Lateral Thinking in the Classroom
Remember the old trash compactors? You shoved in as much garbage as possible, compressed it and added some more. Neat, tidy bundles of waste, prepared for dumping, dense and inert. Lot's of energy goes into packing, but once they are imbedded in the ground, how useful are they? Clearly some material can be recycled. But how do we begin the sorting process?
How much information that we impart to kids today will be useful to them and society in the future? Are we helping them sort the trash or just cramming in more?
You hear complaints from educators that; "kids today just can't think for themselves." Well aren't we partly to blame? Education in Israel today seems to be driven by quantity and not quality. We aren't transferring the skills necessary for individuals to manage their lives and information in the 21st century. Students often have no idea when to listen, how to direct their attention or understand the patience necessary to open their minds to a new concept.
Israel languishes at the bottom of the world table when it comes to demand for achievement, with most developed European and American countries ranking above it. Ironically, as reported by Yulie Khromchenko, in Ha-aretz, analysis of data appearing in the Program for International Student Assessment from 2003, shows that the level of support an Israeli student receives from a teacher is relatively high. Well what kind of support are we giving them?
According to professor Zemira Mevarech and Dr. Bracha Kramarski of Bar-Ilan Universiy, "the study paints the picture that teachers in Israel spoon-feed the material to the students and don't challenge them." For shame I say. This is the year 2007. Top-down didactic teaching methods are not enabling children to reach the higher cognitive levels necessary for real learning. Ask any engineer who applies lateral thinking to solve concrete problems. If you can't look at a problem from a variety of angles, you may never find a solution.
Take for example the major limitation for the Romans in their numbering system. A system in which 9 was represented by IX and 16 by XVI. As a counting system, this was workable, but for multiplication, factoring, fractions, or any kind of advanced numerical calculation it was hopelessly inadequate. Guess who solved this dilemma? The Arabic civilization which built on a completely different concept and introduced a radically new idea – the zero.
Israel's industry and high-tech were once well known for their "out of the box" abilities to think. I think many would agree that we are rapidly losing our competitive edge in this vital capacity. So why aren't we fostering this more readily in our early education?
I say open every school day with "a stumper" in order to practice lateral thinking. Here's one for you I've used with all my classes from Test Your Lateral thinking IQ, by Paul Sloane:
The Barber Paradox.
In a town in ancient Greece there was a law stating that all men must be clean-shave and that no man might shave himself. The only person allowed to shave people was the licensed town barber (who was forty years old). There was only one barber. Since the barber was bound by the same law, who shaved the barber?
Did you solve the puzzle? Here are some clues:
- The barber did not break the law.
- There was no beard, moustache, or whisker on the barber's face, yet that face was not shaved by the barber.
- Check all your assumptions about the barber!
Can you believe that after just two months of exercises like the above, with students as young as 7th grade, they were better able to able to identify their assumptions from past learning and quickly solve puzzles that contained ambiguities.
The Barber Paradox had lead to heated debate in many classes about gender differences (that's a heavy clue). Soon we had uncovered some real sexist attitudes among many of the boys towards their cohort girl students. In following the students suggested more lessons to deal with this issue, as they felt it was rampant in their friendships and familial relations.
I want to build a nation of youth who are both critical thinkers and well-rounded individuals, adults who have their values intact and are prepared to view situations from a variety of perspectives, not just linear thinkers but lateral ones.
Next column we will discuss values based learning in education.
(puzzle solution: The barber is a woman).
For Hire Now!
Summaries
Upcoming Events
You might want to look at this link about invention of the Zero.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html
It is not true that "The Arabic civilization which built on a completely different concept and introduced a radically new idea – the zero."
What we call "Arabic numerals" are not used in Arabic as one can easily is any Arabic newspaper, licence plate, etc. They are actually Indian numerals. The Arab civilizations transmitted them but did not invent them.
I have pasted some quotes from the article above (see also Encyclopedia Britannica, Encyclopedia Americana and any history of Math).
********
... work of the Indian mathematicians was transmitted to the Islamic and Arabic mathematicians further west. It came at an early stage for al-Khwarizmi wrote Al'Khwarizmi on the Hindu Art of Reckoning which describes the Indian place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. This work was the first in what is now Iraq to use zero as a place holder in positional base notation. Ibn Ezra, in the 12th century, wrote three treatises on numbers which helped to bring the Indian symbols and ideas of decimal fractions to the attention of some of the learned people in Europe. The Book of the Number describes the decimal system for integers with place values from left to right. In this work ibn Ezra uses zero which he calls galgal (meaning wheel or circle).
The Indian ideas spread east to China as well as west to the Islamic countries. In 1247 the Chinese mathematician Ch'in Chiu-Shao wrote Mathematical treatise in nine sections which uses the symbol O for zero. A little later, in 1303, Zhu Shijie wrote Jade mirror of the four elements which again uses the symbol O for zero.
Fibonacci was one of the main people to bring these new ideas about the number system to Europe.
In Liber Abaci he described the nine Indian symbols together with the sign 0 for Europeans in around 1200 but it was not widely used for a long time after that. It is significant that Fibonacci is not bold enough to treat 0 in the same way as the other numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 since he speaks of the "sign" zero while the other symbols he speaks of as numbers. Although clearly bringing the Indian numerals to Europe was of major importance we can see that in his treatment of zero he did not reach the sophistication of the Indians Brahmagupta, Mahavira and Bhaskara nor of the Arabic and Islamic mathematicians such as al-Samawal.
...
etc.
You can see the full article from the link at the top.
Thanks for the correction! I dropped a note to the author from Test Your Lateral Thinking to advise him of your link. Many students think everything they read is "laid in stone." Educators have to explicitly teach students how to understand sources, how printed information is documented, as well as historically revised. Keep the comments coming!
In our modern times, children spend hours on the internet sitting in front of the computer satisfying curiosity, communicating, and playing games.They really can enjoy instant gratification.This may not be such a good thing. The ability to create play from one's own imagination and experiance is being lost.Instant gratification disables a child's patience and persistance at arriving at some finding, solution, or goal.
As a computer user myself I understand the attraction, but at least when I was growing up pre-computer I had to think of original ways to entertain myself and my friends. That is being lost.This achievement is being lost.
Teacher's must deal with students who now want instant gratification and computer like efficiency.I imagine it must be tough to teach.