The Math/Science Online Newsletter

Fall 2002
Texas A&M University
College Station, TX 77843-3368
USA

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. 

Using Technology as a Teaching and Research Tool in a Special Topics Course in Differential Equations
Lawrence E. Levine

Anywhere, Anyplace, and Interactive - Wireless Networked Education
Virgil E. Varvel Jr.
Announcements
Editorial Board

The next generation of Internet software technology

One of the more powerful enhancements to almost any teaching function is motion. On the Internet one type of motion is animation. To illustrate a concept, whether it be showing the changing slope of a line to showing the secant line approach the tangent line, the animated image conveys the understanding virtually beyond the best efforts of classroom instructors

What features can an online course have that a traditional classroom format cannot? The list is growing. What can an online course do that a classroom teacher cannot do? Again, the list is growing. The content can be ever present, but that is easy. With simple tools such as an HTML editor, a graphics editor, and a bit of scripting, an author can show almost any image imaginable with vibrant colors, consistent and tasteful style.

However, making animations for the Web is one of the more exotic Web activities and seems to be somewhere on most everyone's "to do" list. Making interactive animations and movies is the most desired Web activity for educators, the belief being that motion is a powerful visual and educational tool and interactivity simulates (somewhat) the activity of the teacher. Allowing student experimentation is naturally good, but showing the dynamics of an intrinsically changing situation is often as good. A non-interactive but animated visual experience can be a powerful teaching tool, as well. Indeed the animated image is one of those growing number of online features that have transcended the best that the traditional classroom offers.

What is critically important for a serious online presence of mathematics and science education efforts is the availability of development technology that is at once powerful and easy to use. While the production studios can produce true marvels to view, it has been impossible to use their work beyond the fixed work. One important advance for mathematics education is the ability to graph a function. With the Flash "front-end" and JavaScript "back-end" function graphing is relatively simple - certainly not requiring anything like the effort required with Java. Here's a working function grapher example. Of course, once function parsing is possible, a great part of the visual mathematics world is opened.

In the past few years Macromedia's Flash has been emerging as a software with production possibilities sufficient to attract the serious developer but with an underlying simplicity that allows faculty and others to create useful and even dazzling applications with minimal training. This speaks to the underlying design to which Macromedia's engineers deserve much credit, but also to the potential now possible with high speed computers. The fundamental design concept is that almost every animation shares many types of requirements. Implement those requirements and the result is a powerful tool that almost everyone can use.

The success of Flash, now in its sixth release (called Flash MX), is evident by the premium prices that Flash training tutorials command. Nominal costs for a two-day hands-on training course range from $800 and up.

With Flash it is possible to create interactive feedback responsive quiz instruments with randomizing. Indeed, Flash MX comes with a shared library of quizzing components that the user can use, inserting only the content. This brings us very far from intrinsic difficulties of Java and JavaScript. One can even put animations within the questions or answers. For example, it would be possible to ask what type of motion represents a compound spring, with the answers being four different motion animations. Questions of this type are essentially impossible, particularly within the traditional classroom, without sophisticated animation tools.

Using Technology as a Teaching and Research Tool in a Special Topics Course in Differential Equations

Lawrence E. Levine
Department of Mathematical Sciences
Stevens Institute of Technology
Hoboken, NJ 07031
and
United States Military Academy
West Point, NY 10996
llevine@stevens-tech.edu

Abstract: This talk deals with a special topics course that the presenter recently taught while he was a Visiting Professor at USMA. The course was taught in USMA's Advanced Technology Learning Laboratory. This is a classroom equipped with wireless connections and a host of other state of the art technology. The students (cadets) used Dell Latitude laptops both in and outside of the classroom. In addition to the "normal" Windows software, Scientific Notebook (SNB) and SyncronEyes were used. Scientific Notebook is a word processing package with a Maple kernel, and SyncronEyes is package that allows the instructor to monitor a student's machine, project the screen of a student so that all can see it, or take control of a student's machine. The instructor did not write one thing on the board the entire semester, but instead relied on technology for everything that took place in the classroom.

The course used technology in two ways. First of all, SNB was used to prepare lecture notes to present such topics as infinite series, series solution of differential equations, boundary value problems, Fourier series, and separation of variables for partial differential equations. In addition, SNB was used as a research tool to discover results about when polynomial solutions of nonhomogeneous differential equations exist. In particular, the nature of the solutions of the classic equations of Chebyshev, Hermite, Legendre and Laguerre when they have polynomial right hand sides was studied.

Conditions were obtained that insure that these equations will have polynomial solutions. The approach was as follows: SNB will not solve an initial value problem for one of these equations with xⁿ on the right hand for any n. However, it will solve the initial value problem for any specific value of n. By looking at the solutions to the initial value problem for a number of specific values of n one then attempts to extrapolate to a general result. Then one uses this to prove that this is indeed the required condition and to obtain an expression for the solution to the initial value problem for any n. Without the use of the Maple kernel one would never be able to arrive at the form of the initial conditions, since solution by hand is so tedious that one would never do more than one or two specific cases.

In summary, the course integrated technology in a manner that enhanced teaching and learning and also served as a catalyst to discover new mathematical results. Such an approach has applicability in other mathematics courses as well as in courses in other disciplines.

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Introduction

Every so often, promises are made that can never be kept within the context or time frame of that promise. This practice is not necessarily a purposeful action, but is driven more by those envisioning potentials for the next up and coming idea without properly assessing the myriad of contexts present with any new implementation. Such has often been the case with technology implementations in education. No one can predict every nuance let alone the effects that such nuances will have on the individual, the community, or society. Yet, one should not let such difficulties dissuade one from the act of implementation. Rather, one can maintain a critical eye and continually address the effectiveness of a program.
This mindset is how the implementation of a wireless networked portable computer lab (iLab) was approached in the College of Education in the University of Illinois at Urbana-Champaign beginning in the spring of 2000. Computers are widely used on our campus to the point that our computer labs are often continually booked. Therefore, we needed an extension of our computer services that would require minimal space. In the process of searching for this extension, the recent affordability, power, and usability of laptop computers became a viable option. Furthermore, an affordable wireless information transmission system in conjunction with portable computing promised that students would gain the possible benefits of being able to connect to the Internet without the constraints of a wired computer lab while the use of laptops allowed for an extension of the standard classroom context to include computer use. The question then becomes whether such a promise could be kept.

System Design

The iLab was designed around the principles of usability, portability, and minimal alterations in classroom dynamics. Usability involved the ability to provide computer systems and software packages that could facilitate student coursework while also providing technology support for the instructor. The technology support is a key to the design and existed as part of our College's Office of Educational Technology. Often, technology fails because no direction is given for its use or the instructor has little idea how to integrate the technology into the classroom rather than centering the classroom around the technology. The instructors that used the iLab in our study; however, had clear ideas that would allow for integration without alteration but rather with anticipated enhancement of previous curriculum for their courses.
Portability existed on several levels. First, the laptop itself provides a portable computing environment with which students can experience computer enhanced learning within a standard classroom context. Rather than taking an entire computer lab, the computers could be quickly and easily transported throughout our college on a custom built cart. Finally, through the use of wireless networking, even the power of the Internet became portable and available to the students without the constraints of network wiring or stationary desktops.
Classroom dynamics were also important. Wireless networked laptops within a standard classroom setting have the potential of yielding minimal effects to the classroom environment. Rather than the student going to the computer, the computer comes to and with the student. Furthermore, a classroom can be a highly interactive environment. Educators are often proclaiming the hopes of anytime, anyplace learning that can take place with laptop computers. Well, a book is anytime, anyplace as well, but it is not interactive. The iLab design, by providing portable networking, was intended to allow for anytime, anyplace computer enhanced learning while maintaining classroom dynamics and interactivity including mediated interactivity that can occur over a computer network.

Outcomes

From perspectives collected from students and instructors via pre- and post-surveys, video observation, and conversation, certain outcomes from both the instructor and student perspectives were evident from the iLab implementation. Of course, of paramount importance is the encompassing educational goal of learning, but learning is extremely difficult to judge based on the variety of interpretations that can be made due to the wide variety of educational policies. Still, responses from participants fell in such a broad spectrum of categories, that learning appears to be positively affected to unaffected by the iLab implementation dependent on the area observed.
First of all, for an instructor to plan to meet the needs of all of the intelligences or learning styles of the learners, the instructor needs to have multiple options available when designing instructional units. The iLab can become one of these options. Both instructors and several students cited the increased instructional choices available with the iLab to be beneficial and appealing. Computer enhanced activities could coincide with standard classroom discussion with quick transitions between various activities could facilitate various learning styles.
These instructional choices did not necessarily have to be new ideas, but could also be the enhancement of old lessons or assessments. Noted in our survey was the use of online quizzing by one of our instructors. Open ended items where still included that the instructor would evaluate, however, fill-in-the-blank, matching, and multiple choice items could be immediately graded during class by the computer (using WebCT, http://www.webct.com), providing feedback to the students that could then be used to promote concurrent in-class discussions. The method of quizzing used, reduced the instructors work of grading and allowed instruction to be directed around student performance.
Another telling enhancement occurred without prior instructor design. One activity used in a mathematics instruction course involving the use of objects and measurements in order to visualize large numbers was modified by the students due to the presence of the iLab. In addition to the prescribed method of using rulers to measure quantities, the students were able to use the Web, without the instructor's prompting, to determine exact penny (the item being used in the exercise) widths from the U.S. Mint Web site, followed by comparisons of multiples of that width to the actual heights of skyscrapers found using the Web rather than the use of estimates by the students as had previously been done in the class. The availability of the Web and the unobtrusive nature of the wireless Web facilitated the natural progression of this activity. While the exercise may have given the students only a slightly better understanding of large quantities as was the lesson goal, of particular importance in this activity was the increase in student motivation noticed by the instructor.
Motivation was thus another category of outcomes with the use of the iLab. Several students and the instructors noted that in general, their motivation was increase due to the presence not just of the laptop computers, but the added benefit of the wireless network. Sometimes the students could attribute the motivation to the possibility of learning a new tool. Some of the students felt initially that they would have a difficult time due to their lack of computer knowledge, but perhaps due to the unobtrusive nature of the iLab on the classroom dynamics they became comfortable and some noted learning computer skills as an outcome.
Classroom dynamics were a key for the instructors. Their prior courses had used the standard computer lab setting for computer-based activities, but with the iLab, they had the convenience (also noted by students) of doing the activities in the standard classroom due to the iLab size and mobility. Students could place the computers on their desks when they needed to be used and then place them to the side when it was time for discussion. One student in particular noted the effectiveness of the iLab due to the ease with which the class could make this transition.
Although many educational theorists may ask that a reduced importance be placed on student test scores, it is still important to ask whether the iLab had an apparent affect on such a widely used assessment method. With the iLab implementation, no noticeable variation was seen in student grades compared to past courses based on instructor perceptions. Therefore, we cannot say necessarily that the students have learned more or (more importantly) less of the content on which they were tested, but based on the discussion above, we can say that they learned more about computers and their own future pedagogical choices (as many of the students were in the teacher education program) in an environment that appeared conducive to learning by both students and instructors.

Discussion / Conclusion

Based on the positive reviews received from our initial survey of iLab use, we were confident that a wireless networked portable computer lab could continue to serve the needs of our college. Instructors and students submitted numerous benefits with no Likert scaled survey items yielding a negative response. Instructors in particular were exited to be able to use advanced technology within the classroom context. Furthermore, many of the benefits related to the often unheard aspects of education such as motivation and convenience that while not necessarily increasing test scores, can lead to a much more fulfilling educational experience.
Part of the key to the success of the iLab however was the notable presence of a knowledgeable support staff. Not only support of the technology itself, but support of the instructor. We acknowledge that for such a lab to be a success requires the development and proper implementation of pedagogically appropriate and meaningful computer enhanced activities, with enhanced being the key word. Educational appropriate activities are not based on computers (CBL) but on sound pedagogy and they are not necessarily assisted (CAI) by computers in that to assist would mean that instruction is somehow easier or dependent on computers. Often, adding activities that take advantage of what new technology has to offer can take additional time and energy on the part of the instructor, but computer enhanced instruction when properly implemented can make this time and energy well spent.

A more complete version of this study is currently under review for publication.

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Announcement and New Products

1.      ICTCM – 2001.  The ICTCM is celebrating its 15th Anniversary in Orlando, Florida, October 31 - November 3, 2002 and this year's host is Valencia Community College. A wide variety of topics will be covered across the curriculum from pre-algebra through post-calculus mathematics. Featured strands include Internet/ Distance Learning Technologies, Online Tutoring, Web Animation, Assisted Web Instruction, and other new technology options. The program includes lecture sessions, hands-on computer minicourses, professional development workshops, hands-on calculator workshops, and exhibits.

At ICTCM, you will find the opportunity to meet with creative and dedicated people who share your interest in technology and mathematics. It's about sharing and learning from each other and about seeing the latest in technology and its uses in the classroom. You can expect a cross-section of mathematics educators and researchers from four and two -year colleges, and high schools. See http://www.ictcm.org/ for more information.

2. Presta digitization. This free software allows one to digitize any JPEG image and create a digital record of point. Students have a real chance to explore nature and the world around them from a mathematical viewpoint. Like only a few technologies, the digital camera and mathematics are perfectly matched for making connections. Students can answer for themselves questions such as:

Is the Houston Astrodome actually round?
What is the height of a building?
What is the volume of an egg?
What is the slope of a roof? of a windshield?
How many gallons of water does that water tower hold?
Is that really a catenary?
What is the area of a polygon?
What is the ratio of semi-major and semi-minor axes.

Call for manuscripts.

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.

Send your article to any member of the editorial board for review.

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