Math/Science Online Newsletter

The Math/Science-Online Newsletter is focused on the issues surrounding online science and mathematics online for high school students, undergraduates, and graduate students. In the interest of seeing as many techniques as possible we are interested in almost all online experiments that our readers have tried or are trying. Success stories are especially welcome. However, as most of us who work in the sciences and mathematics know well, what is tried first often doesn’t work. We know that the ongoing worldwide experiment in online course delivery is itself (or will be) a science that needs years of patient research. The potential seems to be there for all to see; it is the reality we seek.

The Internet has not yet fulfilled a fraction of its promise; the dot-com bubble has already burst; the critics are in a frenzy feeding on disaster. Meanwhile, visionaries see wireless technologies bringing us smart clothes, smart cards, smart toys, and some even see smart students; a few believe that wireless applications could bring the next wave of the dot-com torrent.

The promise is there. Its impact may be as profound as the computer itself, possibly greater. As with new technology, all the possibilities are as yet invisible. For the most part, we envision enhancing what we can already do with existing technology. For wireless, even that holds remarkable potential, and when applied to education the potential reaches to the impossible.

At its base the possibility of inexpensive, broadband, wireless devices holds the promise of "mobile" education. Education on demand and education at a distance will be supplemented by education anywhere, education everywhere, and more spectacularly education instantaneously.

As university education has adapted to the increased use of technology, the growing numbers of non-traditional students, and the need to train students for a digital economy, it needs now to adapt to the desire of students to "bring the classroom to them." The promise of wireless is

1. Conducting digital classrooms in the field.
2. Assessing student performance in wireless environments.
3. Using wireless technology within existing classrooms and courses.

Wireless technology does bring the possibility of anytime, (almost) anywhere, delivery of instructional material. For example, a veterinary or medical researcher can supervise and interact with a group of students, each pursuing independent tasks in differing locations. In such environments, where surely no hard-wired ports are realistic, the student could benefit from added imaging technology. In another venue, consider the ever-present problem of determining whether students are in fact actually learning: "Do they understand the basic concepts?" "Do they understand the method just explained?" "Can they solve a similar problem?" Traditionally, these problems have been addressed by applying various tools - paper and pencil tests, projects, oral examinations, portfolios, etc. With wireless technologies, these issues can be addressed instantly - both instructors and students will share and benefit from such rapid feedback.

The hallmarks of success for wireless technologies not only have not been realized, but also haven't yet been conceived.

To accomplish all this the hardware and software developments must proceed in tandem with users developing appropriate and meaningful tasks. It is clear that wireless telecommunications technology is an area that is receiving tremendous attention. Several flagship institutions have made major commitments to deploying wireless networks campus-wide. For example, Dell Computer Co. has recently announced several initiatives aimed at getting laptops with wireless LAN cards into the classroom. The National Science Foundation (NSF) has awarded a $2.3 million, three-year research grant to UC San Diego to create, demonstrate, and evaluate a non-commercial, prototype, high-performance, wide-area, wireless network for research and education. Principals on the proposal are with the National Laboratory for Applied Network Research (NLANR) at SDSC, and the Scripps Institution of Oceanography (SIO). Carnegie Mellon University, with the "Wireless Andrew Project," recently became one of the first completely wireless accessible campuses. Their project conforms to the 2.4Ghz 802.11b standard.

Currently, shortcomings such as bandwidth, color, resolution, and input simplicity are obstacles to small (PDA) wireless applications, but this will change rapidly. Compensating for the wide differences in user input and display size, as well as the fact that wireless clients are in fact mobile and require the capability to be connected to different access points, offers unique challenges for the design of instructional delivery and assessment systems.

Universities have a unique opportunity to keep pace with this emerging technology. It fits well with their mandate to produce an educated citizen; it blends well with local technical and educational expertise; it can provide a revenue source for ever-strained campus budgets.

LiveMath Maker 3.0 is a new, exciting, and dynamic CAS from Theorist Interactive, LLC of Cambridge, MA. If the company's name sounds familiar it is because LiveMath was originally introduced to the mathematics community 10 years ago as the software program Theorist by its original author Alan Bonadio. Alan is still the chief software architect for LiveMath on the Mac, and soon to be released Linux versions. Presently LiveMath is available in both Windows^TM and Mac^TM versions and is available in a multitude of languages including American English, British English, Spanish, French, German, Japanese, Italian, Portuguese, Gaelic, Russian, Korean, and Thai.

LiveMath is actually two software programs. The first, LiveMath Maker 3.0, is a CAS which enables the user to create mathematical workspaces called "notebooks". These notebooks are symbolically correct, interactive, mathematical canvases which can be explored and interacted with by others to demonstrate key mathematical concepts step by step. In addition, there is also the free LiveMath browser plug-in, which empowers instructors and students to view, and moreover, to interact with these notebooks live on the web. This article will make use of the web-based interactivity of LiveMath. Please point your browser to http://www.livemath.com to download the free plug-in. For more information on what the plug-in can do, click here.

LiveMath is easy to use and learn. There is no messy code or syntax to learn. Everything within a LiveMath notebook is symbolically correct. When LiveMath opens, both a tool palette and a workspace open up.

Expressions can be entered from the keyboard using conventional keyboard strokes such as ^ for exponents and / for divide, or using keyboard combinations which are unique to LiveMath such as Shift $ for the integral sign. Clicking on icons in the palette also allows the easy input of symbolic math. Many of the icons in the palette have drop down submenus allowing the input of even more symbols by just the click of a mouse. The following expressions were created with a few clicks of a mouse and/or a few keyboard strokes. They were then copied and pasted as pictures right into this document. Anything created in LiveMath Maker can be copied and pasted (as a picture) into any other program such as Word, PowerPoint, or and HTML document.

Copy and Paste is just one small feature of this very powerful program. Its power comes from the dynamic recalculation features that works in the classroom, in a lab, and on the web. It is similar to the recalculation in a spreadsheet, except this is mathematics, factoring, graphing, derivatives, expanding, etc. The mathematics and all of the symbolic notation updates with each change. This powerful teaching tool allows the students to explore a mathematical situation, draw conclusions, and learn by the discovery method. For web-based notebooks, clicking the refresh button within the browser window returns the original notebook for more explorations. The notebooks can be printed right from the browser before and after any dynamic changes. Right-clicking on a notebook enables it be downloaded and saved (if they are not password-protected).

A student is given this function, enters it into a LiveMath Maker notebook, and graphs it. He is asked to explore the effect that the coefficient of x has upon the graph. He highlights the 6 and changes it to another number. LiveMath updates immediately. Look at the four graphs below to see those changes.
He might then wonder how the x³ affects the graph and experiment with that part of the function to see its effect A student with the live notebook can also zoom in and explore even further. He can change the exponent of x³to see that effect on the graph. There is almost no limit to the type of questions that can be posed by the instructor with this dynamic feature.

Click here to explore this LiveMath notebook. The LiveMath plug-in must be installed.

The same dynamics that allow the explorations of 2D graphs also allow explorations of 3D graphs. LiveMath can graph 3D surface, spherical, cylindrical, and space curves on the fly. Drag them with a mouse and watch them rotate and spin, even on the web. Web-based mathematics is no longer static; but alive and exciting with almost no limitations of what can explored. Even lower level students can see the effects of a value change on a 3-dimensional graph. Math no longer must be flat. We live in a 3D world and with a dynamic and webified computer algebra system at their disposal, they can explore this world, mathematically. Students can now experiment with 3D graphs and see correlations between what is mathematical in class and what is real to them.

Notebooks may be created so that some, all, or none of the intermediary steps are shown.
Look at the notebooks below to see how the dynamic recalculation feature works with symbolic expressions.

	Original problem
	Problem being updated after change
	Updated Problem
Click here for Live Notebook.		Click here for Live Notebook.

LiveMath notebooks also enable to the user to add text and graphics within a notebook. Fonts can be sized and colored. The image to the right is an example of the versatility of LiveMath.

Click here for the Live Notebook.

LiveMath Maker comes with two built-in features that allows the user to webify a LiveMath notebook. The first (Copy HTML Tag) automatically creates the code which is then pasted into the HTML source - with just a click of a mouse. The second method (Save as Plug-In with HTML) saves the notebook and creates an HTML document with the notebook embedded, with just a click of the mouse - no syntax, no code. All that is left to do is to upload it to the server.

LiveMath can be used as a teaching tool in the classroom, in the computer lab, or on the Internet. It integrates well with online course management systems such as WebCT^TM, BlackBoard^TM, and IntraLearn^TM, and works well with streaming applications such as the Tegrity^TM WebLearner system and Windows^TM NetMeeting^TM. Students can send assignments to their instructor or post their notebooks for classmates to see and interact with. LiveMath comes with LiveMath Board, a free web-board that allows users to post and comment on live notebooks in a threaded discussion forum. Additionally, LiveMath offers free storage space for notebooks and their accompanying web pages for teachers who do not have school web space. The teacher resource pages have information on topics from How to Embed LiveMath into a PowerPoint presentation to information on finding grant money. There is a teacher's discussion board and samples of the moat popular help movies from the AskSally collection.

LiveMath also comes with 1000 Starter notebooks from the pre-algebra level through advanced calculus, differential equations, linear algebra, and statistics. These notebooks are available for license key holders to use in an educational setting. Use them "as is" right out of the box or customize them for classroom use. Click here for a online sample. Many of these are animated and can be used as lesson demonstrations or "mathlets."

The program comes with both online and local (CD) multimedia help and documentation. Included are hundreds of QuickTime^TMand Real^TM Video movies with audio explaining how to use LiveMath. The website includes links to student and teacher resources as well as to a Gallery of LiveMath websites from users worldwide. LiveMath has been adopted by many publishers for

In conclusion, LiveMath Maker 3.0 is an easy to learn, powerful CAS which can be an effective teaching tool for most undergraduate mathematics courses. It can be used as an in-class tool live within a PowerPoint presentation, in a lab setting, as an online enhancement, or as a basis for an online distance learning course. The instructor drives the curriculum creating his own notebooks or using those that come with the program. Creating symbolically correct math is easy with the drag and drop features and the one-click animation feature. A 30 day trial version is always available at the website, http:/www.livemath.com, as is the free LiveMath plug-in. LiveMath has base price of $99 for the downloaded version. Site Licensing is available.

As one might expect from C*ODE*E (Consortium for ODE Experiments), the authors stress modeling far more than the algebra or analysis of differential equations. The CD-ROM contains thirteen modules, most developing a classic model of a significant differential equation. For instance, the first module purports to be a tutorial on using the ODE Architect Tool, but in fact it develops models using exponential growth, carrying capacity, logistic growth, and finally logistic growth with harvesting.

The second module "Introduction to ODEs" typifies the entire package. It contains four submodules (most have three.) The first submodule is a standard introduction to the idea of solutions and solution curves. The screens have a very simple layout, and the last page of each submodule contains four Things to Think About exploration questions. Most of these open-ended questions refer the student to an ODE Architect Tool worksheet, where one can explore the effects of changing parameters. The worksheet has numerous graphs and data tables to assist the students in their exploration. The authors claim the Tool is powerful enough for research mathematicians, though its interface is designed for students.
[Figure 1: Slope Fields Submodule: The students click points to create solution curves]

Figure 1. Slope Fields Module: The students click points to create the solution curves.

My students and my preteen children both loved the second submodule. Three interactive screens introduce the idea of a vector field, then the fourth screen shows a golf putting green! The user chooses one of five given vector fields, representing slopes on a golf green. The goal is to place the ball at the correct location so it rolls into the hole. The sixth hole allows the user to define the vector field; it is easy to find impossible putting greens.

The third submodule begins with comic juggling by Matt Matics, the robotic hero in many of the video intros of the package. After developing two-dimensional projectile motion with appropriate references to Newton, the fourth submodule deals with skydiving, one-dimensional projectile motion with friction. It ends with typical open-ended Things to Think About questions: how much would you need to increase the damping constant to survive a free fall? If one uses the Newtonian model for damping, how would this affect the time in free fall? Experiment with your own damping formula.

The next module "Cool ODEs" deals with Newton's model for cooling. The submodules progress from a hot egg cooling in a room of constant temperature, next, house temperature in a changing external environment, ending by modeling a house with air conditioning. Since the ODE Architect Tool has square wave and sawtooth wave functions built in, the exploratory questions can ask the student to create and test models for a combined air conditioner/heater. A few students from a second semester calculus class spent hours in my office experimenting with this module.

Other modules introduce sensitivity analysis (throwing a ball at a carnival dunk tank), stability and saddlepoints (linear 2 by 2 matrices and a non-linear model for a spinning tennis racket), Bessel series solutions (decaying spring constant), Hopf bifurcations (autocatalator chemical reactions) and chaos (damped forced pendulum). The model of a saxophone reed caught my interest. The section on pendulums includes a sophisticated discussion and model of a child swinging.

Figure 3: NonLinear Systems: the Saxophone. Students investigate solutions with arbitrary
initial conditions from the phase space.

ODE Architect includes a large library of models, such as the forced damped spring, van der Pol circuit equation, predator-prey, Lanchester's Combat model, the crazy-eight cycle graph, SIR epidemic model, and Lissajous figures from coupled masses and springs.

A proper review must note any flaws, and naturally ODE Architect has some. I noted a few typos in equations, though far fewer than first editions of many textbooks. The authors consistently use British units; the consistency is admirable, the frequent reference to slugs is not. The students use the ODE Architect Tool to examine most of the exploration questions that end each submodule; this software is more student friendly than Maple but still has a moderate learning curve. Finally, I installed the program on two machines; the first installation worked flawlessly, while the second gave a division by zero error when loading. The Wiley technical support staff did call within 24 hours as their web page promised, and located the problem.

The strong points of ODE Architect are pleasant to recite. The screen layout is simple and easy to follow, emphasizing graphical and visual cues. The authors resisted the urge to include too much text, and concentrated on the graphical and visual aspects. (The Companion book to ODE Architect contains succinct textbook explanations for each submodule.) Occasional slapstick humor will catch student interest, but the videos and graphics emphasize ideas not entertainment. In spite of being the work of sixteen academicians, ODE Architect has a common look and feel throughout. Most importantly, the C*ODE*E authors have carefully crafted the submodules to build increasingly complex models.

One question remains; how does one use this package in an ODE course? Every student should see the classic ODE models developed here. Each submodule builds its model in a painless way that would motivate typical students. Many of the introductory sections fit well into the second semester of calculus. My calculus student volunteers indicated that ODE Architect would be a fun and effective introduction to Newton's law of cooling, kinematics of a ball with air drag, and logistic growth.

In an ODE class, I would use class time to emphasize the basic models and the algebraic aspects of solutions, then assign ODE Architect to introduce significant extensions to the models. The students could profitably surf through the first few modules as motivation for ODEs and an introduction to modeling. In particular, the second module explains slope fields nicely. I would then sample from the remaining modules for group projects. I happen to have a physics bent, so would assign Longer to Rise or Fall, Saxophone, and Coupled Springs, while a course aimed at biology students might assign Allergy Relief, Competition in Ecology, and the Autocatalator Model. Finally, the course could end by having the students surf through the last two modules on chaos. Although chaos is not central to an ODE course, my students had all heard about chaos and wanted to explore these sections.

A word on group projects: each submodule concludes with four "Things to Think About" exploration questions. Unlike their painless clicking through the carefully crafted screens in the submodules, students will find the exploration questions open-ended and frankly challenging. The instructor will need to provide more detailed instructions to guide the students' explorations. Students at Harvey Mudd, RPI, and Cornell may be self-motivated and willing to follow the instructions to "put in some values for the damping constants c1 and c2, and see what happens." Unfortunately, most of my students need more explicit guidance. With more detailed instructions or instructor feedback on a preliminary project draft, these open-ended questions provide an abundance of challenging group projects.

Figure 5: Each submodule ends with "Things to Think About," challenging extensions of the models.

Overall, ODE Architect is a worthy presentation of the accomplishments of the Consortium on ODE Experiments. The modules are carefully sequenced to emphasize the modeling process, professional graphics enhance the goal of understanding models, and the exploration questions will challenge the very best students. The ODE Architect CD-ROM plus the Companion book is $47.95, or only $10 to $15 extra when packaged with a Wiley textbook. It is definitely worth your students' investment!

1. ICTCM – 2001. The annual ICTCM conference is scheduled this year November 1-4 in Baltimore. There you will find the state of the art teaching-with-technology people. Talks will all phases of classroom technology from Java JavaScript applications to using calculators to teach math. Specialists in the major CAS engines, Derive, Maple, and Mathematica, experts with TI and Casio calculators, and an assortment of tutorial sessions will all be available. See http://www.ictcm.org/ for more information.

2. Apple Computer (AAPL) , Cisco (CSCO) Systems, Kasenna, Philips Electronics and Sun Microsystems (SUNW) announced the founding of ISMA in a press release, saying they are joining forces to promote open standards for developing end-to-end media streaming solutions over IP (Internet protocol). The founders say their collaboration will accelerate adoption of open standards and interoperability, while encouraging the development of competitive streaming-media software

3. Dreamweaver 4 has been released. This state-of-the-art Web page development tool is bigger and better. Three new features alone make the upgrade worth the price. View Coding has never been easier. The new Code View allows access to the (also new) integrated Text Editor. With it one can view HTML code or split the screen to view both the Code and Design views simultaneously. The JavaScript Debugger for client-side JavaScript lets you watch JavaScript execute in Netscape Navigator or Internet Explorer, helping you understand how each browser implements JavaScript. From the integrated O'Reilly Code Reference you can get reference information quickly. The new Code Reference feature delivers information on JavaScript, HTML, CSS, and Browser DOMs. A fourth feature, the Layout View, gives the user total control over the appearance and placement of objects on the page.

We are interested in articles for one of the following sections. Article should be interesting but brief: 500-1200 words. Longer articles will be considered on an individual basis.

· Vision. The focus is on the future: what may happen, what certainly will happen, and what will not happen as technology advances into learning and education.

· Case Studies. Especially important are examples of technology application that really work in the classroom. Data is important here

· Commentary. Timely observations and opinions on the use of technology to enhance Mathematics and Science education.

· Faculty development. How are faculty supported, trained, and encouraged in the integration of technology into Mathematics and Science education? How are faculty rewarded – or should be rewarded.

· Book and Software Reviews. With the ever-accelerating pace of hardware and software development, and with the continuing application of technology in the classroom, it is more important than ever to keep in touch with new methods and software.

· Letters to the editor. If some technology issue is significant, or if some point in an article is noteworthy, this section allows feedback for the editors or readers.

We gratefully acknowledge the support of the Department of Mathematics at Texas A&M University for preparation costs.

Editorial Board

G. Donald Allen, Editor
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
email: dallen@math.tamu.edu
Phone (409) 845-7950
Fax (409) 845-6028

Gary Helmer
Department of Mathematics
Mohawk College of Applied Arts & Technology
Box 2034
Hamilton, Ontario, Canada, L8N 3T2
Email: helmerg@mail.mohawkc.on.ca

Robert J. Lopez
Department of Mathematics
Rose-Hulman Institute of Technology
Terra Haute, IN 47803-3999
email: r.lopez@Rose-Hulman.edu

Lawrence E. Levine
Department of Mathematical Sciences
Stevens Institute of Technology
Hoboken, NJ 07030
email:llevine@stevens-tech.edu

Jonathan Lewin,
Department of Mathematics,
Kennesaw State University,
Kennesaw, GA 30144
email: lewins@mindspring.com

Mirek Majewski
Director of the M.Sc. in Information Technology Program
Inter-University Institute of Macau
NAPE Lote 18, Rua de Londres – P
Edf. Tak Ip Plaza, R/C – 3 andar,
MACAU
email: majewski@iium.edu.mo

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Click here for Live example	Click here for Live Example