**A Creative Expression of Your Understanding of Communities of Practice, Connectivism, Personal Learning Networks**

**Explanation:**

The Fibonacci sequence exhibits a certain numerical pattern. It can be used to model or describe a variety of phenomena, in mathematics and science, art and nature. The mathematical ideas in the Fibonacci sequence lead to many critical mathematical concepts such as the golden ratio, spirals and self-similar curves. In mathematics, each successive number in the series is the sum of the two preceding numbers. As the numbers grow larger, if we divide one number in the series by the number to the right of it, we will get the ratio 0.618, aka “The Golden Ratio.”

The video above illustrates many of the situations where the Fibonacci sequence can be seen or applied to real life. The sequence or curve can be seen in the example in the uncurling cactus, the spiral of numbers, the fruitlets of a plant or the arrangement of leaves on a stem, the artwork of the Mona Lisa, wind currents or curves of a wave, the spirals of a shell, and a storm in the ocean. The Fibonacci numbers and principle are also used in the financial markets, in trading algorithms, applications and strategies.

The music in the video is also based on Fibonacci. Notes in the scale of western music are based on natural harmonics that are created by ratios of frequencies. Ratios found in the first seven numbers of the Fibonacci series ( 0, 1, 1, 2, 3, 5, 8 ) are related to key frequencies of musical notes. Classical music tends to represent the series best.

**How does Fibonacci, CoPs, Connectivism, and PLNs all relate to each other? ** The relationships we build are all tightly connected. In science, the Fibonacci leaves are connected as to maximize space. In music, it creates the foundation of pattern. In art, the proportions are carefully based on the Golden Ratio. Professionally, we connect in order to learn from others’ experience or knowledge in order to maximize our own knowledge. By using the principles foundational to Social Networking, we connect to one another for the benefit of ourselves and our students.

* Communities of Practice – *Is working together with others who have the same interests and goals. According to Muller, a Community of Practice, “… are groups of people who share an interest in a particular domain. By interacting and collaborating around problems, solutions, and insights they develop a shared practice, i.e. a common repertoire of resources consisting of experiences, stories, tools, and ways of addressing recurring problems.” It is founded on three components: domain, community, and practice.

In my artistic representation, the Community of Practice is represented by the Golden Ratio that is the foundation of every image and the music. The goal is to create harmony and beauty through the connections.

* Connectivism – *Connectivism is making connections from professional and personal learning experiences that enhance knowledge. According to Downes, “Learning is the creation and removal of connections between the entities, or the adjustment of the strengths of those connections.” In essence, it is connecting your knowledge with that of others in order to benefit everyone.

Connectivisim is represented in this presentation by the music that utilizes the Fibonacci sequence in it’s representative pattern. The music plays throughout the entire presentation, emotionally and literally connecting everything.

* Personal Learning Networks (PLNs) – *A personal learning network is a tool that allows people, of a common interest or with a common goal, to connect with each other. These connections are typically made through social media outlets including Google+, Twitter, Facebook, Linkedin, etc. Based on the definition, as applied to education, “a personal learning network allows educators to seek advice, trade best practices, or simply network with other professionals. Educators who build a powerful personal learning network are connected educators with the means to grow and improve continuously.”

PLNs are more personal than the Community of Practice and allow individuals to connect with others on a more specific or detailed level. They support individual learning as part of a smaller group. They enhance the ability to directly connect and collaborate with others with similar interests.

Personal Learning Networks are represented in my presentation as the start of the Fiboncci sequence, 1 1 2 3 … or the center of the spiral. In the sequence, everything builds on the previous values in the sequence: 1 +1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on. In my presentation, every screen and every musical note has the same foundation. Yet, by continuing to acquire knowledge, through working with others, we can construct our own knowledge pyramids. Working with a PLN, through collaboration and sharing ideas, the different members can have the same foundation but the individual results are boundless.

** Resources:**

**Task:**

Create a “product” to represent your understanding of the concepts also addresses (1) that we have become producers as well as consumers in this age of social networking and Web 2.0; and (2) according to neuroscientist, John Medina, visuals are very powerful means for learning and understanding.

So in order to express your understanding of Communities of Practice, Connectivism, Personal Learning Networks:

- Create one or a combination of the following to demonstrate your understanding of these concepts: a slide show or Glog of images, an audio cast of sounds, a video of sights, a series of hand drawn and scanned pictures, a mindmap of images, a mathematical formula, a periodic chart of concepts, or another form of nonlinguistic symbols. Your product should contain the major elements discussed in this module: CoPs, Connectivism, and Personal Learning Networks. These are connected yet different concepts. As such they should be portrayed as separate, yet connected elements. In other words, you should use at least one symbol per concept and somehow show how they are related and connected.

- Upload your “creative expression” to your blog and write a paragraph or two that explains it. Use references discovered in the first part of this module to support your ideas. Your references should reflect all three of the driving concepts: Connectivism, Communities of Practice, and Personal Learning Networks.

- Post a link to your blog post that contains your creative piece and reference list in our Facebook group.
- It might also be fun to Tweet in out with the #EdTechSN hashtag and see what type of feedback you get.
- Make comments about your identified class PLN’s (see above) via their blog post or on Facebook to demonstrate your understanding of and connection to their works.

I enjoyed your Creative Expression. I viewed your presentation several days ago, and I suspected that it would deal with the Fibonacci Sequence. However, I was not sure how it would connect with COP, PLN, and Connectivism. You did a great job explaining the connections. I particularly liked the closing paragraph as you described the every growing pyramid of knowledge and its limitless potential.

Thanks Lisa, I use Fibonacci in so many levels of math that I was inspired to “connect” it to this lesson. I kept going back to the visual of the pyramid of numbers. The sequence grows and grows and so does our knowledge. But we constantly must “look back” and build on the values or lessons previously learned. I’m glad you enjoyed it and I appreciate the specific feedback.

Kimberly,

Nice product! Your video was very nicely done in so many ways. First off the music really emphasized the artistic portion of the music. I have never really seen the Fibonacci sequence before and was amazed at how its design, or spiral portion was seen in so many other images. One thing that I took is that the spiral is connected to so many other things like the learning and knowledge connections that are made in Connectivism, PLN’s and CoP’s. The spiral seems to lead to one specific place, which I think is knowledge. Just my thoughts. Really cool job!

Matt Smeller

Thanks Matthew. I really enjoyed this project. I hope it inspired you to check out Fibonacci! Math really is “connected” to everything … the hard part is making those connections.

Kim, excellent video! I love how you connected the Fibonacci sequence to personal learning networks, connectivism and communities of practice. All of these things share similar aspects, but yes still very distinct in their own way. I think your video is excellent in describing what the Fibonacci sequence is to those people who have never heard of it. I thought it was so creative how you connected the music to the video with the Fibonacci sequence with the first seven numbers of the sequence, I would have never thought of that! It is neat to show that this particular sequence can be found anywhere in life and that also holds true with personal learning networks, connectivism and communities of practice. I think you did a great job and your video was very well done!! 🙂

Thank you Katie, I appreciate the feedback. I am glad you are part of my PLN! I think the music was a critical component to really connect Fibonacci to CoPs, PLNs, and Connectivism. I hope this expression inspires others, especially mathematicians, to think “outside” the box. So much of what we do really can be expressed in creative ways.

Thank you for such a creative and thoughtful contribution to this. You obviously thought very deeply about a way to represent these concepts. I found that I watched it several times. Your articulation above really helps to expand on your video and articulates what you have learned. I especially like your final paragraph where you use the pattern of the Fibonacci sequence to represent PLN’s. Clever! Great to finish on the word boundless, I think you are correct on that front. Cheers A

Thank you so much! I am so glad that I was able to express how I saw the connections in a way that others would also be able to see!