It's been awhile since we were last together, so I will take a moment to up-date everyone on our last class of 2012.
Before the break, we re-visited the ever popular topic of paradoxes, but this time we spent more time defining the meaning of a true paradox (a logical statement that leads to a contradiction) and identifying them. It's more difficult than it seems to distinguish a paradox from a fallacy! We also broke up our paradox discussions with three hands-on puzzles: spatial thinking and reasoning, a Christmas cryptograph (de-coding) and a tangram-type challenge.
We ended the day with an intro to Pascal's Triangle, which allowed us to stretch our mathematical muscles and discover patterns hidden in the triangle -- the counting numbers, the triangular numbers, the Sierpinksi Triangle, the powers of 2, the exponents of 11, the Fibonacci Sequence, and last but certainly not least, symmetry!
This class provided us with a nice sampling of many of the types of problems we have covered this semester and introduced some new material with Pascal's Triangle. For more information on these triangular patterns, click on any of the hyperlinks in the text above.
We use curriculum in part from Art of Inquiry, LLC.
Today's class took us away from paradoxes and brain teasers and landed us on the moon!
After a briefing on some of the most basic of the moon's characteristics, students received a worksheet that required them to rank the importance of 15 items that survived a spaceship crash-landing on the moon. These items will assist the survivors of the space craft in reaching the mother ship on the lighted side of the moon.
I asked that the students take a minimum of 10 minutes to complete this task, which is outside of our normal comfort zone! We are doing much better at taking our time to think through things thoughtfully and carefully, and most students used all of the ten minutes allotted.
Without discussing the "answers," we next divided into three groups of three and filled out another blank sheet. This time, the students were challenged to arrive at a consensus with their teammates before deciding on a ranking AND write down the rationale for their decisions (new vocabulary words for the day: rationale and consensus building!).
I was very pleased that the groups took all of the allotted thirty minutes to discuss and debate amongst their teammates. The last phase of the exercise had us forming one large group and devising a methodology to arrive at one answer for each item that the entire group could agree upon. We found ourselves deep in heated discussions, and will have to finish next week!
At the end of the exercise next week, we will reveal the "answers" according to NASA, and individual responses will be scored as well as the small group answers. These will be compared with how we fared as one large group, answering the ultimate question: Is consensus building more effective than an individual making decisions on his or her own, or vise versa? Personally, I am anxious to know the results, so stay tuned for the up-date next week.
Since we didn't finish the exercise, there is no homework this week. Three more classes and we will turn your creative thinkers out into the world. :>)