ALL ABOUT EDUCATING MATHEMATICS

The Six Pillars of Character®

2011-07-30T07:53:00.000-07:00

The CHARACTER COUNTS! approach to character education doesn't exclude anyone. That's why we base our programs and materials on six ethical values that everyone can agree on — values that are not political, religious, or culturally biased. Use the points below to help young people understand the Six Pillars, and use the mnemonic devices at right to help them remember.
For a more detailed discussion of the Six Pillars, consult our book, Making Ethical Decisions, reprinted in part here .

Trustworthiness

Be honest • Don’t deceive, cheat, or steal • Be reliable — do what you say you’ll do • Have the courage to do the right thing • Build a good reputation • Be loyal — stand by your family, friends, and country

Respect

Treat others with respect; follow the Golden Rule • Be tolerant and accepting of differences • Use good manners, not bad language • Be considerate of the feelings of others • Don’t threaten, hit or hurt anyone • Deal peacefully with anger, insults, and disagreements

Responsibility

Do what you are supposed to do • Plan ahead • Persevere: keep on trying! • Always do your best • Use self-control • Be self-disciplined • Think before you act — consider the consequences • Be accountable for your words, actions, and attitudes • Set a good example for others

Fairness

Play by the rules • Take turns and share • Be open-minded; listen to others • Don’t take advantage of others • Don’t blame others carelessly • Treat all people fairly

Caring

Be kind • Be compassionate and show you care • Express gratitude • Forgive others • Help people in need

Citizenship

Do your share to make your school and community better • Cooperate • Get involved in community affairs • Stay informed; vote • Be a good neighbor • Obey laws and rules • Respect authority • Protect the environment • Volunteer

Source : charactercounts.org

Kissing, Necking, Petting, dan Intercourse

2011-07-30T07:22:00.000-07:00

Pernah dengar istilah-istilah itu?
Kissing = Berciuman biasanya identik dengan ciuman di bibir (cium tangan orang tua dan cium di jidat dari orangtua tidak termasuk). Cipika-cipiki (cium pipi kanan- cium pipi kiri), sampai french kiss.

Necking = Secara bahasa artinya berpelukan (bukan pelukan kemenangan para pemain olahraga, bukan pelukan saat sedih, bukan pelukan dari orangtua ke anak). Kata wikipedia tidak hanya terbatas pada leher. Jadi bisa saja sampai telinga dan sekitarnya.

Grinding = Saling menggesek-gesekkan tubuh dengan tekanan secara bersamaan di ddaerah rangsangan seksual dengan berpakaian (juga disebut dry humping).

Petting = Menyentuh dan memijat daerah rangsangan seksual dengan berpakaian (Rabaan atau petting). Menyentuh penis dan memijat daerah rangsangan seksual dibalik pakaian (petting kelas berat) (Wikipedia). Menggesek-gesekkan penis pada vagina tanpa memasukkan juga merupakan petting

Intercourse = Secara tradisional (biasanya) artinya hubungan seks ( masuknya penis pada vagina). Dalam perkembangannya ada berbagai macam intercourse (seks, anal, dll).

Kita tidak akan membahas tentang bagaimana proses terjadinya. Sudahkah melakukan minimal salah satu?
"janganlah mendekati zina..." nah ini kronologisnya (kecuali ada unsur paksaan dan kejahatan).

Pertama akan terjadi kissing. Biasanya tahap paling pertama dari apa yang disebut pacaran. masih adakah yang pacaran hanya berjalan berdua dengan pegangan tangan dan bercana tawa? Saat ini godaan yang paling berat sebenarnya ada di sini. Selama bisa menjaga untuk menghindari kissing maka tahap-tahap selanjutnya tidak akan terjadi. Kissing sering dijadikan alasan untuk mengetahui bahwa seseorang benar-benar sedang berpacaran.
Setelah beberapa hari atau bulan dalam tahap kissing biasanya rasa ingin tahu menyebabkan pasangan sering menggoda untuk melakukan lebih dari kissing. Mulailah pepindahan bibir. Biasanya hanya mendarat di sekitar wajah kali ini mulai mengubah arah sasaran. Sasaran paling empuk adalah leher. Kenapa leher? Karena leher mempunyai daya rangsang baik bagi pria maupun wanita (jangan coba sebelum menikah). Rasa geli yang ada saat leher dicium akan merambat ke bagian-bagian tubuh yang lain. Biasanya ke otak dan ke syaraf kemaluan. Ciuman-ciuman yang awalnya iseng menjadi kebiasaan yang kemudian ditolerir oleh pasangan. Kegiatan ini disebut necking. Mulai dari leher naik ke telinga atau berputar ke tengkuk merupakan jurus awal dalam melakukan necking. Saat pasangan mulai terlenan dengan kebiasaan ciuman di sekeliling leher, tangan mulai beraksi dengan meraba-raba bagian tubuh. Mulai dari rambut(biasanya dari awal sudah dilakukan), semakin turun-semakin turun hingga melewati leher.
Saat mulai ada keinginan untuk melakukan necking seharusnya menjadi sirene tanda bahaya bahwa gaya pacaran yang dijalani sudah mulai TIDAK SEHAT (kecuali pacaran setelah menikah). Saat itu kedua orang yang berhubungan harus menyadari arah dari hubungan yang dibangun. Jangan sampai ada penyesalan setelah semuanya terjadi. Perlu pemikiran yang matang dan banyak sekali introspeksi dalam melanjutkan hubungan yang dibangun.

Seandainya secara sadar berkeras untuk melanjutkan apa yang telah dimulai hendaknya segera hubungi KUA terdekat. Paling tidak siapkan kondom untk berjaga-jaga selama beberapa bulan kedepan. Hal yang akan ditulis berikut hanya bertujuan sebagai peringatan dan tidak dianjurkan untuk dilakukan SEBELUM MENIKAH!!!

Apa yang terjadi saat necking? Tentunya saat itu berbagai rayuan maut telah dilancarkan seorang pria untuk merayu pasangan. Mulai dari rasa sayang, putus, mencoba hal baru, agar tidak kampungan, dll (anda bisa mengetahuinya). Seandainya memang belum cukup mapan dan belum mantap sebaiknya jangan lakukan paling parah hanya patah hati beberapa hari lalu selesai. Daripada menyesal selamanya.
Tangan pasangan yang mulai bergerak menuju sasaran berikutnya akan membuat semuanya terlambat saat sudah mulai tersadar. Pertama leher, kemudian punggung, bergerak maju menuju salah satu kebanggaan dan kehormatan wanita yaitu payudara. Disini akan memakan waktu lama karena secara naluri pria sangat suka berlama-lama disana. Dari pertama necking sampai tahap selanjutnya dapat memakan waktu lama bisa juga sebentar. Namun saat seorang pria telah berhasil membobol payudara biasanya hampir setiap bertemu pasti akan disentuh. Jangan kaget dan menyesal. Hentikan saat masih bisa.
Grinding termasuk bagian dari petting. Pada saat pertama melakukan petting hanya coba-coba. Setelah itu akan ketagihan. Sex is like a drug. Seks itu seperti narkoba. Sekali mencoba akan ada keinginan untuk mencoba lagi. Saat sudah terbiasa melakukan akan ada rasa hampa saat tidak melakukannya dan tidak ada rasa puas saat melakukannya. Hampa. Bukan karena seks itu membosankan tapi makna dari hubungan seks telah hilang. Petting yang semula hanya bumbu justru menjadikan hubungan terasa hambar. Akibatnya tentu dapat diprediksi. Jika saat pertama melakukan hanya dry humping dengan masih berpakaian maka akan berlanjut menjadi heavy petting. Saat ini telah ada resiko kehamilan.
Jangan pernah termakan omongan bahwa petting tidak bisa menyebabkan kehamilan. Selalu ada resiko kehamilan saat sperma bermain dengan sel telur. Contohnya : jika tangan yang tanpa sengaja terkena sperma lalu digunakan untuk menggosok vagina maka sperma dapat ikut masuk dan mungkin bisa membuahi sel telur.
Kalau petting saja bisa menimbulkan kehamilan, maka tidak perlu ditanyakan apakah intercourse bisa menyebabkannya. Kecuali ada masalah dengan kondisi badan maka intercourse adalah awal dari adanya manusia (kecuali Adam dan Hawa). Apa dianggap anak manusia berasal dari batu atau burung bangau yang membawa bayi dari entah dimana? Tidak.
Manusia berasal dari bertemunya sel sperma dan sel telur. Cara alami dan paling umum adalah intercourse (kawin suntik/kloning tidak termasuk). Tahap puncak dari hubungan seks adalah intercourse. Secara tradisional intercourse digunakan untuk meneruskan keturunan. Saat ini intercourse digunakan untuk berbagai tujuan. Bahkan ada penelitian yang mengatakan seks baik untuk kesehatan.
Seks yang pada lalu menjadi makna bagi intercourse yaitu masuknya penis pada vagina telah mengalami perubahan seiring dengan berjalannya waktu. Saat ini proses seksual dapat dikatakan mulai dari kegiatan mencium pasangan hingga "silaturahmi kelamin". Jadi saat berciuman sebenarnya kita telah melakukan hubungan seks. Hanya saja kissing merupakan aktifitas seks paling ringan tetapi juga paling berbahaya karena semua bermula dari Kissing.

Setelah membaca dan memahami apa yang ditulis diharapkan pemahaman dan kesadaran akan seks meningkat. Hal ini perlu agar berbagai kasus aborsi tidak terjadi di Negara ini. Sudahkah melakukan salah satu atau beberapa kegiatan diatas? Hentikan segera jika belum siap untuk berkomitmen.

Penyakit Menular Seksual

2011-07-30T07:21:00.000-07:00

Penyakit menular seksual adalah penyakit yang menyerang manusia dan binatang melalui transmisi hubungan seksual, seks oral dan seks anal. Kata penyakit menular seksual semakin banyak digunakan, karena memiliki cakupan pada arti' orang yang mungkin terinfeksi, dan mungkin mengeinfeksi orang lain dengan tanda-tanda kemunculan penyakit. Penyakit menular seksual juga dapat ditularkan melalui jarum suntik dan juga kelahiran dan menyusui. Infeksi penyakit menular seksual telah diketahui selama ratusan tahun. (wikipedia)

Berikut ini akan dipaparkan sepuluh faktor resiko teratas yang berpengaruh pada peluang Anda terkena PMS.

1. Seks tanpa pelindung
Meski kondom tidak seratus persen melindungi Anda, ia tetap merupakan cara terbaik untuk menghindarkan Anda dari infeksi. Penggunaan kondom dapat menurunkan laju penularan PMS. Selain selibat, penggunaan kondom yang konsisten adalah proteksi terbaik terhadap PMS. Biasakanlah memakai kondom.
2. Berganti-ganti pasangan
Anda tidak perlu belajar matematika untuk mengetahui bahwa semakin banyak pasangan seksual Anda, kian besar kemungkinan Anda terekspos suatu PMS. Apalagi, orang yang suka berganti pasangan cenderung memilih pasangan yang suka berganti pasangan pula. Jadi, Anda tidak lepas dari pasangan-pasangannya pasangan Anda.
3. Mulai aktif secara seksual pada usia dini
Kaum muda lebih besar kemungkinannya untuk terkena PMS daripada orang yang lebih tua. Ada beberapa alasannya, yaitu wanita muda khususnya lebih rentan terhadap PMS karena tubuh mereka lebih kecil dan belum berkembang sempurna sehingga lebih mudah terinfeksi. Kaum muda juga tampaknya lebih jarang pakai kondom, terlibat perilaku seksual beresiko dan berganti-ganti pasangan.
4. Pengggunaan alkohol
Konsumsi alkohol dapat berpengaruh terhadap kesehatan seksual. Orang yang biasa minum alkohol bisa jadi kurang selektif memilih pasangan seksual dan menurunkan batasan. Alkohol dapat membuat seseorang sukar memakai kondom dengan benar maupun sulit meminta pasangannya menggunakan kondom.
5. Penyalahgunaan obat
Prinsipnya mirip dengan alkohol, orang yang berhubungan seksual di bawah pengaruh obat lebih besar kemungkinannya melakukan perilaku seksual beresiko/tanpa pelindung. Pemakaian obat terlarang juga memudahkan orang lain memaksa seseorang melakukan perilaku seksual yang dalam keadaan sadar tidak akan dilakukan. Penggunaan obat dengan jarum suntik diasosiasikan dengan peningkatan resiko penularan penyakit lewat darah, seperti hepatitis dan HIV, yang juga bisa ditransmisikan lewat seks.
6. Seks untuk uang/obat
Orang yang menjual seks untuk mendapatkan sesuatu posisi tawarnya rendah sehingga sulit baginya untuk menegosiasikan hubungan seksual yang aman. Kemudian, pasangan (pembeli jasa) memiliki resiko terinfeksi PMS yang lebih besar. Jadi, baik pembeli maupun penjual sama-sama dirugikan.
7. Hidup di masyarakat yang prevalensi PMS-nya tinggi
Ketika seseorang tinggal di tengah komunitas dengan prevalensi PMS yang tinggi, ketika berhubungan seksual (dengan orang di komunitas itu) ia lebih rentan terinfeksi PMS.
8. Monogami serial
Monogami serial adalah mengencani/menikahi satu orang saja pada suatu masa, tapi kalau diakumulasi jumlah orang yang dikencani/dinikahi juga banyak. Contoh gampangnya (yang juga banyak terjadi di masyarakat kita) adalah orang yang doyan kawin-cerai. Perilaku begini juga berbahaya, sebab orang yang mempraktekkan monogami serial berpikir bahwa mereka saat itu memiliki hubungan eksklusif sehingga akan tergoda untuk berhenti menggunakan pelindung ketika berhubungan seksual. Sebenarnya monogami memang efektif mencegah PMS, tapi hanya pada monogami jangka panjang yang kedua pasangan sudah dites kesehatan reproduksi.
9. Sudah terkena suatu PMS
Kalau Anda sudah pernah berkenalan langsung dengan suatu PMS (apalagi sering), Anda lebih rentan terinfeksi PMS jenis lainnya. Iritasi atau lepuh pada kulit yang terinfeksi dapat menjadi jalan masuk patogen lain untuk menginfeksi. Karena Anda sudah pernah terinfeksi sekali, bisa jadi ada faktor tertentu dalam gaya hidup Anda yang beresiko.
10. Cuma pakai pil KB untuk kontrasepsi
Kadang orang lebih menghindari kehamilan daripada PMS sehingga mereka memilih pil KB sebagai alat kontrasepsi utama. Karena sudah merasa terhindar dari kehamilan, mereka enggan memakai kondom. Ini bisa terjadi ketika orang tidak ingin menuduh pasangannya berpenyakit (sehingga perlu disuruh pakai kondom) atau memang tidak suka pakai kondom dan menjadikan pil KB sebagai alasan. Yang jelas, perlindungan ganda (pil KB dan kondom) adalah pilihan terbaik…meski tidak semua orang melakukannya.

resep.web.id

Siapa Aku

2009-03-16T20:39:00.000-07:00

Setelah semua yang terjadi ternyata keberadaanku tetaplah maya. Eksistensi yang selama ini ku kira adalah diriku ternyata semu. Apakah aku? Siapakah diriku? Semakin kupahami diriku semakin samar keberadaanku. Apakah sebenarnya yang dapat menjelaskan keberadaanku? Apakah aku ada karena aku berpikir? Cogito ergo sum ? Ataukah aku sebenarnya tidak ada?
Berbagai pertanyaan yang aku mampu tanyakan. Apakah jawabnya? Apakah aku harus bertanya pada Orangtua Berambut Putih? Apakah dia cukup tahu tentang diriku? Ataukah aku yang harus mencarinya?
Kata Bapakku : Hanifan : Lurus maknanya orang itu harus lurus sesuai dengan aturan yang telah di tetapkan oleh agama. Jadilah anak yang berbakti pada orangtua, agama dan masyarakat.
Mong :Harimau maknanya sebagai seorang yang kuat di tengah rimba hidup. Tegar, tegas dan berpendirian.
Anggero:Mengaum maknanya berani mengutarakan kebenaran dengan lantang. Bahwa yang benar itu benar dan yang salah itu salah.
Kata Ibuku : Kamu anak satu-satunya dan sudah dibiayai untuk belajar sengan segala kekuatan maka mau tidak mau harus berhasil.
Kata Tunanganku : Kamu adalah masa depanku, segala harapanku ada padamu. Berusahalah mencapai cita-citamu sebelum kamu mengajakku pulang. Tanggung jawabmu untuk menafkahiku dan anak-anakmu!

lalu, siapa sebenarnya aku?

We Will Not Go Down Gaza - Michael Heart

2009-03-12T05:09:00.000-07:00

WE WILL NOT GO DOWN (Song for Gaza)

(Composed by Michael Heart)

Copyright 2009

Versi Terjemahan Bahasa Indonesia secara bebas a la penggemarsetia

Kilau cahaya putih yang membutakan

Menyerang langit gaza malam ini

Orang-orang berlari mencari perlindungan

Tanpa tahu apakah mereka mati atau hidup

Mereka datang dengan tank-tank dan pesawat-pesawat

Dalam kobarang api yang membinasakan

Dan tak ada yang tersisa

Hanya suara yang berteriak dalam kabut

Kita tidak akan kalah

Di malam hari, tanpa perlawanan

Kamu(israel) bisa membakar masjid kami dan rumah kami dan sekolah kami

Tapi semangat kami tidak akan pernah mati

Kami tidak akan kalah

Di Gaza malam ini

Tanpa peduli, wanita dan anak-anak

Dibunuh dan dibantai malam demi malam

Sementara pemimpin terkenal dari negara yang jauh

Berdebat tentang siapa yang salah atau siapa yang benar

Tapi kata-kata lemah mereka tak berguna

Dan bom-bom tetap berjatuhan bagai hujan asam

Tapi dibalik airmata dan darah dan rasa sakit

Kalian masih dapat mendengar suara dibalik kabut

Setelah tahu lirik seperti ini, siapa yang tidak terbakar hatinya?

Bukan lagi masalah muslim dan yahudi, masalah ini adalah antara keadilan dan kejahatan.

Apa yang dilakukan warga Gaza?

Anak-anak itu? Orang tua itu?

A little secret of keys

2009-01-28T08:19:00.000-08:00

Do you ever fell confused when doing an equations and don't have equations editor in your program?
May be this post can help.
shortcut to create square

a² alt +2+5+3 = kuadrat ( square)

find out your self, don't fear to try!!!

make square in blogger or blogspot
membuat tanda kuadrat dan pangkat lainnya di blogspot, blogger

How To Teach Mathematics II

2008-12-30T10:42:00.000-08:00

When looking to teach maths, sometimes you are faced with a complex curriculum which outlines various ways to manipulate numbers – these are not as easy to understand as the writers think – thus the following list outlines the ways to find your way through the maze!

Number Skills

Sorting- objects sharing a common attribute are grouped together.
One-to-one correspondence – this is necessary before counting can begin.
Counting- matching number names in one-to-one correspondence to a set of object.
Ordinality- ordering according to position
Cardinality- identifying sets that is the same number of members.
Conservation- recognizing that number is conserved whatever the arrangement of the members of the set.
Symbol recognition- recognising the abstract number symbol and relating them to the sound of the number words.
Place value- the position of a digit indicates its value, for example, 7, 73 and 741 each assign a different value to the digit 7.
Number operations
Addition- counting on from an identified point
Subtraction- taking away object from a set
- Working out the difference between 2 sets
Multiplication- adding equal sets (2+2+2=)
- enlargement (2,4,6,8,10)
- arrays e.g. 2 types of bread = 6 types of
3 types of fixing sandwich

Division- sharing amounts equally between a given number of sets.

Division- establishing how many sets of a given number can be made
There are 6 fish
(e.g. how many cats can have 3 fish each? )
Fractional parts-
1/3 can represent:
- one whole divided into there parts
- a share of a number that is divisible by three
- a share of a number less than three
- a share of a number not divisible by three
- a share of three
- a share of a number less than one

ALGEBRA- a generalisation of numerical relationships

Number patterns- portrayed numerically, algebraically and geometrically
e.g. patterns of number bonds
Patterns in place value
Patterns of multiplication and division
Patterns of equivalence and specific number patterns
Manipulation of unknown quantities.
- use of letters and symbols
- use of graphs and co-ordinates

Bibliography

How to teach maths by Stephanie C Mills 2008

Myers - Briggs Type Indicator INTRODUCTION!

2008-09-03T05:45:00.000-07:00

Understanding one's temperament is a central part of any personal development. The purpose of this site is to give a detailed explanation about one of the most popular and influental psychological methodology known nowadays.

When Katharine Briggs and her daughter Isabel Myers designed Myers-Briggs Type Indicator(MBTI), they took Jungian typology as the basis. Here you will find some facts about Carl Jung, as well as the most important chapter of his book "Psychological types". Jung used 3 scales to measure people.

The first one was (E)xtroversion vs. (I)ntroversion. This stands how people prefer to focus their attention(interest) and get/spend energy. In the extraverted attitude the energy flow is outward, and the preferred focus is on people and things, whereas in the introverted attitude the energy flow is inward, and the preferred focus is on inner thoughts and ideas.
(S)ensing vs. i(N)tuition. Sensing and Intuition are the perceiving functions. They indicate how a person prefers to receive data from the environment around him. These are the nonrational functions, as a person does not necessarily have control over receiving data, but only how to process it once they have it. Sensing prefers to receive data primarily from the five senses(sight, hearing, taste, smell, touch), and intuition prefers to receive data from the unconscious, or seeing relationships via insights. Often it is called "sixth sense" or "gut feel".
(T)hinking vs. (F)eeling. Thinking and Feeling are the rational functions. They are used to make rational decisions concerning the data they received from their perceiving functions, above. Thinking is characterized as preferring to being logical, analytical and thinking in terms of "true or false". Thinking decisions tend to be based on more objective criteria and facts. Feeling, which refers to subjective criteria and values, strives for harmonious relationships and considers the implications for people. Feeling decisions tend to be based on what seems "more good or less bad" according to values.
And the 4th scale even it could be met in the Jungian works was truly added by Myers-Briggs team. (J)udging vs. (P)erceiving. It shows how people relate to the world around them. The J person tends to prefer to create and live in an ordered environment. Words like "structured" and "controlled" come to mind. Js tend to "plan their work and work their plan." They often come across as "decisive". The P individual tends to prefer a flexible, wait-and-see environment. Words like "spontaneous" and "adaptable" and "open-minded" best describe him or her.

All these scales explained above, describe contrasting preferences. Practically it is hard to find someone that is extrovert or thinking to the absolute extreme. He/she could be 80% thinking and 20% feeling type and usually one of the preferences is dominant. So using MBTI short-hand, we can describe people by their expressed preferences: ISFJ, ENTP, and so on. There are 16 different combinations of letters - giving us the 16 different "psychological types".

From : E-MBTI.com

Proof by Intimidation

2008-08-10T11:59:00.000-07:00

Proof by intimidation is a jocular term used mainly in mathematics to refer to mathematical proofs which are so complex, so long-winded and so poorly presented by the authors that others are simply forced to accept it, lest they be forced to sift through its minute details. The term is also used when the author is an authority in his field presenting his proof to people who respect a priori his insistence that the proof is valid or when the author claims that his statement is true because it is trivial or because he simply says so. Usage of this term is for the most part in good humour, though it also appears in serious criticism. More generally, "proof by intimidation" has also been used by critics of junk science to describe cases in which scientific evidence is thrown aside in favour of a litany of tragic individual cases presented to the public by articulate advocates who pose as experts in their field.

Gian-Carlo Rota claimed in a memoir that the term 'proof by intimidation' was coined by Mark Kac to describe a technique used by William Feller in his lectures

taken from Wikipedia.com

Mock Mathematics

2008-08-10T11:40:00.000-07:00

A form of mathematical humor comes from using mathematical tools (both abstract symbols and physical objects such as calculators) in various ways which transgress their intended ambit. These constructions are generally devoid of any "real" mathematics, besides some basic arithmetic.

Mock mathematical reasoning

A set of equivocal jokes applies mathematical reasoning to situations where it is not entirely valid. Many of these are based on a combination of well-known quotes and basic logical constructs such as syllogisms:

Example:

Premise I:	Knowledge is power.
Premise II:	Power corrupts.
Conclusion:	Therefore, knowledge corrupts.

This is used to demonstrate that studying causes one to fail.

Study = No fail	No Study=Fail
Study + No Study = Fail + No Fail
Study (1 +No) = Fail (1+No)
Study ~~(1 +No)~~ = Fail ~~(1+No)~~
Study = Fail

There are also a number of joke proofs, such as the proof that women are evil:

Women are the product of time and money:	women = time × money
Time is money:	time = money
So women are money squared:	women = money²
Money is the root of all evil:	money = √evil
So women are absolutely evil:	women = (√evil)² = abs(evil)

Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:

Examples:

That is, the limit as x goes to 8 from above is a sideways 8 or the infinity sign, in the same way that the limit as x goes to three from above is a sideways 3 or the Greek letter omega.

(That is, the "n" in "sin" cancels with the "n" in the denominator, giving "six" and 1 respectively.) See also Anomalous cancellation.

taken from Wikipedia.com

Stereotypes of Mathematicians

2008-08-10T11:14:00.001-07:00

Some jokes are based on stereotypes of mathematicians tending to think in complicated, abstract terms, causing them to lose touch with the "real world".

Many of these jokes compare mathematicians to other professions, typically physicists, engineers, or the "soft" sciences in a form similar to those which begin "An Englishman, an Irishman and a Scotsman…" or the like. The joke generally shows the other scientist doing something practical, while the mathematician does something less useful such as making the necessary calculation but not performing the implied action.

Examples:

A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space. "How did you like it?" the mathematician wants to know after the talk. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?" "Well, it's not even difficult. All I do is visualize the situation in n-dimensional space and then set n = 13."

A mathematician, a biologist and a physicist are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty."

An example of a joke relying on mathematicians' propensity for not taking the implied action is as follows:

A mathematician, an engineer and a chemist are at a conference. They are staying in adjoining rooms. One evening they are downstairs in the bar. The mathematician goes to bed first. The chemist goes next, followed a minute or two later by the engineer. The chemist notices that in the corridor outside their rooms a rubbish bin is ablaze. There is a bucket of water nearby. The chemist starts concocting a means of generating carbon dioxide in order to create a makeshift extinguisher but before he can do so the engineer arrives, dumps the water on the fire and puts it out. The next morning the chemist and engineer tell the mathematician about the fire. He admits he saw it. They ask him why he didn't put it out. He replies contemptuously "there was a fire and a bucket of water: a solution obviously existed."

Mathematicians are also shown as averse to making sweeping generalizations from a small amount of data, preferring instead to state only that which can be logically deduced from the given information – even if some form of generalization seems plausible:

An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one field, containing at least one sheep, at least one side of which appears black from here."

A variant has the punchline "No," says the mathematician, "all we can say is that there is at least half of a black sheep in Scotland." Another variant with cows was featured in the book The Curious Incident of the Dog in the Night-time by Mark Haddon.

Pure mathematicians are mainly concerned with the properties of the abstract systems under study, not their actual applications. However, such applications are sometimes found in mathematics itself, resulting in new insights as old problems are cast in new light. In striving not to miss such connections, mathematicians often see problems in novel (but theoretically valid) ways, which unfortunately are not always as illuminating as one could wish for:

A sociologist, a physicist and a mathematician are all given equal amounts of fencing, and are asked to enclose the greatest area. The sociologist pauses for a moment and decides to enclose a square area with his fence. The physicist, realizing he can fence off a greater amount of land with the same amount of fencing, promptly sets his fence in the form of a circle, and smiles. "I'd like to see you beat that!" he says to the mathematician. The mathematician, in response, takes a very small piece of his own fencing, and wraps it around himself, proclaiming, "I define my location to be outside of the fence!"

A small set of jokes involves only mathematicians, such as the following involving statisticians:

Three statisticians go duck hunting. Their dog chases out a duck and it starts to fly. The first statistician aims and takes his shot, and it misses a foot too high. The second statistician aims and takes his shot, and it misses a foot too low. The third statistician says, "We got him!"

The humor there is derived from the fact that the average of the shots hits the duck, and so it is dead.

An engineer and a physicist are in a hot-air balloon. After a few hours they lose track of where they are and descend to get directions. They yell to a jogger, "Hey, can you tell us where we're at?" After a few moments the jogger responds, "You're in a hot-air balloon." The engineer says, "You must be a mathematician." The jogger, shocked, responds, "yeah, how did you know I was a mathematician?" "Because, it took you far too long to come up with your answer, it was 100% correct, and it was completely useless."

taken from Wikipedia.com

Three is equal to four

2008-06-18T08:49:00.001-07:00

Theorem: 3=4
Proof:

Suppose:
a + b = c

This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c

After reorganizing:
4a + 4b - 4c = 3a + 3b - 3c

Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)

Remove the same term left and right:
4 = 3

One equal to one half

2008-06-18T08:45:00.000-07:00

Theorem: 1 = 1/2:
Proof:

We can re-write the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9)
+...

as 1/2((1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9) + ... ).
All terms after 1/1 cancel, so that the sum is 1/2.

We can also re-write the series as (1/1 - 2/3) + (2/3 - 3/5) + (3/5 - 4/7)
+ (4/7 - 5/9) + ...

All terms after 1/1 cancel, so that the sum is 1.

Thus 1/2 = 1.

Teachers Need More Knowledge of How Children Learn Mathematics

2008-06-18T08:31:00.000-07:00

by Constance Kamii

Teachers need as much scientific knowledge about how children learn mathematics as physicians have about the causes of illnesses. Because of this need, teacher-preparation programs must change. Specific examples from classrooms illustrate this need.

I once wondered why some first graders were getting such answers as 3 + 4 = 4 (*1+1=11). By watching them, I found out that they were putting three counters out for the first addend and then four for the second addend, including the three that were already out.

Errors of this kind result from prematurely teaching a rule to follow. According to this rule, one must put counters out for the first addend, more counters for the second addend, and count all of them to get the answer. This rule works for children who already know that addition is the joining of two sets that are disjoint. However, the rule is superfluous for those who have constructed this logic, and it causes errors for those who have not constructed it.

Another example of imposing a rule that is either superfluous or premature is teaching counting-on to children who are counting-all. Counting-all refers to solving 3 + 4 by counting out three counters, then four other counters, and counting all of them again ("one-two-three-four-five-six-seven"). In counting-on, by contrast, children say "four-five-six-seven."

With scientific research replicated worldwide, Piaget showed that all children construct, or create, logic and number concepts from within rather than learn them by internalization from the environment (Piaget 1971; Piaget and Szeminska 1965; Inhelder and Piaget 1964; and Kamii 2000). Studying the research leads teachers to understand that addition involves part-whole relationships, which are very hard for children to make and which cannot be taught through practice and memorization. To add two numbers, children must put two wholes together ("three" and "four," for example) to make a higher-order whole ("seven") in which the previous wholes become two parts. When young children cannot think simultaneously about a whole and two parts, they count-all by changing both the "three" and the "four" into ones. Making them count-on is harmful when they cannot mentally make the part-whole relationship necessary to count-on.

When teachers study Piaget's theory and replicate the aforementioned research, they can understand why some first graders cannot count-on. When children have constructed their logic sufficiently to make the part-whole relationship of counting-on, they give up counting-all, just as babies give up crawling when they can walk. I hope that the day will come when teachers entering the classroom and those already in the classroom have as much scientific knowledge about how children learn mathematics as physicians have about the causes of illnesses. To reach this vision, the teacher-preparation programs must change.

References

Inhelder, Barbel, and Jean Piaget. The Early Growth of Logic in the Child. New York: Harper & Row, 1964.

Kamii, Constance. Young Children Reinvent Arithmetic. 2nd ed. New York: Teachers College Press, 2000.

Piaget, Jean. Biology and Knowledge. Chicago: University of Chicago Press, 1971.

Piaget, Jean, and Alina Szeminska. The Child's Conception of Number. New York: W. W. Norton & Co., 1965.

Constance Kamii, ckamii@uab.edu, is a professor of early childhood education at the University of Alabama at Birmingham. She studied under Piaget for parts of fifteen years to become able to use his theory in early childhood education.

*in indonesia often happened

How to calculate square roots without a calculator

2008-06-18T08:27:00.000-07:00

Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

Finding square roots of of numbers that aren't perfect squares without a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect square numbers it lies between.

Solution:
3² = 9 and 4² = 16, so lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

http://www.math.com

The Advantages of Organic Food

2008-06-18T08:01:00.000-07:00

You Are What You Eat

Do you really know what goes into your food? Discover the advantages of organic food on this site and see exactly what producers have been adding to your fruit and vegetables to make it less healthy than a few years ago.

In the rush to produce more and more crops to satisfy growing demand producers have had to resort to using a lethal cocktail of pesticides to control disease and insect attack.

Good news for their bank balances perhaps but not good news for your health, this is why you need to be informed of the advantages of organic food.

Did you know that if you consumed an average apple you would be eating over 30 pesticides, even after you have washed it?

The quality of food has definitely gone down since the second world war. For instance, the levels of vitamin C in today's fruit bear no resemblance to the levels found in wartime fruit.

Organic food is known to contain 50% more nutrients, minerals and vitamins than produce that has been intensively farmed. Read more about this here.

You will have to eat more fruit nowadays to make up the deficiency, but unfortunately that means eating more chemicals, more detrimental affects on your health eating something that should be good for you!

Also don't forget about the cocktail of anti-biotics and hormones that cattle and poultry are force fed.

What happens to those chemicals when the animal dies?

Digested and stored in human bodies is the answer, have you seen pictures of animals in severly cramped conditions in battery farms?

It just does not make sense to state that any animal kept in these conditions is healthy and produces high quality food.

If you are as worried as I am about the health of your family then you need to read the articles on this and seriously consider converting your family to the organic lifestyle with the organic food information you are going to learn on this site.

Trust me, once you try some organic produce and taste an apple the way it should be, and perhaps how you recall it tasting in your youth, you will never go back to mass produced fruit again.

Sure there are issues with availability and cost but with a bit of research you should be able to find local stores who stock organic produce.

Also, don't forget about your local farmer, I'm sure you will be able to find one that has seen the light and opened up a farm shop to supply local residents.

You should be able to get some very keen prices from these shops, why not take a look around and see who is offering produce in your area?

Some more startling facts now. Pesticides in food have been linked to many diseases including:

Cancer
Obesity
Altzheimer's
Some birth defects

Not a nice list is it? There are probably others but if you think about it, how can it be okay for you to eat chemicals and not expect some form of reaction in your body. Our bodies are delicately balanced wonderful machines. Any form of foreign chemical is bound to cause irritation at the least.

Please take advantage of the organic food articles and information on this site and do consider taking a closer look at what you are eating. It's for your health after all!

Virginia Louise

www.organicfoodinfo.net

The Idea Of Gardening

2007-10-19T09:17:00.000-07:00

“In my garden there is a large place for sentiment. My garden of flowers is also my garden of thoughts and dreams. The thoughts grow as freely as the flowers, and the dreams are as beautiful.” - Abram L. Urban

A home flower garden is above all a place to create and dream. It is also a place to play, to work hard, and to rest, contemplating what human beings and nature can create by working together.

No matter the size of the garden plot you have to work with, your time and budget constraints, or your personality, you can design a flower garden that allows you to expressive your creativity, to get closer to nature, and to further enjoy being human.

Planning and setting up a flower garden may initially seem like a daunting task, but learning a few basics will set you firmly on the path to joy and beauty.

Flower Gardening Methods: How to Get Closer to Nature
“Gardening is any way that humans and nature come together with the intent of creating beauty.” - Tina James, 1999

There are two basic kinds of gardening methods. Unfortunately, the most common gardening done today uses chemical fertilizers, herbicides, and pesticides. These chemicals over the long run destroy helpful soil organisms and throw flowers and other plants out of their natural balance. This system of gardening focuses on treating plant diseases and pests without strengthening the plant’s immune system and is harmful to the environment. Sadly, today it is practiced by most commercial gardeners and farmers.

The other method is organic gardening, which works to create a natural balance in your flower garden. This approach considers your garden as a living ecosystem, and uses the laws of nature to produce healthy plants that are resistant to diseases and pests. Organic gardening focuses on building up the soil, using plants wisely, and maintaining an ideal balance. Organic gardeners recognize that pathogens attack weak plants that live in poor soil. An abundance of soil organisms, from earthworms to fungi, provide needed nutrients to plant roots and keep your flowers healthy.

Organic gardeners also understand that some plants grown together will benefit the entire garden-ecosystem. Roses and garlic are a classic example and are discussed in detail in the book Roses Love Garlic, by Louise Riotte. Likewise, some plants grown together may actually create problems for overall garden health. This concept is called " companion planting."

We recognize that organic gardening is closest to nature and is beneficial to the environment and to your family. For this reason, it is the method that we’ll focus on in this website. If you are looking for a good source of organic fertilizers, organic pest control products, and quality gardening tools, we recommend Clean Air Gardening.

These ultra thin-but-tough nitrile gardening gloves let you feel what you're doing while weeding, thinning, pruning, even picking up individual seeds.

Considering Your Region: Looking to Nature’s Garden

“None can have a healthy love for flowers unless he loves the wild ones.” - Forbes Watson

When you begin thinking about planting a new flower garden or expanding your current flower garden, you can look to the natural landscapes of your region for ideas. Wherever you live, there exists a diversity of micro-climates and eco-zones to explore. Next time you take a drive or a walk in the country, pay close attention. Depending on where you live, grassy plains may give way to rolling hills which turn into steep, rugged mountains. The edges of streams and creeks near your home also have unique, “riparian” ecosystems. Each of theses areas represents a unique community of plants working together in harmony.

It’s important not only to pay attention to the individual plants, but how they interact. Note the way larger plants provide shade for low-lying plants. What other relationships do you observe? Study these landscapes and take notes.

While the natural scenery that surrounds us is a work of nature created over hundreds of years by environmental conditions, gardens are our immediate creative expressions using the raw ingredients of trees, plants, soil, rocks, etc. Nature has worked hard to find a balance of soil, climate, plants, insects and animals. For this reason, we can look to the native plants of our state for inspiration. If we plant a flower garden primarily of natives in thoughtful combinations, we will inevitably create a more harmonious and carefree garden. Using natives, your flower garden can also read like a picture book of the natural history of your region, blending the open spaces around your city or town with your created landscape. You will also attract birds and beneficial insects and your garden will become an extension of the natural world that surrounds you.

The Nature of Natives: Deciding Which Flowers to Plant
“We learn from our gardens to deal with the most urgent question of the time: How much is enough?” –Wendell Berry

Native plant species can form the basic template for our garden design. However, it is important to remember that the natural landscapes that surround us are dynamic. Climates change and ecosystems shift. Throughout time, humans and animals have introduced non-native plants and they have naturalized to our area to become common sights.

With this in mind, how do we define what a native plant is? This is a very complex topic worthy of a long discussion. To get a basic idea, we recommend reading plant identification books and other references specific to your area. These books will help you find plants that professional botanists consider native and which are relative newcomers. This government website can also help you explore the idea of native flower gardening (link is to a PDF file).

As far as your flower garden is concerned, you can be as strict as you wish when planting your garden and using natives. There are many non-natives that are very adaptable and will fit in very well with natives without disrupting local plant communities. The key is to find a combination that works for you while being environmentally responsible.

You don’t have to give up your favorite ornamental non-natives, but be aware that many exotic species can be aggressive and disruptive in your garden and out-compete natives. Many exotics are weedy and aggressive simply because their natural predators are not present in their new environment. The more you educate yourself about the natural history of your state, the better. The North American Native Plant Society maintains an excellent website.

Planning: Flower Garden Ideas with Nature in Mind
“Who would have thought it possible that a tiny little flower could preoccupy a person so completely that there simply wasn't room for any other thought....” - Sophie Scholl

Once again, the best lessons for planning your flower garden come from nature. Take the time to closely observe relationships in local plant communities and you will learn a great deal. Also, it’s good to familiarize yourself with the different forms of plants that exist in nature and how they grow. In this website we’ve arranged information that will introduce you to the basics of perennials, annuals, bulbs, vines, etc. Read over this information briefly to get yourself further acquainted with the wonders of the plant world.

As soon as you’ve read this information and you’ve got a good picture of what’s out there in your natural landscapes, write down your observations and start thinking about plants and plant combinations you’d like to try in your flower garden. Next, consider issues such as your available space, and your time and budget constraints.

It may be useful for you to start looking at flowers in nurseries to see what they have in stock. We recommend shopping at your local family-run nurseries that specialize in native plants. They are generally more helpful and knowledgeable than the big chain nurseries and can assist you in choosing specific plants and give you tips on planting and maintenance.

You may also chat with other gardeners where you live about what has worked for them. Visiting their gardens will also generate new ideas. Local extension agents are another source of information and most now have web-based services.

Next, consider that a flower garden should appeal to all five senses. Picture the flower colors you’d like and the color combinations you think might go well with your home and your yard. Also reflect on the texture of the flowers and plants, as well as their heights. You should plan your garden in three strata: trees, shrubs, and groundcovers. Think about the smells you’d like to have in your garden, and perhaps choose a few plants that also provide edible fruits. Also think about the possibilities of raised beds, borders, walkways, benches, trellises, and other peripherals. Clean Air Gardening is one site that sells containers or planters for gardening that might be helpful.

If you have recently moved to a new home and are planning your garden, it may be better to wait a year before planting a large, elaborate flower garden. This way, you can observe the amount of sun and shade, temperatures, soil conditions, etc. that you’re working with. Also, if you’re relatively new to gardening, you’ll probably want to start small your first year to see what works and what doesn’t. You can add to your garden each year as you discover nature’s secrets.

Flower Garden Specifics: Map it Out
“Just living is not enough ... One must have sunshine, freedom, and a little flower.” - Hans Christian Anderson

Now it’s time to determine the size of the plot you’re going to plant and to make a rough sketch of your property in relation to the plot. If you like, you can buy drafting paper and draw your map to scale so that it is more accurate. Color pencils are great for making maps so buy a set. Tracing paper is also a useful tool so you can make different layers of trees, plants, grasses, etc. and experiment before making your final drawing.

As you make your sketch, don’t forget to map out utility poles, faucets, existing plants and trees, sidewalks, etc. If you’ve done a good job of watching the sun and shade patterns of your yard, you can map these out as well. Make note of seasonal changes in sun and shade with different colors. If you’re interested in blocking out the wind with shrubs, draw in the direction of prevailing winds with arrows and indicate the season as well. Other factors to include in your map are slopes or hills, gullies, areas of special interest such as nice views you want to preserve, etc. The Garden Composer computer program might be helpful if you have a large and complex area to plan.

All this information you’ve compiled can now serve as your base map. Now you can begin the exciting process of defining your vision for your flower garden.

Flowers and Design: Working with Nature

“The Earth laughs in flowers.” - Ralph Waldo Emerson

As different flowers come out at different times of year, you should think about the time you want your flowers to bloom and for how long. You can have them bloom all at the same time, or you can stagger them throughout the growing season so your flower garden evolves through time.

This is a wonderfully creative element to flower gardening. Imagine seeing your spring flower garden emerge in blues and purples with grape hyacinth and lilacs and then evolve to a rainbow of colors as your Four O’clocks come out later in the year. Read up on the flowers you want to use to familiarize yourself with their flowering times.

Another fantastic part of planning your flower garden is that you can actually set up thematic sections in yard. Consider these themes for your gardens: Butterfly Garden, Bird Garden, Wildlife Garden, Rose Garden, Perennial Garden, Shade Garden, Succulent Garden, or Water Garden, among others. This U.S. Department of Agriculture has great tips on adding unique and ecologically-minded themes and features to your flower gardens.

Now that you’ve got your base map and you’ve got a set of ideas and tools to work with, you can map out which plants you wish to place in your yard. There are no hard and fast rules when drawing your design, but in general it’s best to draw large shapes for themes such as “shade garden” and use symbols for more specific features such as an individual tree or a bird bath. You should draw in the shapes of trees and shrubs as if they were their mature sizes, not their planting size. This technique will help you visualize your mature garden and reduce crowding.

When you have finished making your design, you can actually map it out in your yard. Place string, pegs, rocks, or other markers to outline the shape of the garden plot. Outline the shapes of the various plant concentrations. You might even want to lay out colored paper or something similar to represent the flowers and other plants. Mapping your garden accurately will give you a good idea of how it will look when it is done, and what effect it will have on the appearance of your house and the rest of the yard.

You can consider purchasing several samples of each of the flowers you are thinking of using and placing them in the appropriate locations in your mapped-out flower garden. You can take back the ones that aren’t quite right and purchase others. You will eventually find the perfect flowers and other plants for your garden. After you have a good idea what your garden will look like, you’ll need to prepare your soil for planting.

Preparing Your Flower Garden for Planting: Here Comes the Digging!

“My green thumb came only as a result of the mistakes I made while learning to see things from the plant's point of view.” - H. Fred Ale

Soil Basics for Flower Gardening
Soil is often divided into various categories, such as clay, sand, silt, and loam, although there are actually an infinite number of soil varieties because soil compositions can vary widely in organic matter, large and small rocks, minerals, pH, and other factors.

Most gardeners consider soil that has a combination of sand, silt, clay, and organic matter to be good soil. Measuring the pH of your soil is also a good indicator of how your flowers will perform and will help you determine if you need to make changes to the soil composition. Here is a terrific little electronic soil testing tool that can tell you how your soil is doing quickly and easily.

pH and Flower Gardening
pH is a scale used to measure the concentration of hydrogen ions in a solution. The pH scale ranges from 0 to 14. Acidic substances have smaller pH numbers and more hydrogen ions. Alkaline substances have larger pH numbers and fewer hydrogen ions. 0 is extremely acid; 7 is neutral; and 14 is extremely alkaline. Limestone is an example of a very alkaline mineral. Sulfur is an example of a very acidic mineral. Note that arid regions tend to have alkaline soils and regions with heavy rainfall tend to have acidic soils.

Although the pH scale only has a 0 to 14 range, it is a logarithmic scale that is designed to measure vast differences. Think of the Ritcher Scale of earthquake magnitude as another example of a logarithmic scale. For example, a pH of 7 is neutral, but a pH of 6 is ten times more acid than a neutral 7. A pH of 5 is a hundred times more acid than a neutral 7, and a pH of 4 is a thousand times more acid than a neutral 7. Likewise, a pH of 8 is ten times more alkaline than a neutral 7. A pH of 9 is a hundred times more alkaline than a neutral 7, and a pH of 10 is a thousand times more alkaline than a neutral 7.

Testing Your Soil pH
To test your soil, it is a good idea to dig out samples from several places to see what the soil is like. Soil that hasn’t been worked is seldom ready for new plantings. It may have too much clay, too much sand, tons of rocks, very little organic material, a high or low pH, or other issues that you’ll need to deal with before you plant.

A good way to test the texture of your soil is with the “Ribbon Test.” After you take a soil sample, roll it back and forth in your hand. If it sticks together easily, it is high in clay, if it simply falls apart, it is probably has a lot of sand. Clay soils don’t drain well and are difficult for the roots to penetrate. Sandy soils drain well but don’t retain nutrients. Adding organic material will help both sandy and clay soils

You can test the pH of your soil with a simple pH testing kit. A good quality pH test kit is worth the extra expense because inexpensive ones are often inaccurate. The most accurate way to test the overall health of your soil is with a Garden Soil Testing Kit. These kits are relatively inexpensive and come in various styles. You can even buy an electronic soil tester that will also test the pH, as well as fertility, how much light you are getting, and other aspects for effective flower gardening.

The Magic of Compost for Successful Flower Gardening
If your soil is extremely acid, which can happen in an area with heavy rainfall, or with soil that has had overdoses of chemical N-P-K fertilizer, you may need to add limestone to ‘sweeten’ the soil.

Adding compost can also work wonders if your soil is out of the ideal pH range. This technique will also improve soil that is too sandy, has too much clay, or is low in the organic material that plants need to thrive. If you don’t know much about composting, don’t worry. You can find more information on composting at the Compost Guide.

Soil drainage is also critical to flower gardening. Mixing in compost is the best way to improve drainage. You can also try digging out a good quantity of the soil, around 16 inches deep, and placing a layer of fine gravel at the bottom.

Mulch and Flower Gardening
If you don’t have humus available from well composted material, you can help your garden through mulching. Mulching is nature’s way of composting. Forests provide a good example of nature’s mulching and composting system.

Forests are a complex growing community. Everything in a forest is related and works together. Leaves and dead branches fall from trees and other forest plants. Bacteria, fungi, nematodes, earthworms, and other habitants of the soil help break down the leaves and other debris into humus.

Humus is a natural living environment that benefits tree and plant roots.
To reproduce the mulch that forests naturally create, you can use garden waste from your home, such as shredded leaves, hay, shredded bark, or other similar substance. By spreading the material over the top of your garden dirt, you are mimicking the decomposing leaves and branches that make up a forest floor.

Mulching helps to keep weeds from growing and facilitates moisture retention in the soil. Mulching also begins the process of natural composting. Between treatments, soil organisms help to decompose the mulch that is closest to the ground. Earthworms and other critters that live in the soil pull composted material into the ground and naturally feed your plant’s roots.

You should add a little more mulch each year to your flower garden to keep the process going. You can use mulch even when your soil is in excellent shape. The mulch will keep the soil healthy and productive. You can further support your soil by adding a dose of organic fertilizer. Your mulch will work best when you add this natural fertilizer over the entire garden bed so that the whole area will gradually become healthier.

You can also go here for more information on mulching.

Flower Planting Tips: Off to the Right Start
“There is no spot of ground, however arid, bare or ugly, that cannot be tamed into such a state as may give an impression of beauty and delight.”- Gertrude Jekyll

-- Make sure you’ve got healthy soil with plenty of organic material and an appropriate pH level.

-- It is best to plant your flowers, trees and shrubs on a cool or cloudy day to minimize the stress of transplanting. Planting in the early morning or late afternoon also helps.

-- Most flowers should be planted in the spring. Some plants can be planted during other times of the year. Ask your local nurseries for planting tips on the specific plants you want to use.

-- Dig a hole in your freshly worked soil. Put the soil aside to fill the hole back in later. The diameter should be about twice the diameter of the root ball but the same height as the root ball.

-- Take out the plant from its container, and gently work you hand over the root ball to stimulate the roots. For trees and shrubs, remove any wires, burlap, etc. from the root ball after taking your plant out of the container.

-- Place the plant in the hole. Make sure it’s positioned at the correct soil line. It’s very important to place the roots at the proper level so that the plant’s roots aren’t exposed and the foliage of low-lying plants doesn’t get too wet. Some plants such as strawberries are subject to rot if their foliage is planted so that it remains wet.

-- Fill the hole about half full with the original soil.

-- Gently pack the soil to remove any trapped air.

-- Give the plant a good drink.

-- Top off the hole with soil, pack it again, and water one more time.

-- You can build up a small berm of soil in the shape of a circle around the hole so that your watering is more effective.

-- Cover the base of the plant with a good mulch. You can use recycled garden materials such as leaves, bark, nut shells, hay, grass clippings, etc. See here for information on mulching.

-- After planting, follow the watering instructions appropriate to your plant. Keep your plants well watered for the first year until they establish a good root system.

How To Get A Scholarship

2007-10-19T09:06:00.000-07:00

1 Step One

Start looking for scholarships at least one year before entering college.

2 Step Two

Consider whether you are a member of an underrepresented group, in financial need, or interested in certain fields of study. Scholarships are available for those with special talents in many areas, including sports, art, science and music.

3 Step Three

Think about applying for a fellowship - a scholarship for graduate students - if you want to go to graduate school.

4 Step Four

Recognize what you can expect from a scholarship when you apply for it. Some schools offer to pay all your expenses, while others only pay for room and board.

5 Step Five

Use a No. 2 pencil to complete the application form.

6 Step Six

Be prepared to answer general questions such as name, address, social security number, date of birth, citizenship status and marital status.

7 Step Seven

Provide any necessary financial information such as total family income, number of children in your household, and number of children in college. Round dollar amounts to whole number values.

8 Step Eight

Supply information about the talent required by the scholarship for which you are applying.

9 Step Nine

Mail all the paperwork to the address listed on the application.

10 Step Ten

Endure the weeks or months of waiting to find out whether you got the scholarship and how much money you will receive from it.

Tips & Warnings :

Talk to your school counselor; he or she is paid to help you make decisions about your future.

Learn How to Win A Scholarship

2007-10-19T08:35:00.000-07:00

To win a scholarship application you need a true strategy. The students that win the most scholarships may not have more positive qualities than you, but they use the following strategy to get noticed by the scholarship committees:

Get Prepared:

Get letters of recommendation from teachers or guidance counselor or leaders in your community. Choose these wisely (make copies). Get a copy of your high school or college transcript (make copies). Get involved in your community or in school activities or in your church. If your time is limited due to personal circumstances, working to help with family expenses is also an advantage. Start writing an essay about your goals and what you have done to date to achieve them. Think about what makes you unique. Get a picture of yourself. A school picture is perfect. Anything smaller than a wallet size head shot, will do.

Buy some clear plastic binders.

The goal here is to have numerous packages made up ahead of time, ready to submit to the various scholarship committees.

The package will include:

* a clear plastic binder and within the package

* the scholarship application ( you will have to insert this later when you have received each individual application)

* followed by an essay that gets you noticed

* followed by your transcript (some scholarships do not require this, but if it’s impressive, send it)

* followed by letters of recommendation and then

* place you picture in the front inside cover(on top of the application) in the lower left hand corner (this is not a requirement, but it helps to put a face to the person, for the scholarship committee deciding who receives the awards)

Get Organized:

Begin researching scholarships that match your criteria. Consider using a scholarship search service, like I used FastWeb! . Once you have the scholarships for which you want to apply, keep track of the deadlines. Create a chart to keep on top of all dates.

The chart should include:

* Scholarship name and phone number

* Date application must be received by scholarship committee

* Date you requested the application

* Date you received the application

* Date application with above package was mailed

* Date you called the Scholarship Agency to verify they received your application package

Get Noticed:

As important as being prepared and organized, it is equally important that you have an essay that gets you noticed. Even if you feel you master the english language, your essay should be critique by someone who has experience in essay writing. Ask an english professor to review your essay or consider using an essay editing service.

Get Prepared, Get Organized, Get Noticed, Be Persistent and Don’t Give Up!

Energy Saving Tropical House - a way to overcome global warming

2007-10-17T11:35:00.000-07:00

25 September 2007

One way to reduce global warming impact is by implementing energy saving tropical house. The fact is energy waste houses, about 80% came from architecture design mistake. Many aspects about saving energy tropical house discussed in One Day Seminar activity "Home Design Going Green (HDGG), at Hotel Ciputra, Jakarta on 5 September 2007.

Activity held by Ciputra, Century 21 Indonesia, TREN magazine and Bintang HOME Tabloid is a manifestation of practitioner of design world's concern in overcoming global warming. It's expected that participants can influence bigger network and promote energy saving house to their clients. WWF-Indonesia highly appreciated design world practitioners contribution in overcoming global warming.

Save the Energy
Dr. Ir. Eddy Prianto CES, DEA, one of speaker, an award winning from Persatuan Insinyur Indonesia 2007 (Indonesia Engineers Forum) for Energy Saving House concept said, "architecture design of a house that respect surround climate condition, sunray, and air flow for people's comfort in doing their activity is a major step. Energy saving tropical house also a response to social context happened such as electricity crisis, electricity saving movement and global warming".

In the discussion, it's exposed that electricity consumption contributes to increase of CO2 release for 19%. At domestic house, air conditioner utilization takes first place on electricity consumption (38%), followed by computer (10%), rice cooker (10%), washing machine (9%), iron (9%); jet pump (6%); lighting (5%); water heater (4%); fan (3%); refrigerator and television (2%) and radio/tape (1%). Meanwhile for building, AC utilization up to (39%), lighting (24%); fan (17%); lift (7%) and other equipment (3%).

The effort to save energy can be done through adaptation with surround environment and reduce heat that come from outside, then follow by reconfiguration the architecture." Now, 2/3 room heat caused by the mistaken on roof design, if we used the clear roof, around 90% heat can be absorb," explained Prianto.

Main Challenge
For Indonesia, with tropical climate, it needs to implement six strategy of green house, which includes building plaster, lighting, heater, air conditioner, energy consumption and waste management.

House with green lighting system can reduce energy consumption. Because of more plants grow around house, the lessen heat intensity. Besides comfort from thermal side, it gives visual side comfort as well.

Unlimited sun energy utilized to create energy independence at home. One way, by design aspect that can place solar panel at house side facing west direction than get the highest and longest sun rays. Besides utilizing energy, this can reduce heat radiate through walls and lessen air conditioner utilization.

It's admitted by participants that the hardest part in designing energy saving house is to change individual habit aspects. When it comes to habit, the most effective way to influence individual to change is by modeling. Design world practitioners also realize that they must have stronger bargaining position in front of client so that they can accept energy saving tropical house design.

This "Home Design Going Green" seminar is an initial step from seminar series to popularize Energy Saving Tropical House design. If more people willing to implement this, the less energy utilized the more comfort the earth can get.

wwf.org

How To Teach Math

2007-10-17T10:29:00.000-07:00

From The MathLab.com :

1. Force Them To Talk

If you really want to TEACH mathematics, you must FORCE YOUR STUDENTS TO TALK!
Remember that humans have a strong need to communicate, especially in their early teenage years. Communicating helps all people to cope with the stresses of life, because it assures them that others have similar problems and experiences.
Teachers can USE this human need for communication to their benefit. Don't fight it. Design your learning environment to encourage talking, and then structure your lessons to FORCE communication about MATH. This will have a tremendous positive effect upon your students because you will be satiating their basic need for communication and at the same time you will be soothing their math anxiety through this communication.
When they are "forced" to talk, which is something they desperately need to do anyway, they will invariably share the stuff that they can't figure out with each other. Before you know it, you have kids, who can't sit and listen to YOU for more than 3 minutes, leading discussions and helping their peers.
Kids NEED to talk about their math because they speak the same language. They will be able to translate the teacher's formal math talk into the language of "kid" far more efficiently than the teacher. Sometimes they get so excited helping each other that you can't believe they are the same kids who ignore your ever so well planned lectures. You will see intelligence where you thought none existed if you can just get them talking about the math.

*As a note here we must emphasize, especially for any of you just starting out teaching, the teacher is SUPPOSED to talk mathematically correct. He or she may do some translating into the common vernacular as needed, but it is too dangerous to wander very far from correct definitions, theorems, and formal algorithms. Remember, in mathematics, words are never used as "fluff", if it's in the definition, then it's necessary. Like the definition of prime number: a number is prime if it has exactly, two, distinct, whole number, factors, one and itself.
Now is the number ONE prime? No, because it has only one, distinct, whole number factor, itself. So the word distinct is really needed here, it's not "fluff".
What about ZERO, is it prime?No, because it has an infinite number of factors. Itself times any number is zero, so the word exactly is essential in this definition.

Okay, with all that said, your next question should be,"How do you get kids to talk about math?"
We have experimented with many scenarios and find that placing your room into groups of two to six people, with four being optimum, is the best way to start. When you want them to talk, they need to be facing each other. That way their attention is focused into the group and the noise level is much more easily contained. They wont need to yell across the room to get someone's attention if they are allowed to be talking in their groups.
Once your groups are established, more about that in "the gentle art of ice smashing", all you have to do is design some sort of GRADED activity that can be done in three to five minutes.
We do "homework quizzes". These are always done after the class has had an opportunity to ask questions on the previous night's assignment. They form their groups, and put their name and all the other names of the people in their group on a piece of paper. Then we place one problem at a time on the board. They will have three to five minutes per problem depending upon its difficulty.
The kids must all agree upon the answer and show all the work to back that answer up. This FORCES them to talk math because at the end of the quiz, we collect only ONE PAPER from each group, they do not know who's paper will be selected, and they ALL GET THE SAME GRADE.
Now this shouldn't be a big deal if indeed they truly all have shared in the ideas. Everyone has a chance to contribute, and they really do, because we walk around the class and listen to them talk. Any student who is not actively involved in the solving is quietly removed from the group and takes the quiz alone. No one wants to be removed from the group, so they all really try.
Then eventually, even the slower kids find that they can contribute something and that maybe they are not the only ones who don't understand everything. It is actually quite a math anxiety reliever and a tremendous TEACHING TOOL. This type of quiz is meant not so much to evaluate as to TEACH.
Getting mathematics into students in this way is a strong attitude enhancer too. They enjoy the talking, and arguing, and sometimes even laughing about math. And when people enjoy something, they do it. It's just human nature. Never underestimate the teaching power of a well motivated study group!

2. The Gentle Art Of Ice-Smashing

Group work will not be successfull unless you GENTLY SMASH THE ICE.
People set up natural barriers bewteen themselves and the rest of the world. It's a self defense mechanism, and we all do it to a certain extent. If you want teenagers to work together on math, you need to smash through those barriers and give them some common ground.
Most likely your groups will be mixed between sexes, abilities, and more, importantly social cliques. It is most productive to mix the groups in every imaginable way. It gives the kids more life coping skills and promotes an overall unity of classroom as the kids move from group to new group throughout the year.
So how do you get the homecoming queen girl with perfect nails, the fat smelly kid with zits, the loud mouthed football running back, and the multipierced black stained goth chick to pull together as a productive math unit? YOU PLAY A GAME!
There have been a few times where we thought all the kids knew each other and they didn't really need the ice smashing activity, so we skipped it, only to have a whole nine week period pass with no fun and more than a few fights. ICE SMASHING IS ESSENTIAL for group bonding. Never overlook this step if you are serious about having your students learn together.
Here is a partial list of some of the games we have played over the years.
Micro-Pictionary
How big is my belly
Mystery sight
Speed acting
Rock Bands and Math Pods
Test of genius

3. Doing Is Everything

Get your students DOING math every lesson.
All people need varying degrees of "hands-on" experience to truly master a topic. Some need a lot, others a little, but we all need a portion, so be sure to supply it EVERY LESSON.
Introductory warm-ups are a great way to start a lesson. They can be different each day and act as a lead in to the lesson topic. They can be used to reinforce a skill that will be essential to the day's lesson.
Things to remember are:
Let them be short, 3-7 minutes.
Have the students use their hands as well as their minds, to cut paper, or fold paper or arrange items, etc.
Keep it fresh so the class will look forward to what you are going to pull out of your hat each day.
You may be saying, "Oh sure, how am I supposed to come up with an enticing, fun, hands-on activity every day for every class and one that actually applies to the lesson at hand?"
This is a logical question. And the answer is, STEAL. Until you have taught long enough to have a wonderful repertoire of self made wonder gems, you will simply have to do what everyone else does, use other people's ideas, and modify them to fit your own teaching style and students. themathlab.com is packed with some of our best wonder gems, but we also highly recommend the book MATH STARTERS.

Also remember, once the formal lesson begins they still need to be doing math. Be sure to throw out lots of questions like, "What would happen to this expression if..., Okay, now flip it over and what will it look like, draw this..., Will it work for negative one..., Will it work for zero...., Where does this fail to be true..., Draw me an example of one that wouldn't work...,etc.
When you throw out these type of questions, GIVE THEM TIME TO THINK, walk around the classroom and look at what they are writing. You can also encourage them to come up with a group consensus, if they are sitting in groups. Communication between learners is essential. You'll be surprised, when you open the math up to the kids, they will almost always come up with something that you haven't thought of. Thus your own breadth of knowledge will be enhanced. It's a very positive experience for everyone.
The next logistical consideration is, "How do you get them ALL working when you have a class with 20 or more students?" It's seems impossible to get them all working and give feedback to each one quickly. If you could only see what they were all doing with just a glance it would be so much easier. Now if you have lots of chalk board space, you can send them all to the board, but in many instances this is not possible.
Here's an idea that we use all the time. We use "think-boards". These are mini chalk boards about one foot square. They fit on top of the student's desks. They write their responses and then hold up the boards. We can see in just a few seconds who understands and who doesn't. We keep chalk and clean washrags with these boards. Students pick these up as they enter the room on days that we are using the think-boards. Some students opt to dampen their washrags in the restroom before class starts. Everyone knows this is fine as long as it's done before class starts.
You can make a classroom set of think boards. Simply buy a sheet of 4' x 8' masonite or 1/4 inch smooth plywood. Paint it on one side with a dark, FLAT, paint using a smooth roller, we recommend two coats. Let the paint dry, and then cut it into 12 inch square boards. If you don't have the tools to cut the boards, ask your industrial arts teacher to cut them for you.

*NOTE OF EXTREME IMPORTANCE: If you want your students to do math willingly and with enthusiasm, never ridicule a student for giving a wrong answer. Find something good about their response, then rephrase the question or modify it in a different way and ask them again. This gives the individual a chance to publicly redeem themselves and not feel stupid. It also sets a tone of respect and safety in your classroom that will be appreciated. You will get a great deal more participation if everyone knows that they are not in danger of ridicule.

4. It's Okay To Be Wrong

You must have one cardinal, unbreakable, totally accepted rule in your classroom. IT'S OKAY TO BE WRONG!!!. NEVER, under any circumstances, ridicule or be sarcastic to a learner who makes a mistake.
We all make mistakes, and nothing destroys a person's desire to try, faster than public ridicule.
If you want your students to do math willingly and with enthusiasm, never ridicule a student for giving a wrong answer. Find something good about their response, then rephrase the question or modify it in a different way and ask them again. This gives the individual a chance to publicly redeem themselves and not feel stupid. It also sets a tone of respect and safety in your classroom that will be appreciated. You will get a great deal more participation if everyone knows that they are not in danger of ridicule.
A nice result of this rule will be that your students will extend the same respect to you. When you screw up, and you will, they will politely correct you and the atmosphere of trust will be protected.
If you, the teacher, violate this rule even one time, you will lose the trust of your students and the environment in your classroom will deteriorate immediately. You will see the students shut down. They will instantly believe that if you can embarrass one student you can do it to them too. So NEVER VIOLATE THIS RULE!!!
If for some reason, like lack of sleep or complete frustration, you let a rude or sarcastic comment pass from your lips, your only hope is to publicly acknowledge your mistake and apologize to the student you insulted in front of the others. Make sure you are sincere too or it will worsen the insult. Most people will give you one more chance if you are willing to publicly admit your mistake. But again, these infractions must be very rare or you will lose the trust of your whole class.

5. Keep Your Class Fresh

Would you want to eat the same stale tasteless meat day after day after day after day after day? No, of course not. So DON'T SERVE STALE MEAT TO YOUR STUDENTS.
Keep your classes FRESH!

People learn at different rates and in different ways. So if you do the same thing everyday, you will be doing a tremendous disservice to a large percentage of your students. Vary your methods of instruction frequently and you will keep more students learning.
Remember there are few people in the world who can learn just by hearing, these are auditory learners. Some can learn by just watching an example or two, but the majority of people need to involve more than just their ears and eyes. They need to touch it, sing it, dance to it, build it, draw it, write about it, act it out, argue about it, or in general just EXPERIENCE what they learn.
Okay so how do you get your students to EXPERIENCE their math? Give them something fresh and a bit fun every day. Here are some things that our teachers do to get you thinking of possibilities:

Games
mini-lectures (five minutes of talk, five minutes of try the idea)
boardwork
groupwork
individual work
projects
videos
writing assignments
discovery lessons
computer practice
Internet research
spreadsheet explorations
humorous stories
lively historical anecdotes and facts
one on one peer tutoring
experiments
timed drills
self checking worksheets with answer banks

7. Become Skillful THIEF

You must become a creative, skillful, THIEF.
No, we are not kidding.It is absolutely essential that you become an expert at sniffing out the best ideas and techniques of successful teachers. Once found, you must STEAL THEM and make them your own.
The key here is the "make them your own" part. The act of using someone else's activity will become worlds richer when it is tailored to YOUR teaching style and personality and of course to your students.
To help you in your quest to steal the best and nothing but the best, check out these links.

TheMathLab.Com

TEACHING AS A PROFESSION

2007-10-17T09:53:00.000-07:00

By FRANK ROSCOE
Secretary of the Teachers Registration Council

The title of this chapter is prophetic rather than descriptive for although teachers often claim for their work a professional status and find their claim recognised by the common use of the phrase "teaching profession" yet it must be admitted that teachers do not form a true professional body. They include in their ranks instructors of all types, from the university professor to the private teacher or "professor" of music. Their terms of engagement and rate of remuneration exhibit every possible variety. Their fitness to undertake the work of teaching is not tested specifically, save in the case of certain classes of teachers in public elementary schools, nor is there any general agreement as to the proper nature and scope of such a test, could one be devised. Usually, it is true, the prospective employer demands evidence that the intending teacher has some knowledge of the subject he is to teach. He may seek to satisfy himself that the applicant has other desirable qualities, personal and physical, which will fit him to take an active and useful part in school work. These inquiries, however, will have little or no reference to his skill in teaching, apart from what is called discipline or form management.

The characteristics of a true profession are not easily defined, but it may be assumed that they include the existence of a body of scientific principles as the foundation of the work and the exercise of some measure of control by the profession itself in regard to the qualifications of those who seek to enter its ranks. Taken together, these two characteristics may be said to mark off a true profession from a business or trade. The skilled craftsman or artisan may belong to a union which seeks to control the entrance to its ranks, but the difference between the member of the Amalgamated Society of Engineers and the member of the Institution of Mechanical Engineers is that the former belongs to a body chiefly concerned with the application of certain methods while the latter belongs to one which is concerned with those methods, not only in their application but also in their origin and development. It is recognised that there is a body of scientific knowledge underlying the practice of engineering, and the various professional institutions of engineers seek to extend this knowledge, while claiming also the right to ascertain the qualifications of those who desire to become members of their profession. The same is true in different ways with regard to the professions of law and medicine. It is to be noted also that within these professions the admitted member is on a footing of equality with all his colleagues save only so far as his professional skill and eminence entitle him to special consideration.

It will be seen at once that there are great difficulties to be overcome before teaching can be truly described as a profession. The diversity of the work is so great that it may be held that teaching is not one calling but a blend of many. It is difficult to find any common link between the university professor, the head master of a great public school, an instructor in physical training, and a kindergarten teacher. It is not easy to bring together the head master of a preparatory school, working in complete independence, and the head master of a public elementary school, dealing with pupils of about the same age as those in the preparatory school, but controlled and directed by an elected public authority under the general supervision of the Board of Education. Yet despite these apparent divergences of aim all teachers may be regarded as pursuing the same end. They are engaged in bringing to bear upon their pupils certain formal and purposeful influences with the object of enabling them to play their part in the business of life. Such formal influences are seconded by countless informal ones. School and university alone do not make the complete man and it is an important part of the teacher's task to second his direct and purposeful teaching by the influence of his own personality and conduct, and by securing that the form or school is in harmony with the general aim of his work.

Skill in imparting instruction is by no means the whole of the equipment required by a teacher. It is indeed possible to give "a good lesson" or a series of "good lessons" and yet to fail in the real work of teaching. In some branches far too much stress has been laid on the more purely technical and mechanical attributes of good teaching as distinct from the finer and more permanent qualities such as intellectual stimulus, the awakening of a spirit of inquiry, and the development of a true corporate sense. By way of excuse it may be said that teaching has tended to become a form of drill chiefly in those schools where the classes have been too large to permit of anything better than rigid discipline and a constant attention to the learning of facts. Teachers in such circumstances are gravely handicapped in all the more enduring and important parts of their work. Very large schools and classes of an unwieldy size tend to turn the teacher into a mere drill sergeant.

While full provision should always be made for the exercise of the teacher's individuality there must be sought some unifying principle in all forms of teaching work. Unless it is agreed that the imparting of instruction demands special skill as distinct from knowledge of the subject-matter we shall be driven to accept the view that the teacher, as such, deserves no more consideration than any casual worker. No claim to rank as a profession can be maintained on behalf of teachers if it is held that their work may be undertaken with no more preparation than is involved in the study of the subject or subjects they purpose to teach. A true profession implies a "mystery" or at least an art or craft and some knowledge of this would seem to be essential for teachers if they are to have professional status.

The difficulty in this connection is that the principles of teaching have not yet been worked out satisfactorily. Our knowledge of the operations of the mind develops very slowly and those who carry out investigations in this field of research are few in number. Their conclusions are not necessarily related to teaching practice but cover a wider field. The study of applied psychology with special reference to the work of the teacher needs to be encouraged since it will serve to enlarge that body of scientific principle which should form the basis of teaching work. It is by no means necessary, or even desirable, that teachers should be expected to spend their time in psychological research. Their business is to teach and this requires that they should devote themselves to applying in practice the truths ascertained and verified by the psychologists. For this purpose it will be necessary that they should know something of the method by which these truths are sought and proved. It is also an advantage for teachers to learn something of the history of education, not as a series of biographies of so-called Great Educators but rather with the object of learning what has been suggested and attempted in former times. Such a knowledge furnishes the teacher with the necessary power to deal with new proposals and with the many "systems" and "methods" which are continually arising. Instead of becoming an eager advocate of every novelty or adopting an attitude of indiscriminate scepticism he will be in some measure able to estimate the true merit of new proposals, and his knowledge of mental operations will serve as an aid in judging whether they have any germ of sound principle. The alternative plan of leaving the teacher to learn his craft solely by practice often has the result of confining him too closely to narrow and stereotyped methods, based either on the imperfect recollection of his own schooldays, or on the method of some other teacher. Imitation is cramping and serves to destroy the qualities of initiative and adaptability which are indispensable to success in teaching.

It will be noted that no extravagant demand is put forward on behalf of what is called training in teaching. The methods of training hitherto practised have been based too frequently on the assumption that it is possible to fashion a teacher from the outside, as it were, by causing him to attend lectures on psychology and teaching method and to hear a course of demonstration lessons. This plan may fail completely since it is possible to write excellent examination answers on the subjects named and even to give a prepared lesson reasonably well without being fitted to undertake the charge of a form. It should be recognised that the practice of teaching can be acquired only in the class-room under conditions which are normal and therefore entirely different from those existing in the practising school of a training college. When this truth is fully apprehended we may expect to find that the young teacher is required to spend his first year in a school where the head master and one or more members of the regular staff are qualified to guide his early efforts and to establish the necessary link between his knowledge of theory and his requirements in practice.

The Departments of Education in the universities should be encouraged to develop systematic research into the principles of teaching and should be in close touch with the schools in which teachers are receiving their practical training.

The plan suggested will be free from the reproach often levelled against the existing method of training teachers, namely, that it is too theoretical and produces people who can talk glibly about education without being able to manage a class. It will also recognise the truth that the young teacher has much to learn in regard to the art or craft of teaching and that there are certain general principles which he must know and follow if he is to be successful in his chosen work. The application of these principles to his own circumstances is a matter of practice, for in teaching, as in any other art, the element of personality far outweighs in its importance any matter of formal technique or special method. The ascertained and accepted principles underlying all teaching should be known and thereafter the teacher should develop his own method, reflecting in his practice the bent of his mind.

The recognition of a principle does not of necessity involve uniformity in practice. Freedom in execution is possible only within the limits of an art. The problem is to define these limits in such a liberal manner as will allow for variety and individual expression. The saying that teachers are born, not made, is one which may be made of those who practise any art, but the poet or painter can exercise his innate gifts only within certain limits and with regard to certain rules. It is no less fatal to his art for him to abandon all rules than it is for him to accept every rule slavishly and apply it to himself without intelligence.

The acceptance of the principle that there is an art or at least a craft of teaching is a condition precedent to any attempt to make teaching a profession in reality as well as in name.
The further requirement is that those who are engaged in teaching should have some power of controlling the conditions under which they work and more especially of testing the qualifications of those who desire to join their ranks. This demands a recognition of the essential unity of all teaching work and a consequent effort to bring all teachers together as members of one body, possessing a certain unity or solidarity in spite of its apparent diversities. To form such a body is a task of great difficulty since the various types of teachers have in the past tended to separate themselves into groups, each having its own association and machinery for the protection of its own interests. Apart from the teaching staffs of the various universities, there are in England and Wales over fifty associations of teachers, ranging from the National Union of Teachers with over ninety thousand subscribing members to bodies numbering only a few score adherents. These associations reflect the great diversity of teaching work already described, but all alike are seeking to promote freedom for the teacher in his work and to advance professional objects. Such aspirations have been in the minds of teachers for many years and from time to time attempts have been made to realise them by establishing a professional Council with its necessary adjunct of a Register of qualified persons. Seventy years ago the College of Preceptors, with its grades of Associate, Licentiate and Fellow, suggesting a comparison with the College of Physicians, was established with the object of "raising the standard of the profession by providing a guarantee of fitness and respectability." The College Register was to contain the names of all those who were qualified to conduct schools, and admission to the Register was controlled by the College itself in order to provide a means of excluding all who were likely to bring discredit upon the calling of a teacher by reason of their inefficiency or misconduct. The scheme thus launched was, however, not comprehensive, since it concerned chiefly the teachers who conducted private schools and did not contemplate the inclusion of those who were engaged in universities, public schools, or the elementary schools working under the then recently established scheme of State grants. Teachers in schools of this last description were apparently intended by the government of the day to be regarded as civil servants, appointed and paid by the State. Subsequent legislation modified this arrangement, but teachers in schools receiving government grants are still subject to a measure of control, and those in public elementary schools are licensed by the State before being allowed to teach. It will be seen that the effort to organise a teaching profession was hampered from the start by the fact that teachers were not entirely free to set up their own conditions, since the State had already taken charge of one branch, while further difficulties arose from the varied character of different forms of teaching work and from the circumstance that some of these forms were traditionally associated with membership of another profession, that of a clergyman.

Hence it was that despite several attempts to institute a Register of Teachers and to organise a profession the difficulties seemed to be insurmountable. Between the years 1869 and 1899 several bills were introduced in Parliament with the object of setting up a Register of Teachers but all met with opposition and were abandoned. The Board of Education Act of 1899 gave powers for constituting by Order in Council a Consultative Committee to advise the Board on any matter referred to the Committee and also to frame, with the approval of the Board, regulations for a Register of Teachers. It was not until 1902 that an Order in Council established a Registration Council and laid down regulations for the institution of a Register. The Council thus established consisted of twelve members, six of whom were nominated by the President of the Board of Education while one was elected by each of the following bodies: the Headmasters' Conference, the Headmasters' Association, the Head Mistresses' Association, the College of Preceptors, the Teachers' Guild, and the National Union of Teachers. The members of the Council were to hold office for three years, and afterwards, on 1 April, 1905, the constitution of the Council was to be revised. The duty assigned to the Council was that of establishing and keeping a Register of Teachers in accordance with the regulations framed by the Consultative Committee and approved by the Board of Education. Subject to the approval of the Board the Council was empowered to appoint officers and to pay them. The income was to be provided by fees for registration and the accounts were to be audited and published annually by the Board to whom the Council was also required to submit a report of its proceedings once a year.

Under this scheme a Register was set up, with two columns, A and B. In the former were placed the names of all teachers who had obtained the government certificate as teachers in public elementary schools. This involved no application or payment by such teachers, who were thus registered automatically. Column B was reserved for teachers in secondary schools, public and private. Registration in these cases was voluntary and demanded the payment of a registration fee of one guinea in addition to evidence of acceptable qualification in regard to academic standing and professional training. Although teachers of experience were admitted on easier terms the regulations were intended to ensure that, after a given date, everybody who was accepted for registration should have passed satisfactorily through a course of training in teaching. As designed in the first instance Column B furnished no place for teachers of special subjects and it became necessary to institute supplemental Registers in regard to music and other branches which had come to form part of the ordinary curriculum of a secondary school.
The scheme thus provided a Register divided into groups according to the nature of the accepted applicant's work. Such an arrangement presented many difficulties since it ignored all university teachers and assigned the others to different categories depending in some instances on the type of school in which they chanced to be working and in others on the subject which they happened to be teaching.

A professional Register constructed on these lines had the seeming advantage of supplying information as to the type of work for which the individual teacher was best fitted. On the other hand it was held that the division of teachers into categories was unsound in principle and the teachers in public elementary schools were not slow to resent the suggestion that they belonged to an inferior rank and were properly to be excused the payment of a fee. They pointed out that many of their number held academic qualifications which were higher than those required to secure admission to Column B wherein some eleven thousand teachers had been registered, of whom not more than one half were graduates. The views thus expressed were shared by many other teachers and it speedily became manifest that the proposed Register could not succeed. In the Annual Report of 1905 the Council stated that under existing conditions it was not practicable to frame and publish an alphabetical Register of Teachers such as appeared to be contemplated in the Act of 1899. In June, 1906, the Board of Education published a memorandum stating the reasons which had led it to take the opportunity afforded by impending legislation to abolish the Register, and in the Education Bill of 1906 a clause was inserted which removed from the Consultative Committee the obligation to frame a Register of Teachers. This clause was strongly opposed by many associations of teachers. It was urged by these bodies that although one scheme had failed yet a Register was still possible and desirable. It was held by many that the task assigned to the Registration Council had been an impossible one since the conditions of supervision and control imposed under the Act of 1899 left the Council very little freedom and wholly precluded the establishment of a self-governing profession. The general opinion seemed to be that any future Register must be in one column avoiding any attempt to divide those registered into different classes and that any future Council must be as independent and widely representative as possible. This opinion found expression and official sanction in a memorandum issued by the Board of Education in 1911 after several conferences had been held for the purpose of promoting a new registration scheme. The memorandum stated that: "It should not be so much the kinds of teachers likely to be most rapidly or easily admitted to the Register that should specially determine the composition of the Council but rather the larger and more general conception of the unification of the Teaching Profession." This new and wider idea served to govern the formation of the Teachers Registration Council which was established by an Order in Council of February, 1912. The body constituted by this Order consists wholly of teachers and includes eleven representatives of each of the following classes: the Teaching Staffs of Universities, the Associations of Teachers in Public Elementary Schools, the Associations of Teachers in Secondary Schools, and the Associations of Teachers of Specialist Subjects. The Council thus numbers forty-four and it is ordered that the chairman shall be elected by the Council from outside its own body. At least one woman must be elected by each appointing body which sends more than one representative to the Council provided that the body includes women among its members. It will be seen that the constitution aimed at forming a Council wholly independent and thoroughly representative. This quality was further ensured by the establishment of ten committees, representing various forms of specialist teaching and providing that any conditions of registration framed by the Council should be submitted to these committees before publication.

The first Council under this scheme was formed in 1912 and held office for three years as prescribed by the Order in Council. The chairman was the Right Honourable A.H. Dyke Acland and the members included the Vice-Chancellors of several universities and representatives of forty-two associations of teachers. The first duty of the Council was to devise conditions of registration and these were framed during 1913, being published at the end of that year. They provide in the first place that up to the end of 1920 any teacher may be admitted to registration who produces evidence of having taught under circumstances approved by the Council for a minimum period of five years. Regard for existing interests led to the setting up of a period of grace before the full conditions of registration came into force. After 1920, however, these become more stringent and require that before being admitted to registration the teacher shall produce evidence of knowledge and experience, while all save university teachers are also required to have undertaken a course of training in teaching. Under both the temporary and later arrangement the minimum age for registration is twenty-five and the fee is a single payment of one guinea. There is no annual subscription.

The second Council was elected in 1915 and appointed as its chairman Dr Michael E. Sadler, Vice-Chancellor of the University of Leeds. Up to the middle of July, 1916, the number of teachers admitted to the Register was 17,628 and the names of these were included in the Official List of Registered Teachers issued by the Council at the beginning of 1917. The Register itself is too voluminous for publication since it comprises all the particulars which an accepted applicant has submitted. All registered teachers receive a copy of their own register entry together with a certificate of registration. It will be seen that the task of receiving and considering applications for registration forms an important part of the Council's work. But it is by no means its chief function. As is shown in the Board of Education memorandum already quoted the Council is intended to promote the unification of the teaching profession. The Register is nothing more than the symbol of this unity and the Council is charged with the important task of expressing the views of teachers as a body on all matters concerning their work. This is shown in the speech made by the Minister of Education at the first meeting of the Council. After welcoming the members he added:

"The object of the Council would be not only the formation of a Register of Teachers. There were many other spheres and fields of usefulness for a Council representative of the Teaching Profession. He hoped that they would be able to speak with one voice as representing the Teaching Profession, and that the Board would be able to consult with them. So long as he was head of the Board they would always be most anxious to co-operate with the Council and would attach due weight to their views. He hoped that they on their side would realise some of the Board's difficulties and that the atmosphere of friendly relationship which he trusted had already been established would continue."

The functions of the Council are thus seen to extend beyond the mere compilation of a Register of Teachers and to include constant co-operation with those engaged in educational administration. In view of the desire which is now generally expressed for a closer union between the directive and executive elements in all branches of industry it is safe to assume that the Teachers' Council will grow steadily in importance, especially if it is seen to have the support of all teachers.

Meanwhile it furnishes the framework of a possible teaching profession and gives promise of securing for the teacher a definite status by establishing a standard of attainment and qualification. More than this will be required, however, if the work of teaching is to be placed on its proper level in public esteem. Those who undertake the work must be led to look for something more than material gain. The teacher needs a sense of vocation no less than the clergyman or doctor. It has been said that "teaching is the noblest of professions but the sorriest of trades" and the absence of any real enthusiasm for the work inevitably produces an attitude of mind which is alien to the spirit of a real teacher. The material reward of the teacher has accurately reflected the want of public esteem attaching to his work. For the most part a meagre pittance has been all that he could anticipate and this has led to a steady decline in the number of recruits. A profession should furnish a reasonable prospect of a career and a fair chance of gaining distinction. Such opportunities have been far too few in teaching to attract able and ambitious young men in adequate number. The remedy is to open every branch of educational work and administration to those who have proved themselves to be efficient teachers. The national welfare demands that those who are to be charged with the task of training future citizens should be drawn from the most able of our young people, to whom teaching should offer a career not less attractive than other callings. In particular the teacher should be regarded as a member of a profession and trusted to carry out his duties in a responsible manner. Excessive supervision and inspection will tend to discourage and eventually destroy that quality of initiative which is indispensable in all teaching. Freed from the monetary cares which now oppress him, definitely established as a member of a profession having some voice in its own concerns, encouraged to exercise his art under conditions of the greatest possible freedom, and provided with reasonable opportunity for advancement, the teacher will be able to take up his work in a new spirit. We may then demand from new-comers a sense of vocation and expect with some justification that teachers will be able to avoid the professional groove which is hardly to be escaped and which is quite inevitable if the conditions of one's work preclude opportunity for maintaining freshness of mind and a variety of personal interest. Such limitations as accompany inadequate salaries, lack of prospects and absence of professional status convert teaching into "a dull mechanic art" and deprive it of its chief elements of enjoyment, namely the free exercise of personality and the recurring satisfaction of seeing minds develop under instruction, so that we are conscious of our part in helping the future citizens to make the most of their lives. It is this power of impressing one's own personality on the pliable mind of youth which brings at once the greatest responsibility and the highest reward to the teacher and attaches to his task a true professional character since it may not be undertaken fittingly by any who cherish low aims or despise their work.

Taken from : http://gutenberg.net

please read the lisence before copying

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Problem Based Learning In Mathematics

2007-10-17T08:23:00.000-07:00

Problem-Based Learning (PBL) describes a learning environment where problems drive the learning. That is, learning begins with a problem to be solved, and the problem is posed is such a way that students need to gain new knowledge before they can solve the problem. Rather than seeking a single correct answer, students interpret the problem, gather needed information, identify possible solutions, evaluate options, and present conclusions. Proponents of mathematical problem solving insist that students become good problem solvers by learning mathematical knowledge heuristically. Students' successful experiences in managing their own knowledge also helps them solve mathematical problems well (Shoenfeld, 1985; Boaler, 1998). Problem-based learning is a classroom strategy that organizes mathematics instruction around problem solving activities and affords students more opportunities to think critically, present their own creative ideas, and communicate with peers mathematically (Krulik & Rudnick, 1999; Lewellen & Mikusa, 1999; Erickson, 1999; Carpenter et al., 1993; Hiebert et al., 1996; Hiebert et al., 1997).

PBL AND PROBLEM SOLVING

Since PBL starts with a problem to be solved, students working in a PBL environment must become skilled in problem solving, creative thinking, and critical thinking. Unfortunately, young children's problem-solving abilities seem to have been seriously underestimated. Even kindergarten children can solve basic multiplication problems (Thomas et al., 1993) and children can solve a reasonably broad range of word problems by directly modeling the actions and relationships in the problem, just as children usually solve addition and subtraction problems through direct modeling. Those results are in contrast to previous research assumptions that the structures of multiplication and division problems are more complex than those of addition and subtraction problems. However, this study shows that even kindergarten children may be able to figure out more complex mathematical problems than most mathematics curricula suggest. PBL in mathematics classes would provide young students more opportunities to think critically, represent their own creative ideas, and communicate with their peers mathematically.

PBL AND CONSTRUCTIVISM

The effectiveness of PBL depends on student characteristics and classroom culture as well as the problem tasks. Proponents of PBL believe that when students develop methods for constructing their own procedures, they are integrating their conceptual knowledge with their procedural skill. Limitations of traditional ways of teaching mathematics are associated with teacher-oriented instruction and the "ready-made" mathematical knowledge presented to students who are not receptive to the ideas (Shoenfeld, 1988). In these circumstances, students are likely to imitate the procedures without deep conceptual understanding. When mathematical knowledge or procedural skills are taught before students have conceptualized their meaning, students' creative thinking skills are likely to be stifled by instruction. As an example, the standard addition algorithm has been taught without being considered detrimental to understanding arithmetic because it has been considered useful and important enough for students to ultimately enhance profound understanding of mathematics. Kamii and Dominick(1998), and Baek (1998) have shown, though, that the standard arithmetic algorithms would not benefit elementary students learning arithmetic. Rather, students who had learned the standard addition algorithm seemed to make more computational errors than students who never learned the standard addition algorithm, but instead created their own algorithm.

STUDENTS' UNDERSTANDING IN PBL ENVIRONMENT

The PBL environment appears different from the typical classroom environment that people have generally considered good, where classes that are well managed and students get high scores on standardized tests. However, this conventional sort of instruction does not enable students to develop mathematical thinking skills well. Instead of gaining a deep understanding of mathematical knowledge and the nature of mathematics, students in conventional classroom environments tend to learn inappropriate and counterproductive conceptualizations of the nature of mathematics. Students are allowed only to follow guided instructions and to obtain right answers, but not allowed to seek mathematical understanding. Consequently, instruction becomes focused on only getting good scores on tests of performance. Ironically, studies show that students educated in the traditional content-based learning environments exhibit lower achievement both on standardized tests and on project tests dealing with realistic situations than students who learn through a project-based approach (Boaler, 1998). In contrast to conventional classroom environments, a PBL environment provides students with opportunities to develop their abilities to adapt and change methods to fit new situations. Meanwhile, students taught in traditional mathematics education environments are preoccupied by exercises, rules, and equations that need to be learned, but are of limited use in unfamiliar situations such as project tests. Further, students in PBL environments typically have greater opportunity to learn mathematical processes associated with communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999).

TEACHER ROLES IN THE PBL ENVIRONMENT

Within PBL environments, teachers' instructional abilities are more critical than in the traditional teacher-centered classrooms. Beyond presenting mathematical knowledge to students, teachers in PBL environments must engage students in marshalling information and using their knowledge in applied settings. First, then, teachers in PBL settings should have a deep understanding of mathematics that enables them to guide students in applying knowledge in a variety of problem situations. Teachers with little mathematical knowledge may contribute to student failure in mathematical PBL environments. Without an in-depth understanding of mathematics, teachers would neither choose appropriate tasks for nurturing student problem-solving strategies, nor plan appropriate problem-based classroom activities (Prawat, 1997; Smith III, 1997). Furthermore, it is important that teachers in PBL environments develop a broader range of pedagogical skills. Teachers pursuing problem-based instruction must not only supply mathematical knowledge to their students, but also know how to engage students in the processes of problem solving and applying knowledge to novel situations. Changing the teacher role to one of managing the problem-based classroom environment is a challenge to those unfamiliar with PBL (Lewellen & Mikusa, 1999). Clarke (1997), found that only teachers who perceived the practices associated with PBL beneficial to their own professional development appeared strongly positive in managing the classroom instruction in support of PBL. Mathematics teachers more readily learn to manage the PBL environment when they understand the altered teacher role and consider preparing for the PBL environment as a chance to facilitate professional growth (Clarke, 1997).

CONCLUSIONS

In implementing PBL environments, teachers' instructional abilities become critically important as they take on increased responsibilities in addition to the presentation of mathematical knowledge. Beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999). Preparing teachers for their roles as managers of PBL environments presents new challenges both to novices and to experienced mathematics teachers (Lewellen & Mikusa, 1999).

REFERENCES

Boaler, J. (1998). Open and closed mathematics: student experiences and understandings. "Journal for Research on Mathematics Education," 29 (1). 41-62.

Carpenter, T., Ansell, E. Franke, M, Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem solving processes. "Journal for Research in Mathematics Education," 24 (5). 428-441.

Clarke, D. M. (1997). The changing role of the mathematics teacher. "Journal for Research on Mathematics Education," 28 (3), 278-308.

Erickson, D. K. (1999). A problem-based approach to mathematics instruction."Mathematics Teacher," 92 (6). 516-521.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The Case of Mathematics. "Educational Researcher," 12-18.

Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. "Educational Researcher," 26 (2). 24-26.

Krulik, S., & Rudnick, J. A. (1999). Innovative tasks to improve critical- and creative-thinking skills. In I. V. Stiff (Ed.), "Developing mathematical reasoning in grades K-12." Reston. VA: National Council of Teachers of Mathematics. (pp.138-145).

Lewellen, H., & Mikusa, M. G. (February 1999). Now here is that authority on mathematics reform, Dr. Constructivist! "The Mathematics Teacher," 92 (2). 158-163.

Lubienski, S. T. (1999). Problem-centered mathematics teaching. "Mathematics Teaching in the Middle School," 5 (4). 250-255.

Prawat, R. S. (1997). Problematizing Dewey's views of problem solving: A reply to Hiebert et al. "Educational Researcher." 26 (2). 19-21.

Schoenfeld, A. H. (1985). "Mathematical problem solving." New York: Academic Press.

Smith, C. M. (1998). A Discourse on discourse: Wrestling with teaching rational equations. "The Mathematics Teacher." 91 (9). 749-753.

Smith III, J. P. (1997). Problems with problematizing mathematics: A reply to Hiebert et al. "Educational Researcher," 26 (2). 22-24.

taken from http://www.ericdigests.org/2004-3/math.html

Math Wars

2007-10-17T08:17:00.000-07:00

Math wars is the debate over modern mathematics education, textbooks and curricula in the US that was triggered by the publication in 1989 of the Principles and Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM). The term "math wars" was coined by commentators such as John A. Van de Walle and David Klein.
Innovative curriculaExamples of innovative curricula introduced in response to the 1989 NCTM standards include:Mathland Investigations in Numbers, Data, and Space Core-Plus Mathematics Project Criticisms of reformCritics of the "reform" textbooks say that they present concepts in a haphazard way. Procedural and traditional arithmetic skills such as long division are de-emphasized, or some say nearly totally deleted in favor of context and content which has little or nothing to do with mathematics. Some textbooks have a separate index solely for non-mathematics content called "contexts". Reform texts favor problem-solving in new contexts over template word problems with corresponding examples. Reform texts also emphasize verbal communication, writing about mathematics and their relationships with disenfranchised groups such as ethnicity, race, and gender identity, social justice, connections between concepts, and connections between representations.One particular critical review of Investigations in Number, Data, and Space says: It has no student textbook.It uses 100 charts and skip counting, but not multiplication tables to teach multiplication. Decimal math is "effectively not present".Traditional textbooksCritics of the "reform" textbooks and curricula support "traditional" textbooks such as Singapore Math and Saxon math, which emphasize algorithmic mathematics, such as arithmetic calculation, over mathematical concepts. However, even many traditional textbooks such as Saxon math usually include some projects and exercises meant to address the NCTM Standards.Supporters of the "reform" curricula, such as Thomas O'Brien , say that supporters of traditional methods, or "parrot math", have "no tolerance for children's invented strategies or original thinking, and they leave no room for children's use of estimation or calculators."NCTM 2006 recommendationsIn 2006, the NCTM released Curriculum Focal Points, a report on the topics considered central for school mathematics. Francis Fennell, president of the NCTM, claimed that there had been no change of direction or policy in the new report, and said that he resented talk of “math wars”. Interviews of many who were committed to the standards said that, like the 2000 standards, these merely refined and focused rather than renounced the original 1989 recommendations.Nevertheless, newspapers like the Chicago Sun Times reported that the "NCTM council has admitted, more or less, that it goofed". The new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn." The new recommendations are that students are to be taught the basics, including the fundamentals of geometry and algebra, and memorizing multiplication tables.
from: wikipedia.com

Opressed Educations

2007-10-17T07:59:00.000-07:00

“Looking into the general educations in Indonesia"

A lot of theories about education that was taught for the teaching student who studying at the university. Theories that were studied almost all referred in the interaction between the educator and participants educated. Not only that, but, the development of participants educated also received the focus from almost the theory whole that was taught. Moreover in the aim of national education Indonesia personally according to government law no 20 year 2003 " Aim to expand competitor educated to in order to become the godly and religious human being to God, Behavior , healthy, bookish, capable, creative, self-supporting and become the democratic citizen and also hold responsible.
In existing in reality, this is very difficult to be done. It’s because of the imitating habit which grows at education culture itself. Existing teachers in this time a lot represent the old teachers. Old system and law which at a period of/to them college applied in this time have experienced of a lot of change. Unfortunately the changes received the not better response so as the development of the method of teaching them to not follow the existing path. While way of their teacher that suspected as represent of the teaching method taught in the era of Dutch colonialization. This is why education system in this time still be related/relevant with the education model applied by former colonization era. One of the causes that was complained about since beforehand was the change in the system almost each Mendiknas change. The change and the finishing of the available system it was considered deviated too far from the system that beforehand. Therefore, the teachers in the level of the executive more liked to use their teaching method personally. The method taught like this was adoption from their teacher's teaching method personally that was received when they learned to teach. Whereas their teacher's method it was warned was the method taught the colonial Dutch time. This why the education system at this time was still related to the educational model that was applied when the colonization time beforehand.
After we knew that the learning models at this time still was linked with the colonization time learning method, we see its study process. This caused the problem if still continued to be applied. At this time, we were prosecuted to have the expertise that could compete with the international market. With the available education system, we could only produce the skilled workers but was in the worker's lowered class. If it still last, forever we could only export manual laborers in order to satisfy the requirement for manpower in the market.
Indonesian must begin in realized this situation. It’s not longer the time for us to educate a multiple-skilled workers. At this time, we must begin to be focused in education specific ability oriented that could fill the international standard. So each individual must be given special provisions that will give him the creating freedom based on what skill that he/ she expert in. Eventually this capacity that will distinguish the individual from the other individual.
If beforehand a car mechanic could repair all part of the car but did not spread everywhere. At this time we must think how educated a mechanic who knew all part of the car but had the special expertise in the certain part. For example, a mechanics knew all part of the car but he had the specialization in the part engine tune up. Whereas if having the problem moreover he must hand over in other mechanics that had the specialization to the component. This must also begin to be applied in the level of basic education. Especially to the primary school. If nowadays one class was only taught by a teacher then this habit must begin to be changed. As being applied to the junior high school and the senior high school.
Several time ago stood the anti corruption school. Why the anti corruption school? Because the school was our first place learned to carry out corruption. Not only student but the teacher. Why was like this? Consciously or not, we trained ourselves for corruption with the habit to enter late and outside the class was earlier. When minor matters like that became the habit then will change to the mental attitude. As a result, this attitude will clear our life field that was other not only was trapped. When at one time we were given by the belief then we little by little processed to take what not our right. Starting from time than to the material. The process like when we were in the classroom. This will become a habit that was regarded as natural and did not cause the problem.
We have to start to realize that the education in Indonesia were an oppressed education. The existing system only accommodates the market demand for skilled man power. On the other hand, both the expert and the process to make the skilled power personally be ignored. The expert with the expertise especially precisely not always being accommodated his opportunity to work. The higher standard of payment was became the most reason for many factory to chose the skilled power with lower education grade. Whereas the deliberate expert was brought in from other country. The process of making the skilled power personally just as banded as the skilled power expert them self. Many children of the school age that cannot finish their education because of the high educational cost. They usually end to the street child or the blue-collar worker the level was lowest. For that we need our government concern as well as any other company that needed educated and skilled manpower to develop this abandon potential recourses.

WELCOME

2007-10-17T07:47:00.000-07:00

Welcome all!!!
This is my blog and I'm trying to make something
If you like what I'm doing, so join me in this team
If you don't I hope you find what you want
Please do not hate me for what I do but correct me if I'm wrong
Just hate me for my lack of power for doing something greater
One step after another, I hope it will be the start
One new kind of educations system is my goal
Democratic mathematics education,
with all student will learn how to tell their idea LOUD AND CLEAR
and the teacher will teach for their love of the student
no more worries about lack of sallary and what we can eat tomorrow

Love full eduations system