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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