Curriculum and HTML

Uses of HTML in the classroom

An example of expressing mathematical ideas was the Fixed Point Theorem found in the General HTML section. To summarize, one can write a mathematical concept for students with a high-level of comprehension in the area, and include hyperlinks to key words and to sentences which further explain the term or sentence. In this example a proof is written in bare-bones form so that an experienced student or one reviewing, can quickly scan the idea. However some of the key terms have links to their definitions, and also some of the sentences have links to further explanations.

• The Fixed Point Theorem. Remember to return to this page, use the Back button in your browser's menu.

An example of using hypertext to create a depot of information is Pat Webmeister's Home Page (and succeeding documents) found in the Writing HTML section. The idea here is that an instructor can refer students to a place where students can retrieve information on a course (or on an instructor). If students miss class or misplace previous assignments, they can call up the home page and get that information. Of course to provide such a resource it must be accessible to students either on the Internet, or on a local server. Some care must be taken to insure that hypertext material on a server is protected from being edited or destroyed by students using it. Since the network setup varies from place to place, the best advise is to contact your system administrator for further details.

• Pat Webmeister's Home Page.

Perhaps the most powerful use of hypertext is for creating mathematical Labs. A HTML document can be used as an entry point for getting students to discover mathematics through software. The following example is a lab for students in a geometry class. The lab, titled Lab 6, has a picture of a triangle with its three medians included. There is a link to a Geometer's Sketchpad file which, if the Sketchpad program is installed, will launch a dynamic version of the triangle which students can manipulate. It is assumed in this lab that students are familiar with Sketchpad, and would be able to use the measure command. In the hypertext document, students are asked a series of questions with two goals in mind. The first goal is that students will conjecture that the three medians of a triangle always intersect at a point, and that for any median, the ratio of the length of the vertex to point of intersection over the length of the median always equals two-thirds. The second goal is that after discovering these two conjectures, students will try to prove them. The hypertext document contains links to various hints which will aid the students in justifying their conjecture. Because it is easy to lose track of one's place in hypertext documents, a link back to this exact place will be included in Lab 6 so that you can return here after viewing the Lab.

• Lab 6.

From previous experience using hypertext labs, here are a few additional suggestions. Students should receive a hard (paper) copy of the hypertext, in addition to viewing the document. Often students will lose track of where they are in the tangle of hypertext documents and also need a paper copy to refer to when the hypertext document is hidden by an additional program.

Working on computer labs lends itself to group work; often one person works the keyboard, another the mouse, and a third person takes notes for the group. However, students may need to be encouraged to switch tasks in group work. Often one student will be doing all the computer work while another will be taking notes and still others will be passive participants.

Formating Issues

Varying Monitor Output

Because HTML documents can be read by several different types of browsers, for instance Netscape or NCSA Mosaic, and can be used by different types of machines, for instance Macs or PCs, hypertext documents can appear differently depending on the browser used, as well as machine being used. Even the same document on two identical machines can appear differently if the preferences in the browser are set differently. For instance two Macintoshs could both be using Netscape, but one machine has the Netscape program's text preference set for "Huge", while the other has the it set for "Small". The way the document appears on various machines can range from slightly noticeable differences to potentially annoying ones. When writing documents for a class, try to keep in mind what browsers are being used, what kind of machines are being used. Lastly if possible, view the hypertext document on these different machines to see the output.

Varying Printer Output

Not only can hypertext documents appear different from machine to machine, but also the printed version may look different than the page view from the screen. For instance in the default mode, Netscape underlines links to other documents on the monitor. However these links may not be underlined when printed out. Also some images may not print. These formating problems vary from printer to printer being used and from computer to computer asking for printed output. Again the best way to understand these problems and get the desired format in print is to know what printers and machines are available and experiment with the browser preferences, printing options, and even the hypertext.

Lack of Mathematical Formula

The most glaring difficulty with using hypertext for mathematical documents is that there are no mathematical symbols in HTML. Future versions of HTML will include mathematical formulae, but for now there are only a few options. The easiest is to try to avoid using mathematical formula at all. However when mathematical formula are essential for expressing ideas, one could include the formula as a .gif file, and then use HTML to view the image. For instance on a Macintosh, the following formula was created using the program MathWriter, then a snapshot of the entire screen was taken. The formula was then selected and copied from the snapshot, and lastly a new .gif file, geometric.gif, was made using the program GIFConverter in which the copied image was pasted. (For more information on how to create images on a Macintosh, read over the section, "Creating Images for HTML on a Macintosh", found in the Writing HTML section.)

You will clearly notice that the formula is an image if you your background is different then white. (The default color for background is grey, so unless it has been changed, you should see a white box around the equation.) Printing mathematical formula works well if the equations are displayed separately from text, but it is difficult to get the images to format well with in-line text. For instance we've included the above formula in this paragraph with the following result: The geometric series is defined to be the following: . Also the size of this image will not vary depending on the text preference. So even if the size of the formula looks good in one format, it may look strange if viewing it in different format. Hopefully the later versions of HTML that are to include mathematical formula will remedy these problems.

Getting Lost within Documents

Although hyperlinks provide an easy way to link information together, they may and often do confuse the reader. Someone reading a hypertext document may take a link to one document, from there link to another document, and after awhile lose track of their initial document. Printing out a hard copy of the base document often remedies this situation. Another remedy is to include a main page that students can always return to if all else fails. For instance in this collection of hypertext documents, the file index.html has links to the three main documents, General HTML, Writing HTML, and Curriculum and HTML. Because hyperlinks often start out as blue and then change to purple after being used, a main page is also useful for the reader so that they can tell which documents they've viewed. When writing a hypertext document it is important think about

• where to include links; is a link here truly useful?
• whether adding a link between two documents confuse the reader?
• whether this configuration of links cause the reader to lose their place?

Planning ahead of time and drawing a flow chart showing the major links is helpful. For instance below is a flow chart showing the links between the major documents in this packet. An arrow from document A to document B indicates that there is a link in document A to document B, and a double-sided arrow (<--->) indicates that both document A and B have links to each other.

System Issues

Operating System:		Windows		Macintosh	
Minimum CPU Processor:		386SX		68020
Disk Space (Hard Drive):	1MB		2MB
RAM (Minimum):			4MB		4MB
RAM (Recommended):		8MB		8MB

Since these are the minimum requirements for running a browser, more memory and diskspace may/will be needed to run other applications. For instance if one wants to create a lab using sketchpad, you will need also sufficient memory and disk space to run both the Sketchpad program and the browser. Also in addition to the disk space used for the program, the browser needs additional disk space for a cache. A browser saves copies of the most recently downloaded document in a cache so that it doesn't need to be continually accessing that document off the Web or the LAN (Local Area Network). It is recommend that 6MB of Disk Space be set aside for the browser to save images and documents (its cache).

Resources Available on the Internet

Places to get Internet Resources

• http://www.ties.k12.mn.us/training/

For more information about TIES, see their home page located at http://www.ties.k12.mn.us/.

Newsgroups

The advantage of reading newsgroups using a browser is that one can select which messages to read, while subscribing to a newsgroup causes every message sent by someone to the newsgroup to be mailed to you. Below are links to three newsgroups related to mathematics and education. Following these links leads either directly to the newsgoups or further information on how to subscribe to the newsgroups.

Geometry Forum Discussion Groups:

http://forum.swarthmore.edu/~sarah/HTMLthreads/index.html

NCTM-L Discussion Group On the Web:

http://forum.swarthmore.edu:2222/PublicNewsreading/NewsGroupPages/forum.swarthmore.edu/local.nctm-l

Scimath MN Discussion Group:

(This link is to a gopher directory with information on how to subscribe to the newsgroups and an archive of previous newsgroup discussions)

gopher://informns.k12.mn.us/11/mn-k12/scimathmn/discuss

Useful Software Available On The Internet

Geometry Forum Software Page:

http://www.forum.swarthmore.edu/mathsoft.html

This cite has demo versions of dynamic geometry software like Caprí and Geometer's Sketchpad.

Place to download Netscape Browser from the Web:

http://home.mcom.com/comprod/mirror/index.html

Place to download NCSA Mosaic Browser from the Web:

http://www.ncsa.uiuc.edu/SDG/Software/SDGSoftDir.html

Web cites with external viewers, i.e. software to use along with browsers:

http://152.157.16.3/doc/resources.html

For the Macintosh Operating System:

ftp://sumex-aim.stanford.edu

ftp://wuarchive.wustl.edu

For the Windows Operating System:

ftp://ftp.cica.indiana.edu

ftp://gatekeeper.dec.com/pub/micro/msdos/win3