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Learning and Teaching Mathematics Using Simulations

Walter de Gruyter
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This book has paperback and “eBook plus” forms. Holders of the printed book can access simulations through a URL provided in the book. This leads to download of a digital package, 700MB in size, including all the software described in the book. Readers of the digital version can access the simulations directly from the e-book, which includes a PDF linked to the simulations. This is a review of the printed text. The magnitude of price difference between the two is about ten times, so serious consideration must be given to choosing which version to obtain. If the idea is to stick with the developed simulations described in the book then, using the e-book is better. If instead the idea is to use the prepared simulations as a departure and to build simulations oneself, then I would think the printed book will provide the required introduction. It would seem that if I had the “plus” version I could start right away running simulations, whereas without it, it took me about an hour of experimentation and reading the additional downloaded documentation to begin running them.

Among the extra documentation is the introductory chapter of a projected book on the platform used to produce the simulations. Reading this additional material was necessary, as the printed book assumes the reader has direct access to the simulations. Thus, the printed text really is an adjunct to the electronic edition. There is some documentation in the book about the directory structure of installed simulations. This shows the folder names in English, whereas they install in German, and the language default presentation of the prepared simulations is a mixture of German and English, although this does not prevent exploration of the capabilities of the program.

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There is a language setting in the software’s main console that does not carry over to the text’s prepared simulations.

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In cases like this, the book’s overview, while not complete, can help greatly to clarify things. The book does not include or cover in detail all of the two thousand simulations packaged in the download. After installation, an html launch page gives access to a wiki with user feedback, bug reports and their status, and other links and documentation.

The framework provided by the install is the Easy Java Simulations (EJS) software tool. This is a Java code generator for creating computer simulations. As expected with a growing open source platform, there is a panoply of pros and cons to this community-driven environment: more recent EJS versions available, an intriguing eBook in Spanish (and only Spanish it seems), some broken links due to inevitable “link rot,” and a gamut of demo programs created with EJS.

These demos are applets embedded in the HTML launch page. Some of the examples are intriguing, such as Kepler’s planetary motion with a planet that can be dragged into different orbits. Some are more basic yet illustrative, as the applet “Throwing a Ball”. This simulation shows the changes in parabolic path, vertex and landing points after changing the initial angle. The ballistic simulation is adapted from the aforementioned Spanish book Creación de Simulaciones Interactivas en Java (F. Esquembre, Pearson Educación, 2004). The planetary motion one is related to an 178-page PDF file included in the download: Planets and Satellites: Computer Simulations (Eugene I. Butikov, Physics Academic Software).

What should be made clear is that the printed book is supporting documentation to a simulation package built on the EJS platform. The simulations are intended as learning or teaching tools for subjects from algebra to differential equations. Through numerous interactive Java simulations on topics from number theory to calculus and partial differential equations, the exploration of mathematical concepts is not as restricted to physics as the title may suggest. The number theory, sequences and series, and integration treatments alone offer much to the non-physics student. Actually, physical applications from mechanics to relativity are only lightly touched in the book where a few pages toward the end refer to those prepared simulations without the additional remarks given to the pure math topics.

The author is convinced that an experimental approach to mathematics via such interactive simulations will build enthusiasm in modern students not sufficiently interested in engineering and scientific studies. For teachers of mathematics and physics, this is a reality that requires fresh approaches, as I can attest. Author Dieter Röss is very much worried about the declining number of students motivated to learn science and engineering. Sparking their interest in this way at introductory levels seems a wise plan. I applaud his approach based on computer simulations, although the finished product needs more work in the user friendliness department before students will do the all-important interaction themselves.

Teachers may find this book and software useful for preparing demonstrations. I like to demonstrations and simulations to my students off the Texas Instruments calculator they are required to have, hoping to get them to explore and set up simulations with a tool I know they will have on hand. Despite my own philosophy on this point, I have decided to work in a few of these simulations next semester, so Herr Röss has won me over. I think if continues on this vector, he will win over some distracted students as well.

Tom Schulte simulates transformations of the conic sections to students at Oakland Community College in Michigan and is Senior Business Intelligence Engineer at Plex Systems.

Date Received: 
Monday, August 29, 2011
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Dieter Röss
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Tom Schulte
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Modify Date: 
Monday, August 29, 2011