid the students' interaction with material they
would have been introduced to elsewhere. In the two example labs provided the
actual calculations involved could be characterised as somewhat tedious, if
completed by hand. Utilising Mathematica as a calculator the student is invited
to explore the calculations and draw conclusions from their results. Indeed
this seems to be what is of most interest to Pau What does the student
understand from this result? Not, can the student calculate this expression.
The methods used to produce the calculations are not masked - students
completing this course will not only be asked to provide appropriate physical
explanations, but pick up a range of general methods, which may be applied to
investigate a variety of other related problems.
Dickson College Calculus Project - Barry Tesman - Mathematica as tutor, not
magician, involves using the Mathematica language to produce useful tools for
students rather than simply relying on its built-in functions. Indeed built-in
Mathematica functions often do not serve the educator or the student well.
Three examples: WhichPlot (for discontinuous functions), Plot (overloading
Plot), and IntByParts (for applying the integration by parts formula) illustrate
how functions can be introduced and modified to provide correct and useful
output for students.
Discovering the Derivative - Steve Hunt - A central goal of this exploration is
to facilitate guided discovery. Providing a framework for an exploration, yet
allowing the student to realize the actual discovery as the encapsulation of
their own insights.
Floating-Point Arithmetic - Alkis Akritas - The various ways computers represent
numbers together with their influence on equality of expressions is clearly
presented by this interactive tutorial - illustrates some of the traps for those
who naively use a computer as an oracle.
On Iteration Methods in Numerical Analysis - Steven Dunbar - A pre-lecture lab!
The focus here is on letting students experint with the concepts prior to
their formal introduction. Reference text in hand, and with carefully crafted
experiments before them on the screen, the student explores principles that will
later be introduced at a lecture. Distinctively, the task is focused on
identifying the answer to a particular question - one imagines the student
spending a good deal of time thinking, rather than just working through
trivially linked evaluations.
OzMATH - Desmond Fearnley-Sander - Notebooks that aid learning the material
introduced in a traditional lecture situation. Through guided experimentation
students are directed to look for certain patterns. Exercises test their
comprehension. Both theory and experiment are intertwined. Examples and
illustrations which could only be introduced vaguely in a lecture at freshman
level, are explicitly explored using Mathematica.
Self-Tutor for Computer Calculus - D Burbulla & Kit Dodson - The strong
instructional aim of this book brings into being some very useful teaching
functions. The functions are included as packages for each chapter. Special
functions that utilise a variety of Mathematica's different capabilities are
introduced. The use of replacement rules to help the student identify the
structural relationships in an integrand and the visualization of the iterative
solution of complex valued equations, provide helpful tools for developing a
concrete understanding of the theory at hand.
The Package NUMERIAL - Jesus Rojo - The errors introduced by the partial
numerical representation of numbers is compounded by certain numerical methods.
In this example, various methods for solving linear systems are explored under
different numerical conditions.
The CSM Program - Jack Cohen & Frank Hagin - Traditionally constructed
worksheets (TeX, here presented also as a Microsoft Word document) form the
basis of a NeXT Mathematica lab exploration. The limited use of Mathematica's
capabilities still enables students to explore calculations that, though basic
in the example lab, would be prone to error if carried out by hand. The
follow-up material from the lab is not based so much on the lab, but continues
the theme of the lab in another direction.
Transitional Maths Project - Phillip Kent, Phil Ramsden, John Wood -
Self-learning modules for students entering undergraduate Science and
Engineering courses. A diagnostic test directs students to the modules they
should study. A study module is divided into two components: An activity
notebook (activities, exercises, investigations), and a booklet of theory
together with explanations of the activities. Special functions which aid the
visualization of the concepts are defined and incorporated into a supporting
package. The question/answer design constantly demands the student to think
through each evaluation.
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