Aug 20, 2015

Ini ada potongan tulisan dari bukunya Alex Bellos (2010) yang berjudul
"Here's looking at Euclid: A surprising Excursion through Astonishing World of Math". Kutipannya tentang bagaimana seekor chimpanzee belajar 'matematika' (lihat video di bawah ini)

Cerita ini, membuat saya berefleksi tentang pendidikan. Apakah pendidikan yang kita berikan kepada siswa-siswa kita memang benar-benar pendidikan yang memungkinkan siswa berpikir secara lebih dalam atau 'pendidikan' (atau mungkin lebih bisa disebut pengajaran) yang tidak beda jauh dengan 'pendidikan' yang diberikan pada Ai (chimpanzee yang ada di tulisan di bawah ini). Seperti yang tertulis di dalam tulisan di bawah ini "Even though Ai had learned to manipulate numbers perfectly well, she lacked human depth of understanding."
Semoga pendidikan yang kita berikan kepada anak-anak (didik) kita tidak seperti itu yah, membuat siswa kita 'lacked human depth of understanding'.
"The lesson of Clever Hans was that when teaching animals to count, supreme care must be taken to eliminate involuntary human prompting. For the math education of Ai, a chimpanzee brought to Japan from West Africa in the late 1970s, the chances of human cues were eliminated because she learned using a touch-screen computer.

Ai is now 31 and lives at the Primate Research Institute in Inuyama, a small tourist town in central Japan. Her forehead is high and balding, the hair on her chin is white and she has the dark sunken eyes of ape middle age. She is known there as a “student,” never a “research subject.” Every day Ai attends classes where she is given tasks. She turns up at 9 A.M. on the dot after spending the night outdoors with a group of other chimps on a giant tree-like construction of wood, metal and rope. On the day I saw her, she sat with her head close to a computer, tapping sequences of digits on the screen when they appeared. When she completed a task correctly an 8-millimeter cube of apple whizzed down a tube to her right. Ai caught it in her hand and scoffed it instantly. Her mindless gaze, the nonchalant tapping of a flashing, beeping computer and the mundanity of continual reward reminded me of an old lady doing the slots.

When Ai was a child she became a great ape in both senses of the word by becoming the first nonhuman to count with Arabic numerals. (These are the symbols 1, 2, 3, and so on that are used in almost all countries, except, ironically, in parts of the Arab world.) In order for her to do this satisfactorily, Tetsuro Matsuzawa, director of the Primate Research Institute, needed to teach her the two elements that comprise human understanding of number: quantity and order.

Numbers express an amount, and they also express a position. These two concepts are linked but different. For example, when I refer to “five carrots” I mean that the quantity of carrots in the group is five. Mathematicians call this aspect of number “cardinality.” On the other hand, when I count from 1 to 20 I am using the convenient feature that numbers can be ordered in succession. I am not referring to twenty objects, I am simply reciting a sequence. Mathematicians call this aspect of number “ordinality.” At school we are taught notions of cardinality and ordinality together and we slip effortlessly between them. To chimpanzees, however, the interconnection is not obvious at all.

Matsuzawa first taught Ai that one red pencil refers to the symbol 1 and two red pencils to 2. After 1 and 2, Ai learned 3 and then all the other digits up to 9. When shown, say, the number 5 she could tap a square with five objects, and when shown a square with 5 objects she could tap the digit 5. Her education was reward-driven: whenever she got a computer task correct, a tube by the computer dispensed a piece of food.

Once Ai had mastered the cardinality of the digits from 1 to 9, Matsuzawa introduced tasks to teach her how they were ordered. His tests flashed digits up on the screen and Ai had to tap them in ascending order. If the screen showed 4 and 2, she had to touch 2 and then 4 to win her cube of apple. She grasped this pretty quickly. Ai’s competence in both the cardinality and the ordinality tasks meant that Matsuzawa could reasonably say his student had learned to count. The achievement made her a national hero in Japan and a global icon for her species.

Matsuzawa then introduced to Ai the concept of zero. She picked up the cardinality of the symbol 0 easily. Whenever a square appeared on the screen with nothing in it she would tap the digit. Then Matsuzawa wanted to see if she was able to infer an understanding of the ordinality of zero. Ai was shown a random sequence of screens with two digits, just as when she was learning the ordinality of 1 to 9, although now sometimes one of the digits was a 0. Where did she think zero’s place was in the ordering of numbers?In the first session Ai placed 0 between 6 and 7. In subsequent sessions her positioning of 0 went under 6, then under 5, then under 4 and after a few hundred trials, 0 was down to around 1. She remained confused, however, about whether 0 was more or less than 1. Even though Ai had learned to manipulate numbers perfectly well, she lacked human depth of understanding.

A habit she did learn, however, was showmanship. She is now a total pro, tending to perform better at her computer tasks in front of visitors, especially camera crews."

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