Fax (409) 845-6028
Phone (409) 845-7950
email: webcalc@math.tamu.edu
The WebCalC Project is the development of a on-line calculus course at the beginning college or AP high school level. What does this mean? Nothing less than a fully comprehensive calculus course to be delivered over the internet. WebMath is a collection of projects dedicated to produce an on-line mathematics curricula from algebra to differential equations. This is what we are about. In this first newletter, we review some of the many questions we’ve been asked at dozens of workshops and presentations. You might call this newsletter a FAC (Frequently Asked Questions) edition.
What are the essential requirements of an on-line mathematics course that actually works? While all the requirements are not known by anyone at this time, there are some necessary conditions that seem without question.
Beginning level students to mathematics need mathematics delivered to them to be nearly as perfect as their textbooks give. Lesser quality, even unusal fonts, can throw students off track, causing more problems than solving.
Reading text, particularly mathematics from a video screen requires sustained, controlled, and concentrated attention. Pages of black (electronic) ink will not communicate with anyone over the long term. Learning mathematics this way is virtually impossible for all but the most dedicated mathematics students. To keep the student involved requires an "interesting " interface that will hold the student’s interest and focus his/her concentration. Bright colors and exciting graphics are exactly what most kids expect and demand if you are to engage them. This they’ve been conditioned to from exposure to TV. Television knows how to hold human interest. We should learn from television. Denying the impact is foolish.
Day-by-day students learning from an on-line course need to know how they are doing. You, the teacher, needs to how they are doing. But with web learning this is not so straightforward. On-line courses must communicate with the student in a realistic way. Several possibilities can be identified. For example, students can take computer-administered tests that are transmitted to the teacher, say by e-mail. The teacher grades the test and returns the results the next day. This fails. Once we enter the realm of television, i.e. video interface, we enter the world of instantaneous feedback. Little else will do. We believe that computer graded, rapidly returned test results are essential. The student wants to know right away what are the results. The student should know. This will give him the confidence to go on with diligence. Now we come to the issue of what kind of tests are most appropriate. Should they be multiple choice? Should they be long answer? Each has advantages and disadvantages. We leave it to the next issue of the WebCalC Newsletter to tackle some of the possibilities, and what it takes to implement them.
When students are working alone at the computer, whether at home or in the school computer lab, they need to solve problems or "experiment" with mathematical concepts. If the teacher is not there to do it in the usual lecture format, they need to work for themselves. They need the software to assist them. This is one of the more subtle aspects of learning mathematics scarcely even noticed by many teachers. The computer assistance can take the form of an expert learning system, which is phenomenally difficult to program or the form of symbolic mathematical capabilities. The latter, though complex in its own right, allows a wider bandwidth of experiment and problems. It also is available in a variety of forms. The key is to get the student to use the possibilities. Without either, many students will be stopped cold, unable to understand some issue upon which future understanding rests. If help isn’t ready, and quickly, learning stops and is tough to restart.
Something a lot of people don’t think of right off is the importance of the interconnectivity via links can be to an on-line course. The logistics are easiest. Procedures are necessary in such courses to replace ability to leaf through a text and go to an index. Therefore, the course must anticipate where the student might need reference to previous material and provide links right off. Using pop-out pages, the course should supply appropriate definitions of new terms when possibly needed. Students these days expect nearly immediate response to their requests for information. Hence, the size of electronic pages must be sufficiently small that long (>20 seconds) download times do not occur. The alternative is that the student will loose interest. It is a daunting task to deliver great looking mathematics and graphics over the internet in acceptably short time frames. We believe our project does this even over that "last mile" of travel; that is, from the local internet provider over a phone line to the school. What about animations? We have selectively included animated gif images wherever they are needed. However, file sizes are normally 100kb or larger. Downloading such files during peak traffic hours can exceed 20 seconds, however. What about audio and video? Since the size of these files is extraordinarily large, it is difficult to manage them in the time frames we require. If you have a T1 line direct to your school, audio and video becomes a reality and we intend to include this feature in the future. It is significant that for most students, an on-line course will be their first experience learning predominantly by visual communication. Most are solely, since kindergarten, accustomed to aural communication --- namely, the classroom teacher.
Who should take and who should NOT take an on-line math course?
It’s not that easy. The experienced teacher and administrator are fully aware of just how difficult teaching mathematics can be. They understand that teaching mathematics requires all the subtleties of visual and aural communication together with intangibles recognized only by the cognizant teacher who anticipates whether classroom understanding is taking or not, and makes teaching adjustments "on the fly." The first question these folks always ask is who should take the course? While strict, never-fail guidelines don’t exist today, such determinations will undoubtedly be common place in the not-to-distant future. Here’s what we recommend now.
Students that are:
Also, WebCalc is perfect for students that have severe schedule conflicts.
Students that:
How should I offer the course?
The guidelines above are about identifying students. Yet, there remains the local logistical question as to how we view this course as potentially beneficial to small high schools that simply can’t afford to offer a regularly scheduled course but wants to make calculus available to its exceptional students. Offering an AP level course has definite advantages to your student body and sometimes monetary advantages to school districts. This on-line course becomes an equalizer to larger school districts with ample resources. The course is also tailor-made for continuing education for adults that perhaps cannot attend regularly scheduled sections. In this context, our course becomes true education on demand. Are there other situations? With the advent of internet based courseware, there are economic and service reasons to supplement a college or high school curriculum with on-line services.
What course format should I use?
First of all, we want you to use the course to your best advantage. You know your territory, what your students can do, and how best to grade their performance. You are also in the best position to decide who should take the course. There are a couple of formats to consider. The "purest" form is to give the student the URL address of the course, some chapter assignments and a date to show up for the next exam. You have just assigned the student to learn calculus as an independent study course. This may not work for many students, even good ones. We recommend that you, the teacher, be readily available at a mentor/tutor for the inevitable questions the student will have. Another format, and the one with which we are most familiar, is to offer the course during a regularly scheduled period in a computer lab. The teacher is available during throughout this period and circulates the lab to answer questions --- and occasionally keep order. We guarantee you will be surprised at the questions, and at the way students learn. Students will talk about the material; this is a spontaneous form of group learning that is highly effective and not in the slightest contrived.
How do I measure student performance?
We provide a course to you with some recommendations. For example, we can supply recommended six-weeks examinations. All we can guarantee is that the student doing well on these exams would have done well taking Engineering Calculus (MATH 151) at Texas A&M University. However, we do not want to be in the business of assessing your students, unless you choose that we do so. You know by far the best what standards to require and how to make the measurements.
What does the course cost?
At this time everyone has 100% access to the course without costs. We freely give the URL, http://www.math.tamu.edu/~dallen/snb/mindex.tex. You only need the Scientific Notebook software to read the files. And the viewer-only version of this software is free. Eventually, we plan to license the course to institutions, probably on a per student basis. This is a couple of years away.
Do my students get Texas A&M University college credit for this course?
Only students enrolled at Texas A&M qualify to earn college Texas A&M credit. At this time Texas A&M does not give dual credit for courses taken here, and it does not give solely TAMU credit to students unless they have been formally admitted. An alternative though is perfectly feasible. Ask you student to enroll for credit in WebCalC at your regional community college. If this is possible, credit will normally transfer to the senior college of the student’s choice. Finally, students completing WebCalC will be well positioned to satisfactorily pass the AP Calculus examination and then to place out of Calculus I at the college of their choice.
What about the software?
If you agree with the features described above that an on-line course should have, even in part, and if you are familiar with html capabilities vis á vis mathematical notation, then the argument that a satisfactory on-line mathematics course is possible without special software is untenable. We agree. Of the five or so possible platforms, MathView, Tech Explorer, Maple V Release 5, Mathematica, and Scientific Notebook, we have selected the latter for two principal reasons. The first is the end cost to the consumer. It’s about $75/copy. The second reason is the ease of use. Of the dozens of demonstrations we’ve given over that past several month, teachers and college professors generally agree, and we have observed, that creating mathematics with Scientific Notebook is so simple that students can pick up the tricks with little or no instructional help. If you’ve seen our demonstration, you may also recall the extensive use of color that is available. Students these days have very high expectations of what software and computer presented products should be --- and that is professional. We do expect html to improve. Indeed, specifications for Mathml (the math add-on to html) have been carefully worked out. It’s just that no browser has yet implemented them. Moreover, the specs for mathematical typographically are so complex that generating course material will be prohibitively expensive. Most of the serious software vendors, such as those mentioned above will write conversion plug-ins to convert their mathematics to Mathml. This is a couple of years away. (As one friend in the computer business once told me about computers and software, "If you wait for the best deal, you’ll never buy.")
Who is the WebMath team?
Each member of the team is experienced with some aspect of the overall course design, insofar as anyone can be considered an expert at delivering instructional materials over the web. Combined we have nearly a century of teaching experience.
Can I view the WebCalc Project free of charge? Yes, and here's how.
We want to hear from you.
Your questions and comment are especially valuable to our continuing project. Your interest in the project is gratifying. If you want to use the course in you school or college or just want more information do not hesitate to contact us. We can fill in even more details about the course than this newsletter covers. If on-line math courses are to be a success, it will take some years of experimentation and a lot of collaboration between professional educators. Our experience at what works and what doesn’t is one of the keys. No amount of technology will succeed without it. If you have questions, let us know. If you want to use our WebCalC, write or call. If you are interested in becoming involved in multimedia development of this sort, let us know. We have several other projects barely begun, for want of authors, graphic artists, programmers, and reviewers.
Please give this newsletter to anyone that may be interested.
An electronic version of this newletter is available at: http://www.webcalc.tamu.edu/newletter.html
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WebCalC
Department of Mathematics
Texas A&M University
College Station, TX 77843-3368