The rationale for this Fibonacci website is two-fold. Primarily, we set out to create a website that would provide interesting mathematical activities for middle school students as well as curriculum resources for teachers. We believe that the student pages we have created are interesting and motivating and that the links within these pages will instill an enjoyment for math and encourage students to explore further. In the teacher pages, we have tried to provide information that would allow an instructor to use the web pages or to conduct more traditional classroom activities related to Fibonacci numbers. In addition, we have included links to other resources which may be helpful, particularly the NCTM Standards and the Illinois State Learning Goals which relate to particular lessons.
The second focus of this site is less readily apparent. We are very aware that many students have been traditionally excluded from math. In an attempt to begin to address the inequity of gender, racial, socioeconomic, and ability-based bias in grouping students, we have constructed a website which may be accessed by anyone! The computer terminal is a totally objective ÒteacherÓ, without even subconscious bias. It is impartial, patient, fair and dispassionate. The use of this sort of technology also allows for a wide variety of ability and interests. It would appeal to a very heterogeneous group of children, and would allow each to pursue their own interests in greater detail. Technology of this sort seems to provide the ultimate in ÒindividualizedÓ education. We hope it will begin to open doors.
In constructing this website, our aim was to appeal to a wide range of student abilities, interests, backgrounds and experiences. As mentioned in teaching article #6, and research articles #2, #7 and #8, many students are traditionally shut out of math--the gatekeeper subject--and technology can be a powerful tool for motivation. We believe the site has activities that would appeal to students who have attention deficit disorders, learning disabilities, physically challenged, those who are at risk, and other disenfranchised students, as well as those who are traditionally successful in academic endeavors. We have witnessed students exploring the website. These students seek little assistance, remain on-task for extended periods and rate the activity very favorably. (Of thirty trial surveys, 26 students wanted to repeat the activity, 3 did not want to repeat it, and one student lost his evaluation sheet.)
Though we do not expect to make major changes in the website in the future, there are a number of additional activities which might be included at a later time, or which may be linked by other teachers. So the website is a work in progress. In addition, it offers a dynamic setting for students. It is very adaptable to student interests. With the links that are provided, students will have ample opportunities to explore and expand their world. Teaching articles #4 and #5 discuss the importance of helping students make connections in their learning. We have purposely tried to include activities and exercises that are not just math related, but interdisciplinary in nature, such as the ÒFibonacci Numbers in NatureÓ pages or the ÒFibonacci PoetryÓ pages.
One major focus in constructing this site was that it would be consistent with the NCTM Standards and the Illinois State Learning Standards. We believe that it does, in fact, address the major themes of the NCTM Standards: Math as Reasoning, Math as Problem Solving, Math as Connections, and Math as Communication. Further, the NCTM Standards call for the use of technology in instruction, and technology in not only incorporated, but is central to this unit.
Because of of the connections to NCTM Standards and to many other math related links on the World Wide Web, we feel confident that the math content in this unit is solid. That , in combination with the use of technology, creates a powerful instructional tool, as related in research article # 6.
In summary, we hope that we have created a website that will be interesting and motivating for students, helpful to teachers, and will help open doors to math learning for all students.
Teaching article #1
Dixon, Juli K. and Falba, Christy J. "Graphing in the Information Age". Mathematics Teaching in the Middle School. March-April 1997, Vol 2, no. 5.
URL <http://www.nctm.org/mtms/1997/03/vol2-no5-dixon.htm> This teaching article presents 5 activities for using the WWW for creation and interpretation of histograms and bar/ line/ circle graphs. These activities are in accordance with the NCTM Curriculum and Evaluation Standards that students summarize statistics, analyze data, make conjectures, and communicate information. In addition, the activities facilitate the use of technology.
Teaching Article #2
Reys, Barbara and Wasman, Deanna, ÒMath is FUNctional! A Math Fair for KidsÓ, Mathematics Teaching in the Middle School, vol. 3, no. 4, January 1998, 260-266.
Organize a math fair for your students. This article describes how to set up a school Òmath fairÓ for show students that math can be recreational as well as practical. Specific organizational tips are given, as well as ideas for booths, games, and activities.
Teacher Article 3
Bowman, Jim. Making math relate to the real world: a math teacher challenges his students with interesting story problems. South Central Regional Technology in Education Consortium, September 19, 1997 Online: <http://www.4teachers.org.>
Jim Bowman believes that the most effective way to get students to solve problems involving advanced material is to make technology (computers and graphing calculators) an integral part of every high school mathematics course. He posed a real life problem from a Texas Instruments newsletter, and gave the students a week to solve it uses various methods and technologies. BowmanÕs role throughout his lesson was that of coach. He reports that this problem created enough interest in using technology to solve problems that many in the class asked for another problem. This teaching article is a very good example of the use of NCTM Standards at work.
Teaching Article #4
Usnick , Virginia and McCarthy, Jane, ÒTurning Adolescents onto Mathematics through Literature, Middle School Journal, March 1998, Vol. 29, No. 4, 50-54.
Many studies have identified common interventions which meet the needs of adolescents in general and at risk students in particular. Strategies such as cooperative grouping, flexible scheduling, personalized instruction, hands-on, interactive learning and integrated curriculum are several of these strategies. NCTM standards call for math as ÒcommunicationÓ and math as ÒconnectionsÓ. This article gives several resources for using literature as a springboard for math instruction in order to help students become engaged and make connections.
Teaching article #5
McWhorter, J. Yvette, and Bullion-Mears, Ann T. ÒWriting Poetry in the Content ClassroomsÓ, Middle School Journal, vol. 29, no. 2, Nov. l997, 46-50.
This article gives a number of specific suggestions for writing poetry (of many types) in the various content areas. If we are to help students make connections and to allow students to use their strengths to improve areas of weakness, this strategy may be very helpful. The authors give not only the rationale, but also illustrations and many ideas for writing poems in math, science, art as well as language arts and reading classes.
Teaching article #6
ÒClassroom Technology: Tool for, or Focus of, Learning?Ó, Mathematics Teacher, vol. 89, no. 2, 134-137.
This article describes how technology turns mathematics into an interactive, hands-on, laboratory experience. Students who are otherwise not interested or not tuned in (at risk, attention deficit disorder, learning and behavior problems, etc.) may be much more motivated with the use of technology.
Teaching site/article#7
Mathematics Teaching and Learning Technologies
<http://www.dse.vic.gov.au/klafocus/maths/index.htm>
This site is provided by the Department of Education (Victoria) to assist teachers efficiently and effectively change learning experiences in mathematics so that the potential of learning technologies is realized for all students.
Technology has for generations been an aid in mathematics and mathematics learning. The pace of technology availability is now challenging many aspects of learning processes and outcomes in the way calculators challenged learning of arithmetic in the 1970s. Technology currently provides opportunities for:
Productivity gains so students can have a wider range of experiences Focusing on understanding rather than processing Focusing on aspects of an algorithm to improve understanding Working with 'real' data Experiences that involve people on a national and international basis Observing patterns in specific examples to understand generalizations rather than just applying generalizations to specific examples Developing n expanded range of problem solving strategies that includes numerical analysis Activities that involve higher order thinking.
Research Article #1
Negative effects of homogeneous grouping in mathematics classes.
Davenport, Linda Ruiz, ÒThe Effects of Homogeneous Groupings in MathematicsÓ, ERIC Digest, Clearinghouse for Science, Mathematics, and Environmental Education, July, 1993
URL <http://www.ericse.org/eric/digests/digest-m05.html>
This article discusses findings from various studies which indicate that tracking and ability grouping for math generally fail to increase learning and widen the achievement gap between students. At particular disadvantage in these groupings are lower SES students, minorities and females, all of whom are under represented in the higher groups or tracks.
Research Article 2
Davenport, Linda Ruiz. ÒPromoting interest in mathematical careers among girls and womenÓ. ERIC, Clearinghouse for Science Mathematics, and Environmental Education, October 1994.
In recent years, gender differences in mathematics achievement and participation in mathematics coursework at the high school level have virtually disappeared. However, few women enter professions that call for substantial backgrounds in mathematics and science. To encourage females in mathematics, programs and resources have focused on the importance of mathematics in their lives; exposing them to higher level mathematics and encouraging confidence in their abilities; providing opportunities for careers in mathematics; and developing support and mentoring systems for girls in mathematics. Some programs and resources mentioned were the EQUALS program; SPACES: Solving Problems of Access to Careers in Engineering and Science; Family Math; How to Encourage Girls in Math and Science: Strategies for Parents and Educators; and Math Equals: Biographies of Women Mathematicians + Related Activities. Several post secondary programs were mentioned: the Women in Science Project at Dartmouth College, and the mathematics program at the State University of New York College at Potsdam. Successful programs were those that promoted instruction that deliberately invokes inquiry, discussion and collaboration. The older, traditional paradigm of instruction from the teacher, students listened, remembered and gave correct answers is being replaced by the newer paradigm that places a strong emphasis on problem solving, reasoning, communication, and connections.
Research Article #3
Tomlinson, Carol Ann and Tonya R. Moon and Carolyn M. Callahan. How well are we addressing academic diversity in the middle school? Middle School Journal: January 1998. pp.3-11.
Despite the range of academic, affective, social, cultural, and gender differences that typify the middle grades, relatively little research has been undertaken to determine how teachers deal with diversity in the middle school. This article examines four key themes from a national study, focusing particularly on beliefs and practices of middle school teachers and principals as they relate to academically diverse learners. Those themes are developing middle schools responsive to student differences, the nature of middle school learners, developmentally appropriate middle schools, and curriculum and instruction at the middle level.
Research Article 4
<http://www.ed.gov/pubs/EdReformsStudies/EdTech/welcome.shtml>
Technology and Education Reform. A Research Project Sponsored by the Office of Educational Research and Improvement, US Department of Education, Conducted by SRI International.
A look at nine schools where staff were active participants in incorporating technology in ways that support education reform. Reasons for the use of technology in the classroom are: to support thinking processes, stimulate motivation and self-esteem, promote equity, prepare students for the future, support changes in school structure, and explore technology capabilities.
Research Article 5
Devitt, Terry. Reasons to infuse science with technology. Electronic Learning: March/April 1997.
This article lists six reasons to infuse technology in science. 1.) to promote reform. 2.) to promote access to inaccessible worlds. 3.) to think like scientists. 4.) to turn data into pictures. 5.) to explore through simulation. 6.) bring teachers Òup to speedÓ.
Research Article 6
<http://www.spa.org/project/edu_pub/summary.htm>
Report on the effectiveness of technology in schools, 95-96: executive summary.
This report, commissioned by the Software Publishers Association and conducted by an independent educational technology consulting firm, Interactive Educational Systems Design, Inc., summarizes educational technology conducted from 1990 through 1995. It is divided into three sections: 1.) the effects of technology on student achievement, 2.) the effects of technology on student self-concept and attitudes about learning, and 3.) the effects of technology on interactions involving teachers and students in the learning environment. The conclusions were that technology is making a significant positive impact in education: technology has demonstrated a significant positive effect on achievement, student attitudes toward learning, the level of effectiveness is influenced by the specific student population, students trained i collaborative learning had higher self esteem and student achievement, and teacher in-service training provides teachers with greater comfort in using computers.
Research Article 7
<http://www.ericse.org/eric/digests/digest-m06.html>
Murphy, Nancy. Multicultural mathematics and science: effective k-12 practices for equity.
This digest identifies references that provide images of effective practices which have increased mathematics and science achievement among diverse student populations. These effective practices are eliminating tracking, increasing expectations and course requirements, and changing course content sequences; utilizing technology; enhancing life skills through math and science literacy; capitalizing on cultural learning styles and culturally relevant curriculum; addressing staffing needs; engaging parents as active partners; and increasing affective and academic support for students.
Research Article 8
<http://inform.ospi.wednet.edu/edtech/app-de.html>
Washington Sate technology plan for k-12 common schools.
This legislative report is based on the premise that technology will play a critical role in studentsÕ successfully attaining the four state learning goals. This review of the literature is not meant to definitively summarize all research on technology in education but rather to answer the more specific question: is there a research base to indicate that technology can play a critical role in studentsÕ successfully attaining the four state learning goals in Washington State? The intent of the integration of technology in schools is to add a catalyst and tools which, combined with other reform efforts, will help schools become learning environments which empower students to successfully attain the new state learning goals. Overall research and survey findings conclude: a significant positive effect on achievement with the use of technology in education; positive effects on student attitudes; the level of effectiveness of educational technology is influenced by the specific student population, the software design, the teacherÕs role, how the students are grouped and the level of student access to the technology; the technology makes learning more student-centered, encourages cooperative learning, and stimulates increased teacher/student interaction.
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