Wednesday, February 11, 2009
PERNAH mempelajari Matematik? Tentu, dan pada sesetengah daripada kita mendapati Matematik adalah subjek yang membosan dan merunsingkan. Apatah lagi kepada para pelajar yang mengambil mata pelajaran Matematik Tambahan.
Namun begitu, tanpa Matematik agak sukar pula bagi remaja kita untuk meloloskan diri ke menara gading. Akibatnya, belajar matematik membebankan tetapi perlu pula sekurang-kurangnya lulus di dalam peperiksaan untuk ke hadapan.
Umum mengetahui kepentingan Matematik kepada seseorang. Malah kepentingan Matematik yang telah berakar umbi dalam tamadun manusia. Tetapi, usaha seorang Profesor Matematik kelahiran Rio de Janeiro telah mengubah persepsi orang ramai terhadap Matematik. Beliau telah memperkenalkan satu sistem pendidikan baru di dalam menerangkan konsep-konsep dalam Matematik, iaitu dengan menggunakan pendekatan sejarah melalui hikayat yang amat menarik. Maka lahirlah salah-satu karyanya yang hebat bertajuk The Man Who Counted. Yang lebih menarik, penulisnya sendiri yang melahirkan pengarang buku tersebut yang lebih terkenal daripada namanya sendiri, yang dikenali sebagai Malba Tahan. Beliau tidak menggunakan nama sebenarnya, iaitu Julio Cesar de Mello, seorang Profesor Matematik di Rio de Janeiro Education Institute, sebaliknya nama Malba Tahan lebih menonjol.
Jalan ceritanya yang bermula dengan pengembaraan Beremiz Samir, yang telah menggunakan kepandaiannya di dalam menyelesaikan masalah dengan menggunakan matematik. Sepanjang perjalanan beliau bersama seorang sahabat, Hanak Tade Maia, telah menyelesaikan beberapa masalah yang menimpa penduduk setempat. Misalnya, masalah perebutan unta sebanyak 35 ekor yang perlu dibahagikan kepada 3 orang adik-beradik yang mengikut wasiat ayahnya, separuh daripada unta itu perlu diberikan kepada abang yang sulung, 1/3 kepada adik keduanya dan 1/9 diberikan kepada yang bongsu.
Jika diikutkan logik fikir, ia langsung tidak dapat dibahagikan secara adil. Jika separuh daripada 35 ekor ialah 17 ½, maka apatah lagi jika dibahagikan kepada 1/3 dan 1/9 yang mustahil untuk didapatkan nombor yang tunggal. Maka di sinilah kebijaksanaan penulisnya. Si hero, Beremiz telah menambah seekor lagi unta, iaitu tunggangannya, menjadikan jumlah 36 ekor.
Dan dari jumlah 36 ekor itu, ½ daripadanya diberikan kepada yang sulung iaitu sejumlah 18 ekor. Yang keduanya, 1/3 daripada 36 ekor, 12 ekor unta diberikan kepadanya, dan si bongsu mendapat habuannya 1/9 daripada 36, iaitu 4 ekor. Apabila ditambahkan semua jumlah itu (18 + 12 + 4) menjadikan ia sejumlah 34 ekor unta. Terlebih 2 ekor unta! Dan si Beremiz mendapat habuan seekor lagi unta tunggangannya.
Di sinilah letaknya kehebatan penulis yang menyelesaikan masalah Matematik dengan logik ‘benar’, dan bukan sekadar ‘logik Matematik’. Buku ini menarik untuk dibaca sebagai salah satu kaedah menyelesaikan masalah masyarakat, yang rata-ratanya berkisar kepada masalah wang, kepuasan hidup, keadilan dan sebagainya.
Tidak mustahil kepada seseorang ahli Matematik yang melihat situasi ini sebagai satu cabaran bagi beliau untuk cuba menyelesaikan permasalahan itu dengan ‘logik benar’ Matematik. Matematik telah lama terbukti sebagai salah-satu penyelesai masalah manusia. Komputer sendiri adalah hasil daripada keajaiban Matematik itu. Cuma, masyarakat kita kurang ‘menggemari’ Matematik, mungkin disebabkan oleh kaedah pengajaran yang kaku dan membosankan. Matematik perlu diajar dan dibaca sepertimana seseorang gemar membaca novel cinta.
Julio Cesar telah membuktikan bahawa kaedahnya adalah antara yang terbaik dan terbukti kepada tiga generasi selepasnya, bahawa Matematik juga adalah satu seni dan perlu dibaca!
Posted by dyana_tahar at 9:58 PM
Thursday, January 8, 2009
The parents of a six-year-old boy in the US have been charged with neglect after the boy drove their car for 10km in an attempt to get to school on time.
Police in Virginia said the boy, who was not named, took the keys to the car after he missed the school bus.
He drove for six miles (10km) on major roads, weaving through traffic and overtaking slower cars, before losing control and going off the road.
The boy told police he learned to drive by playing video games.
Police said the boy was so intent on getting to school after failing to make the bus, that he got the keys to his father's Ford Taurus and took the wheel himself.
"When he got out of the car, he started walking to school. He did not want to miss breakfast and PE," said Northumberland County Sheriff Chuck Wilkins.
His road trip came to an end only after he ran off the road several times before hitting an embankment and utility pole. He was not, police said, wearing a seat belt.
He was treated for minor injuries at a hospital before police took him to school.
It happened at 0740 on Monday, while the boy's mother was still asleep.
Both of his parents have been charged with endangering their child. He and his four-year-old brother are now in protective custody.
Posted by dyana_tahar at 8:28 PM
Wednesday, January 7, 2009
Copyright Prakken Publications, Inc. Jan 2008
THROUGHOUT the United States, initiatives are being launched to extend the school day, increase homework, integrate technology, and require more high-stakes testing. The underlying assumption is that more time in school, more homework, more technology, and more high-stakes testing will produce smarter, better-prepared students.
To realize the ideal of an educated, productive citizenry, however, many countries around the world are employing radically different approaches. Instead of executing a strategy of more and more, some have decided to educate their young people by doing less.
Because the test scores of students from these countries routinely eclipse the scores of American students in two international comparisons of student achievement-Trends in International Math and Science Study (TIMSS) and Programme of International Student Achievement (PISA)-an investigation of educational practices in higher-achieving countries might prove instructive. Four areas where the policy and practice in high-achieving countries run counter to current practice and policy in the U.S. are: (1) time spent at school, (2) homework, (3) technology, and (4) schools as agents of social change.
Time Spent in School
Students in public schools in most countries in Western Europe, Canada, Mexico, Korea, Japan, and Singapore-all members of the Organisation for Economic Co-operation and Development (OECD)-spend an average of 701 hours per year in school. In Finland, where students have scored near the top in comparisons of achievement for a number of years, students spend only 600 hours in school.
In the United States, by contrast, children go to school for six or more hours per day, five days per week, for approximately 185 days spread over a period of 9 or 10 months. The average time spent at school in the U.S. totals over 1,100 hours, almost double that of children in Finland.
By the time children reach the age of 14 in Finland, they will have gone to school for 2,500 fewer hours than students in America (the equivalent of two to four years of schooling). Despite much longer school days, American students routinely score 10 percent to 20 percent lower than Finnish students on international tests.
Studies have repeatedly found no correlation between time spent at school and levels of achievement. Of course, as any teacher in American public schools can attest, time is often wasted on performing nonteaching tasks, organizing paperwork, maintaining discipline, and keeping students "busy."
Some of the more prestigious private secondary schools in America schedule classes in the fashion of universities-90-minute periods that meet twice each week, with one day a week set aside for advising and one-on-one tutoring. If such a schedule were adopted in public high schools, total instructional hours in America would dropsharply.
But such a transformation would mean a departure from the traditional schedule and a retreat from the daily array of "professional development opportunities" such as hall duty, lunch supervision, bus detail, parking lot patrol, and detention hall supervision.
America also leads the world in assigning homework-a whopping 140 minutes per week in mathematics for secondary students. Despite this extra workload, American students post mediocre scores on math tests.
For example, the average score for an eighth grade American student on the mathematics portion of the TIMSS in 2003 was 502. In contrast, the average Korean eighthgrader scored 584. While many may suppose that Korean teachers require more from their students, in actuality, Korean teachers assign 20 minutes less homework per week than their American counterparts.
Time spent doing homework will be unconnected to academic achievement if the time is not spent productively. Because most American teachers assign worksheets and exercises from textbooks for homework, a student's level of engagement working at home may be less than optimal.
Although much has been written about academic learning time (the time students are genuinely engaged in learning), many teachers are more concerned with "keeping up" than with making learning interesting or relevant. Obviously, as teacher salaries are increasingly tied to students' performance on tests, the urge to "cover the curriculum" to be tested is understandable. However, lack of engagement inevitably leads to apathy, frustration, and boredom.
In examining homework policies around the world, researchers have concluded, "The relationship between national patterns of homework and national achievement suggests that... more homework may actually undermine national achievement."
A study of the integration of technology into American classrooms reveals that claims for new paths to achievement come as a matter of course with the development of new machines. In the past, some researchers have claimed academic gains associated with the use of film, radio, the tape recorder, videotape, television, even the overhead projector. After the novelty of a machine fades, so do claims that it will yield dramatic gains in achievement.
Yet many schools in America have spent billions of dollars under the illusion that providing access to computers and the Internet would enhance achievement. While the knowledge available via the Internet is vast, schools must restrict access because too many Web sites feature pornography, ultraviolent images, or other unsuitable material. As a result, computers have taken on the role formerly occupied by encyclopedias-a storehouse of concise, neatly categorized information used once or twice per year for research.
Years ago, some high schools and universities began requiring students to come to class with lap-tops, believing that laptops would enhance achievement. These same schools and universities have stopped requiring laptops because no evidence has surfaced to substantiate that they made any difference.
In the 2003 administration of PISA-across categories of race, gender, and nationality-the factor most strongly associated with high scores on reading, problem solving, and mathematics was the number of books to which a student had access. Unfortunately, in most American schools today
* Students are often forbidden to take books (even textbooks) home.
* If students are allowed to take books home, no more than one may be checked out of the library and only for a short duration.
* Books should be used with care (students may not write in them).
School libraries have morphed into multifunctional media centers, and budgets for print materials have been reduced to keep the computers running. Although school libraries might serve as the sole access point for books, libraries in high-poverty urban and rural areas may have precious few books to lend.
In addition, school libraries in America usually close after the dismissal bell, so students, parents, and members of the community have no time to browse the shelves.
In most OECD countries, books are not treated as artifacts but are given to students to use as they wish. They can take them home, share them, even scribble notes in the margins without penalty.
Schools as Agents of Social Change
Perhaps only in America could standardized testing be considered an antidote to the social problems of the poor and disenfranchised. But No Child Left Behind gained widespread, bipartisan political support by using precisely this logic.
While our federal and state governments have focused on setting curricular standards, specifying performance outcomes, and integrating technology, other countries have taken a broader approach to social problems. Research substantiates that differences in academic achievement are more attributable to differences in social background than to variations in standardized testing.
On international achievement tests, more than one in four American students score at the lowest possible level. In Korea, only 9.6 percent of students score at the lowest tier; in Finland, only 6.8 percent.
The poverty rate in Finland is 5 percent, in Korea it is 15 percent, and in America, it is 12 percent. We can infer that America not only is doing an inadequate job of educating students in poverty but also is failing with significant numbers of the nonpoor.
In recent decades, underachievement in America has been wholly perceived as a "school problem," and solutions have focused solely on interactions with students during school hours. The latest thinking in the U.S. has not been directed toward creating more familyfriendly policies (such as the Canadian and European tax incentives for stay-at-home parents) or broader social initiatives, but toward putting in place more rigorous and frequent testing.
Over the past 50 years, the initiatives of an extended school day, more homework, increased technology, and vigorous standardized testing have done little to enhance achievement, promote positive attitudes, or foster good citizenship. Perhaps it is time to learn from the world, to stop thinking in terms of more and consider what might be achieved by doing less.
by Lawrence Baines, a professor of education, University of Toledo, Toledo, OH. Condensed from Phi Delta Kappan, 89 (October 2007), 98-100. Published by Phi Delta Kappan International, Inc., Bloomington, IN.
Posted by dyana_tahar at 8:58 PM