Math Post week 3

Recently I have stumbled upon some art work that I had kept from an art class I had taken when I was in High school. At first glance I was solely amazed at visual beauty, however, upon further research and analysis, these images took me from a realm of art into the the realms of psychology and mathematics! It was the work of M.C. Escher. There was even a program that aired on the BBC called, The Art of the Impossible: MC Escher and Me that dealt with the subject of his art and its relations to mathematics. This got my mind racing in all directions. I started to think of questions like: 1.) how many other examples are there of things that on the surface may appear to have nothing to do with math, yet upon deeper analysis are very much interconnected, and 2.) will I be able to incorporate these types of things into the classroom in a way that would engage students and fuel a desire in them to learn (mathematics in specific)? It puzzled me greatly for some reason. I find it very difficult to hypothesize on how the minds and heart of others may operate. In the case of these images made my MC Escher for example, if there were students in my class that were passionate about art, then I could easily imagine capturing their attentions by incorporating the works of MC Escher into our discussion and activity, however, the question still remained, would this 'spark a flame' in them? A flame whose fire was inextinguishable? or would these flames only last for the duration of the particular lesson and them just as quickly as it came, fade away? It makes me think of how I can, once having ignited an interest the students, have that same positive effect remain in them permanently. To keep with the same example, if we were studying geometry, and we incorporated some artwork into our lesson that would be great, however, the task seems a lot more difficult if we were to move on to a lesson in algebra. However, as difficult as the task may seem, it is not impossible! I was thinking that instead of constantly using a black marker on a white board, perhaps introducing more colours would also help. Using one coloured marker for all variables on the right hand side of the equation and using another coloured marker for the left hand side may not only catch the eye of the artists in the room, but may also make it easier for many other students to visualize each step at they work through a problem. From my first task, of thinking of ways to keep the artists interested in learning mathematics, the second obvious thing to ask was: how do I keep all students interested in mathematics? everyone from the artists, to the athletes, to the historians, to the scientists, and some others that I am forgetting. This question reminded me of an interview I watched where Professor Richard Feynman spoke about his philosophy of teaching. Professor Feynman said (after a disclaimer that he still h the best way as yet to find the best way to teach) that one way of trying to teach would be to "be chaotic and confusing, in the sense that you use every possible way of doing it...so as to catch this guy or that guy on different 'hooks' as you go along. That during the time when the fella' who was interested in the history is being bored by the abstract mathematics, on the other hand the fella' who likes the abstraction is being bored at another time by the history. If you could do it so you don't bore them all, all the time, perhaps you're better off". I would like to see if we could take Professor Feynman's advice to the next level. Could we have mathematics lessons (or any lesson for that matter) where we are able to throw out many 'hooks' so that we are bound to 'catch' every student in one way or another? This seems like a herculean task, but, with that being said I think it only seems that way because we are at the beginning of the road and trying to imagine a perfect finished product. I think that the ability to engage every student and have them interested in mathematics is not impossible. That doesn't necessarily mean every student will go on to become a mathematician, however, they will leave with a respect and appreciation for mathematics, as well as solid understanding of its fundamentals. we just need to take the first step and the others steps will slowly but surely follow. 3