When I began this inquiry project, I originally wanted to learn about the Fibonacci sequence itself, and why it is such a famous sequence. Once I began the research, I quickly discovered the answer to this question. This sequence has intricacies and subtleties that I never realized existed. I had heard about the Golden Ratio, but I also didn't realize how closely it was linked with the famed Fibonacci sequence. This discovery has made this inquiry a highly worthwhile endeavour.
I wondered how I could teach my students about this sequence in such a way that focused on a problem-solving approach. I didn't want to just tell them "here's the Fibonacci sequence. The numbers in this sequence are 1, 1, 2, 3... and you get each number by adding the two preceding terms". This is a didactic approach and one that will not motivate students to want to learn about the Fibonacci sequence. They will memorize the formula and that will be the end of it for them--in one ear and out the other. The fact that the Fibonacci sequence is so closely related with the Golden Ratio opened up a whole new world of Fibonacci possibilities. Students have tangible examples at their fingertips to see that the Fibonacci sequence has a tremendous impact on many areas of nature, on human and animal body proportions and in many other areas as well.
Because the sequence is so prevalent in many areas that are familiar to students, they will become motivated to learn about this topic and therefore, the knowledge that they acquire will be meaningful to them and processed at a much deeper level.
The great thing about this topic is that students will actually be able to see for themselves the presence of the Fibonacci numbers and the golden ratio. They can measure and observe people and objects around them to find new areas on their own where this sequence can be found. The benefits of having students construct some of their own knowledge about this topic allows for a deeper understanding of it. This constructivist approach is a highly effective way to teach mathematics. As well, adopting a problem-solving approach makes instruction much more effective. Students have to be taught to think logically and critically and a way that this can be accomplished is to let them practice with problem solving approaches that will foster this growth. All areas and topics in a mathematics curriculum should be taught with these philosophies in mind. The end result will be students who are confident and motivated to learn, and this should be of utmost consideration when developing lessons for any topic in a mathematics curriculum.
