1. It must be sensitive to initial conditions.
2. It must be topologically mixing.
3. Its periodic orbits must be dense.
Before we get started, I'm no mathematician, but I can see how scientists could have studied any classroom to develop this theory. I've muddled my way through the basics of this theory and recognise the relevance of applying its properties to our daily teaching lives.
Now to the second property - topological mixing. What is topological mixing? A new cocktail or a new type of speed dating? Let's start with Topology, in a nutshell, it is a major area of mathematics that is concerned with spatial properties that are maintained under continuous deformations or contortions of objects e.g. stretching (that is, our resources and sanity to the limit). How does this correlate to our teaching and classrooms? Believe it or not, it is a part of our lives that is best described as SETS. At some point in our schooling we've all covered sets in mathematics. So, think of yourself, the students and the physical environment as sets. Now you've become topological spaces and with that you inherit - convergence, continuity and connectedness.
a. Convergence - coming together each day as a teacher to deliver processes to assist with learning and as a student to apply those processes to learn. Aaaaah! The idealistic stirrings from my reading of Summerhill by A.S.Neill in 1977. Well you do come together each day with ideals, hopes and strategies, and whether they work or don't that's okay, because this is the chaos classroom theory.
b. Continuity - small changes in the input results in small changes in the output. YES! You can apply continuity to your classroom every day of every year. A hair style probably won't do it unless it changes your overall approach to teaching. Possible but not highly probable! To apply this property you could consider tinkering with your teaching strategies so they reflect the learning styles of the students. BINGO! You're on a winner!
c. Connectedness - nothing surprising here, you and the class are like a VENN DIAGRAM, you are each a distinct object yet as a class you are connected in different ways. The other subsets in your Venn Diagram need you to keep this connectedness strong. How? Take time each day to have a one on one with students. It doesn't have to be a saga like War & Peace, but you'll be amazed how important it is in their lives when a significant other takes the time to chew the fat.
Getting the drift of Chaos Theory? Well down to the third property - dense orbits. Yes, that is the third property and I can hear the giggles, no guffaws this one has caused. Without the coffee I think I'm reduced to a dense orbit. To sum it up my Venn Diagram object, because you and your students are subsets of your class, you are a collection of points in an evolutionary function i.e. you teaching to assist learning and forming relationships. During your time together as a Venn Diagram you and the students will evolve (Mary Shelley's Frankenstein could spring to mind). Continuously for forty weeks of the year, you and your students will be suspended in a dense space (classroom) connected by your converging ideas.
To bring order amidst the chaos you have to be willing to let go of the reins. Not completely because the horse will bolt, but to the point where students are setting behavioural parameters and sticking to them. I'll leave you with an
example of what I've been talking about minus the mathematical jargon. My teaching partner and I developed a learning program (for Year 6 & 7) based on the stockmarket . The truly chaotic time came when we simulated the stock exchange floor. I used a megaphone to make announcements about variables affecting stocks and the mayhem of buying and selling from the students was no lesser than the real thing. Did it work? It was a roaring success even to the point where parents joined in on the fun. My advice, keep it real and fun and you'll have mastered the classroom chaos theory.
Last but not least, no mathematician was harmed during the writing of this article. Hopefully the physicists fare as well when I start on the highly strung string theory.
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