Doing and Assessing a Math Project Reflection

Ralph, Mina and I worked on a project meant for senior level mathematics students on fractals. We spent a lot of time researching the kinds of knowledge based on fractal geometry research and how it affects our current technological age. Our presentation was 'student project' heavy and we had a hard time with what kind of project we could have our students create. The difficulty with fractals was that the rigorous mathematics required to be able to recreate the fractal images was time intensive and became much too mathematically sophisticated too fast. On the other hand, if we were to simplify the math, the project became one based solely on simplistic research or juvenile design that required virtually no mathematical understanding, which was far less desirable. Our original idea was one of design and we were to have our students design fractalized images to put their study materials and superimpose their curricular content onto their presentations to enhance their insight about their own mathematical learning. However, upon reflecting on that idea, we found it to be far too simplistic and mathematically lacking.

Upon revisiting our idea, we were inspired by our professor, Dr Gerofsky, to extrapolate the idea of fractals to what students might be able to see or find in their everyday lives.

The benefits of this project would be:
- affords students the opportunity to visualize how mathematics might fit into their everyday lives
- exposes students to modern mathematical research and provides relevance to other fields of research
- can easily be simplified to accommodate any skill level or lower grade level

The pitfalls of this project would be:
- when simplified, may be too simple for more advanced students but quickly becomes far more complex than most highschool students can understand
- any formal investigation to the mathematical principles become too rigorous very quickly
- an introduction or an example of the fractal sets require significant time and access to technology in order to carry out enough iterations necessary to thoroughly illustrate the principle (however, there are many videos that may be used in place of real-time examples)

A possible modification or extension of the project could be for students to research a field outside of mathematics that has used or is using fractals in order to enhance the study. Students can design a presentation that outlines how fractals are relevant to that field of research and describe the formulations or mathematical content inherent to the development of the idea.