|
|
Why use this resource? Many Liberal Arts Math students have had negative experiences with math at some point in their educational development and have become math-avoiders or math-phobic. In order to refresh and renew their appreciation of math, students need to see the beauty, utility and pervasiveness of math in daily life. Dr. Ron Knott's resource on the Fibonacci Numbers and the Golden Section provides a wealth of relevant and easy-to-use materials for this purpose.
|
|
|
Background This mathematics resource was designed for students of all ages, from middle to graduate school levels; in particular, these materials are well-suited for high school and college math students as resource material for student investigations and reports. This resource can also serve as classroom enrichment for instructors and students and is a good motivational tool. At the college level, this resource is appropriate for Liberal Arts students with little mathematical knowledge as well as for undergraduate mathematics students who wish to learn more of the underlying mathematics associated with Fibonacci numbers. There are many number-theoretic investigations suggested as well as occasional research questions that students may pursue.
|
|
|
|
Learning Activities I have my Liberal Arts Math students read the sections on Fibonacci Numbers and Nature, Parts 1 and 2. Afterwards, they write a short report on the most interesting features that they learned. I also have my students read the section on Fibonacci Numbers and the Golden Section in Art, Architecture and Music to find food for thought and possible ideas for a term report. There is a wealth of web resources and interesting connections contained in these materials Lastly, I assign a few of the Fibonacci puzzles (of the Easier kind) to promote analytical reasoning.
|
|
|
Tips for Teaching This resource is ideal for student reading and reports as well as assignments involving mathematical investigations provided on the site (Things to Do). The site structure is simple and easy to use and the wealth of information and links to other resources are outstanding. Many students have reported that this was one of their favorite resources visited during the semester (during which they visited dozens of math-related web-based resources). I have been especially pleased that some have reported an interest in returning to this site even after completing my Liberal Arts Math course.
|
|
|
|
Impact of Use on Teaching and Learning This resource most definitely engenders and/or renews student appreciation of math with respect to its connections to nature. Students invariably report their amazement at how the Fibonacci numbers appear in plant structures; for many of them, this is their first exposure to these sorts of mathematical connections. This resource opens their eyes to mathematical occurrences in daily life (e.g., the structure of flower petals, pinecones, broccoli, seashells, honeybee families, etc.); they are also amazed and impressed by the connections with art, architecture and music. In addition to providing material for classroom assignments, this resource promotes self-directed learning by students and fosters a realization that math is fun, interesting and accessible, even to students with little mathematical background. I have had students report that they plan to continue using this resource after completing my Liberal Arts Math course. With regard to assessment, I award 10 points (out of a semester total of ~750) for the student report on Fibonacci Numbers and Nature. The rubric is based on report completion: 10 points for completion, 0 points for non-completion. I also award 10 points for successful completion of one or more of the Easier Fibonacci Puzzles. As an example, for the Bee-Line puzzle for cells #4, 5 & 6, the rubric is based on the number of correct pathways submitted; project grade is determined by finding the percentage of correct pathways found (out of 26 possible) and multiplying by 10. I have also included Brick Wall Patterns and Telephone Trees in this assignment.
Student Comments on Fibonacci Numbers and Nature
|
|
|
