MathGroup Archive 1994

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MW - Education Today - Reviews

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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