Chapter 3
METHODOLOGY
The literature supports the need to infuse technology into the mathematics curriculum, as well as a need to introduce students to mathematics as an evolving science, one that is rich in complexity and one that continues to explore and explain the universe. In addition, current brain research has shown us that there is a need to integrate disciplines in order for students to make connections and to form neural networks. The proposed curriculum accomplishes these goals. By studying chaos and fractal geometry, students have an opportunity to mathematically model dynamic systems including investigations in science, art and music.
The primary components of the curriculum design process were:
1. searching the Internet for web sites on mathematics and analyzing these sites for design, content, structure, aesthetics, ease of use, including navigation, and download times,
2. locating sites on chaos theory and fractal geometry and categorizing these using a database,
3. surveying preservice math teachers as to their use of the Internet and their preferences.
There are very few models of websites that develop a full course in any topic in mathematics, so much of the design for the website was based on general principles of graphic design. This information was gained by researching websites that discuss website design.
The survey questions posed to the preservice teachers focused on their use of the Internet, why they did or did not use the Internet, which sites they preferred and what they would like to see in a website for mathematics teachers. See Appendix B for a complete list of these questions. This was an informal survey and was not intended to provide more than cursory information on the preferences of these teachers. Questions were posed via the Math-Ed listserv to preservice teachers enrolled in EDTE 304. Thirteen responses were received from the 80 students enrolled in the course.
The database of websites on Chaos Theory, fractals and fractal geometry was used to organize online information about chaos and fractals and to provide links to other sites. Information included the Uniform Resource Locator (URL), the title of the site, the author and date of the site, category and type of information contained in the site, and a brief description of the site. This database was used to organize the information and to provide hypertext links once the website was completed.
It was necessary to design two websites for this project: one for Mathed-l, currently simply a listserv for students enrolled in EdTe 304, and one on chaos curriculum. The Mathed-l site was designed to provide a medium for future authors to display their curriculum, lesson plans, unit plans, and to provide links to other quality sites in mathematics, as well as providing a listserv for teachers. Site organization follows the strands outlined in the NCTM standards (1989). This site was designed using the web editor software, Claris Home Page and it is located at:
http://home.inreach.com/kfarrell/Index.html. The chaos curriculum website is accessible through the Mathed-l website and it provides links to other online sites that have text or activities on chaos, fractals or issues associated with these topics. This site was designed using Adobe's Page Mill web editor and it is located at: http:home.inreach.com/kfarrell/course.outline.html.
The results of the informal survey of preservice teachers showed that nine of the 13 respondents do not use the Internet. Reasons centered around both a lack of knowledge as to what the Internet offers and inadequate time to explore the Internet. Four teachers, however, did make use of the Internet, primarily to find lesson plans. In addition, all 13 teachers said that their students did not have access to the Internet, although one school had recently installed it. This teacher responded that although the Internet was available it was not being used because the teacher was unsure how to use it, stating, " I would like suggestions on how to use it in the classroom."
Respondents had specific suggestions regarding what they would like in a CSUS math site. Six wanted to see supplemental activities for Mathland, the elementary math program. Four teachers also wanted suggestions from practicing teachers on ways to implement Mathland. Three respondents wanted multicultural activities and information, and six wanted lesson plans in mathematics. One teacher suggested a bulletin board service, one teacher wanted a list of upcoming conferences, one a site that offered support with the basics, and one wanted a site on fractals. Two teachers were very descriptive about organizational details. One requested a site that provided a summary of the website with a description of what would be found. Another stated, "An ideal site: easy to follow format with lesson plans that truly address subject matter in a multicultural way. Also with useful,hands on, interactive activities and definitely with resources for background material."
With this information in hand, as well as information on graphic design principles, the two websites encompass the following:
The over-riding concern when developing these websites was to present the information as succinctly as possible while utilizing an organizational scheme that allowed for annotations. The Mathed-l website is organized hierarchically. The home page uses a table format to list each of the NCTM strands: algebra, discrete math, geometry, logic and language, patterns and functions, probability and statistics, number, and measurement. In addition, there are links to index pages on topics in advanced math, general math, and a page for teacher support. Each strand is annotated so that the reader knows what subjects are available once they access the next level. Each strand is linked to an index page which is arranged according to curriculum, lesson plans, unit plans, projects, examples of student work, and links to other sites which offer information and activities in that strand. Appendix C shows the main menu page, an example of an index page, and the teacher support page. (Please note that there were changes made to the formatting in order to meet printing requirements. To see the original, access the web page.) The index page in each subject area are identical except for the subject area, consequently, only one page has been included.
Several formats were tried for the index pages as seen in Appendix D (again, note that there were changes made to the format of these pages in order to accommodate printing requirements). Although, the table within a table format (Template 1) is aesthetically pleasing and well-organized, it did not leave room for annotations and it was felt that continuing to use a linear table format (Template 2), as used on the first page, would provide continuity for the reader and space for annotations. Once a format was chosen, a template was created in order to ensure continuity from page to page, thereby increasing download times. Also, note that the reader need only move through two pages of menus prior to reaching a site with content. This was done to ensure that readers do not become frustrated by page after page of menus. Currently, only links to other sites and the chaos curriculum are available. Consequently, each page is noted as "under construction" so that readers again, do not become frustrated searching for information that is not available.
The chaos web site makes use of several features: an introduction to the site which informs educators which NCTM strands are covered, curriculum goals, an online text, recommendations for assessment, and teacher support through the Math-Ed listserv and a link to a usenet group. As with the Math-Ed site, once a format was chosen, a template was created. In addition, there is a site map which functions to orient the reader and provide a table of contents. Graphics were chosen which corresponded to the material. Descriptive text was used so that readers who disable the auto-load-image feature could still navigate the site. Topics were arranged with an overview of chaos, a deception of dynamical systems, the mathematics of chaos and nonlinear equations and iterations, graphing these systems, fractals and the history of fractals, and measurement of irregular shapes and scale (Appendix E). Each page has a brief description of the topic and a side bar with hypertext links to sites that provide more information. This allows the reader to keep in mind what is available while reading the text. Advanced or highly technical texts are denoted by an asterisk. Major concepts are supported by online activities and demonstrations available via hypertext links.
Each page is highlighted with a graphic image that provides visual information about the topic., bearing in mind that a picture conveys a thousand words. Each page uses a smaller graphic that replicates the one in the site map. This acts as a visual cue and reminder as to what page a reader found information, since people access sites many times and often do not remember where they found that information.
Sites were uploaded to a server and debugged for formatting, resolution and size problems, anomalies in browsers, and variances in MacIntosh and PC computers. Friends and colleagues were notified and asked to view the results and provide feedback on content, aesthetics, color variations, and size anomalies. Changes were made accordingly. Search engines were notified of the sites.
Research supports the use of technology to present curriculum and it supports the need for a mathematics curriculum in chaos and fractal geometry. Consequently, a website for displaying mathematics curriculum and lessons was designed and a curriculum in chaos theory was created and published via this website. These sites were designed utilizing general principles of graphic design, bearing in mind the suggestions made by
preservice teachers. Chapter four will provide specific suggestions for using this curriculum and recommendations for teachers interested in providing curriculum via the Mathed-l site.
author: Kelleen Farrell