Brain Compatible Education in Practice

Transcription

1 Brain Compatible Education in Practice The science and math of La Ola Derek Pugh BCEI Booklet #8

2 Brain compatible education is about teachers and learners approaching the learning in ways that make the experience more memorable. Studying Mexican waves allows learners to use higher level thinking skills for what at first glance may seem simple. It allows them to be active learners, work with other students, encourages peer teaching and reporting back and teaches much from a range of subject areas concurrently, so it is of high interest. Mexican waves are a fairly young phenomenon. First seen at the 1986 world cup in Mexico, thousands of excited football fans, gripped in a fever of collective human behavior, leap to the air on cues provided by their neighbors. The waves have become so popular some stadiums have banned them, but a football game now seems less likely not to have the wave, called La Ola in Spanish, than it is to have one or more. At the 2

3 2000 Sydney Olympics, the largest recorded wave ever involved 110,000 people. A large organized Mexican Wave has also occurred for charity. The British Heart Foundation had 5805 people in one in April 2002, which Guinness World Records claim to be the longest so far. What does this mean to the mathematician? Well, a number of researchers have examined the phenomenon and there are interesting mathematical connections to crowds and human behavior and nice cross curricula activities are possible in the class room. Farcas, Helbing and Vicsek (2002) analyzed video footage of 14 large football crowds. They determined a normal speed of the wave (12 meters per second), the direction (usually clockwise), and the wavelength (15 seats). They used standard models usually employed in 3

4 the interpretation of excitable media and created two mathematical simulation models. There s a nifty online demonstration of one of these at the web page that accompanies their paper ( The authors determined the probability of individuals or groups of people starting waves. In short, one person could jump up and down till he or she was blue in the face but a wave is unlikely to begin until about 25 people in a group trigger it what the authors called a critical mass of initiators (2002, p131). Farcas et al hope that these models can help us understand crowds, how small groups can take control of a crowd and have implications in riots or other less savory events. In classrooms a Mexican Wave can be reproduced by the students in an artificial, more orchestrated sense by the teacher or a leading student. The class can time their Mexican Waves and work out variables that affect 4

5 the efficiency or neatness of the wave. What does a neat wave look like? What criteria are needed to reach optimal waving? How do Mexican Waves mimic other waves? In 2006 I taught both science and math to an International School grade 6 class that really took the Mexican Wave ball and ran with it. They undertook a range of such activities studying the phenomena and that led to further ideas. They decided the waves are transverse waves like the slinky springs they studied in science, as individuals do not leave their place, but the real leap came when they realized that everyday a variety of Mexican Waves occur on a global scale: people brushing teeth, eating breakfast, mosques calling for prayers, school bells, lunch time, because these things happen to a daily timetable as the Earth rotates. The 2000 millennium celebrations around the 5

6 world were televised globally as they happened, showing a kind of wave that was linked to time zones. In class we imagined that a dedicated and more accurate wave could be organized on a grand scale with a massive publicity push and working out the logistics of such an event became a valuable mathematics activity for my middle school students. We decided that our future global wave was to take 24 hours, so we worked out the ground speed a global Mexican Wave would be for a 24 hour wave at the equator (40076 km). At a stadium s stately wave speed of 12m/sec (43.2 km/h) the global wave would take about 3.9 days so our 24 hour wave had to travel the kilometers of the equator a whole lot faster. We divided km by 24. That s 1670 km/hour, which is as fast as a point on the equator travels as the Earth 6

7 rotates in a westerly direction. This means that as the wave travels west each person in the world could wave at a common time relative to the Earth s rotation we decided each person s actual noon would be a well understood concept. Actual noon and clock time are not necessarily the same each time zone takes up a lot of space and it may be 12 o clock over many hundreds of kilometers at the same time but actual noon is a function of the Earth s rotation, not human time zones. So the kids had to learn about the Earth s rotation and time zones and identify a number of cities that fell in line at increasing longitudes. They then developed a model whereby the populations of these places would know when to participate in the wave. They worked with the 360 of longitude and calculated that each degree (111.3 km at the equator, decreasing towards the poles) would need four minutes for the wave to pass. 7

8 The longitude of Zero degrees runs through Greenwich, as does 360 degrees, so we started the clock at 00:00 Greenwich Mean Time (GMT). It was then a matter of multiplying degrees longitude by four to work out the time for people at those longitudes to participate. This is our formula: T = G + 4L (where T is the participation minute after start, G is GMT and L is the degrees longitude) Los Angeles, at 118 W Longitude would participate at exactly 472 minutes (7.87 hours) after Greenwich, or, if the wave started in Los Angeles, the good folk at Greenwich would participate 968 minutes (16.13 hours) later as the wave passed through England on it s way back to Los Angeles, where it would arrive at the 24 8

9 hour mark. In both cities it would be noon if it was noon when the wave started. Longitude is divided into east and west, each with 180. Wavers would need to determine their wave time in terms of western longitude. For example Jakarta is at E which is equivalent to W. Jakartans would wave at the minute mark (18.2 hours) after Greenwich or minutes (5.8 hours) before. With the simple time formula all people need to know is their longitude to work out their own personal wave time and their local time when the wave started to join in accurately. Imagine office workers in Europe leaping to their feet at noon one day as part of a global wave because someone had done the same thing on the opposite side of the world exactly 12 hours before at their own noon. 9

10 Imagine a crowd of shoppers in a market in South Africa or a group of school children in Brazil dropping everything and leaping with joy as part of a global sharing of a fun idea, a unification of global human behavior. Wow, it would really be something. My students were enthused by the idea too and developed plans whereby they could create the biggest intentional wave of human kind. Perhaps one day we ll see it happen, after all, you only need 25 people in a sports stadium. Connections to the real world were important for the kids. They already knew of the 2004 tsunami s devastation across the Indian Ocean and the speed the wave traveled and we d measured the speed of transverse waves in the school swimming pool. Our conclusion was that a global human Mexican wave is, 10

11 as yet, an untouched resource for the planet, ripe for a major charity drive or world celebration perhaps. But, in the meantime, it sure is fun maths. References: Farcas I., Helbing D., and Vicsek T., (2002) Mexican Waves in an Excitable Medium, Nature, Vol 419, p Visit for more free information booklets about brain compatible education. 11

12 The Author Brain Compatible Education in Practice La Ola Derek Pugh is an experienced Principal and teacher in both Australian and International Schools. He now runs workshops in Brain Compatible Education for students, teachers, parents and corporate groups worldwide. Workshop participants discover the latest in neuroscience and why knowledge of the brain is a powerful tool in education; the SEWBaD secrets of preparation for learning; what brain plasticity means to education; individual learning profiles and how to use them for effective learning and teaching; how to teach or learn efficiently; and models of brain operation and function. He is the author of The Owner s Guide to the Teenage Brain and numerous articles on brain based learning. derekpugh@braincompatibleeducation.com Illustrations Khan Wilson 2011, 12

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