Mengajarkan Matematika Pada Anak

Mengajarkan Matematika Pada Anak

Ketika akan mengajar matematika kadang anda berhadapan dengan suatu garis besar dalam kurikulum yang kompleks yang menawarkan berbagai jalan untuk mengerjakan angka-angka – ini tidak mudah untuk dipahami sebagaimana yang penulis pikir – dengan demikian berikut ini adalah daftar jalan / tatacara untuk temukan cara melalui teka-teki itu !
Kemampuan mengolah angka

Mengelompokkan

Benda-benda dengan ciri-ciri yang sama dikelompokkan dalam satu kesatuan. Misalnya kelompok bunga mawar

Korespondensi satu-satu

Ini penting sebelum mulai mengajar berhitung.

Berhitung

Memasangkan nama angka dengan sekelompok benda (misalnya angka 2 dengan dua ekor ayam)

Pengurutan

Mengurutkan berdasarkan letak.

Pengelompokan

Mengidentifikasi himpunan yang memiliki jumlah anggota yang sama.

Penetapan

Mengetahui bahwa simbol angka sifatnya tetap bagaimanapun peletakan anggota himpunan itu.

Pengenalan simbol

Mengenali simbol suatu angka dan menghubungkannya dengan cara ucap simbol tersebut. Misalnya 2 dibaca dua.

Mengenal nilai tempat

Posisi suatu angka menentukan nilainya. Misalnya, 7, 73 dan 741 masing-masing memiliki nilai yang berbeda untuk angka 7.

Operasi Hitung

Penjumlahan

Menghitung maju dari suatu titik yang diketahui.

Pengurangan

Mengambil sejumlah benda dari suatu himpunan.

-Memecahkan perbedaan antara 2 himpunan

Perkalian

Menambahkan himpunan yang sama (2+2+2=)

– Kelipatan (2, 4, 6, 8, 10)

– Penjabaran misalnya, 2 jenis roti                        =   6 jenis

masing-masing terdiri                 Roti lapis

dari 3 jenis yang sama

Pembagian

Membagi dalam jumlah yang sama suatu kelompok bilangan

Menentukan berapa jumlah anggota himpunan yang dapat dibentuk.

Misalnya : Ada 6 ikan. Jika dibagi untuk 3 ekor kucing, berapa yang didapatkan masing masing kucing?

Pecahan

1/3 dapat mewakili :

– Satu bagian dibagi menjadi tiga bagian.

– Suatu angka yang dapat dibagi tiga

– Suatu angka yang tidak dapat dibagi oleh angka tiga

– Sebagian dari tiga (sepertiga)

– Suatu angka kurang dari satu

Aljabar

Generalisasi suatu hubungan (pola) angka

Pola angka

Pola penomoran, aljabar dan geometris.

Misalnya : Pola dalam nomor

Pola dalam nilai tempat

Pola dalam perkalian dan pembagian

Pola kesamaan dan pola angka khusus

Pengerjaan angka yang tidak diketahui (persamaan)

– Gunakan huruf atau simbol

– Gunakan grafik dan koordinat (persamaan)

Mengajarkan Matematika Pada Anak

Back To Tempat Les (Sesi 2)

Seperti yang telah diberitakan sebelumnya bahwa tempat belajar saya selain kampus tercinta adalah ruang number 3 A Children Center.

Sebagaimana brosur diatas, nah, saya ngajarin anak pake baju pink yang lagi nulis angka ga jelas itu.

Enough for the promotions. Back to topic.

Setelah hampir sembilan bulan menjadi seorang “guru les”(cie..cie… guru?belom lah) akhirnya saya sadar tentang apa yang saya kerjakan selama ini. tentang bagaimana belajar yang efektif itu. Ga mesti berkelompok sesuai umur tapi harus benar-benar mendapat bimbingan yang memadai. memang benar sebaiknya anak-anak dikelompokkan sesuai dengan tingkatan kelasnya atau kemampuannya. Hanya saja, beberapa anak terlalu spesial untuk disamaratakan dengan teman sebayanya.

Ada anak yang memiliki kecenderungannya sendiri dalam belajar. Ada pula anak yang selalu membawa keceriaan dalam kelas. Selama bekerja ini, beberapa anak telah mendapat tempat istimewa dalam hati saya. Anak yang cukup special untuk membuat keceriaan di kelas. Pengkondisian kelas menjadi salah satu syarat dalam pembelajaran yang baik dalam suatu bimbingan belajar. Berbeda dengan kelas-kelas konvensiaonal yang ada disekolah dimana mau tidak mau anak harus belajar disitu dalam jangka waktu tertentu. Sebuah bimbingan belajar dituntut untuk menyediakan fasilitas (kelas, alat, materi, budaya belajar, lingkungan belajar) yang memadai sehingga anak yang belajar di sana dapat berkembang sesuai dengan kemampuannya.

Seminar tentang MBTI (Myers-Briggs Type Indicator) menyadarkan saya betapa ilmu yang didapat di bangku kuliah sangatlah kurang untuk mengetahui sifat manusia yang unik. Manusia adalah individu yang unik (kata bu Endang), nah seminar setengah hari tentang MBTI telah memberikan apa yang selama ini dijelaskan itu. Well, mungkin masih ada cara lain untuk mengetahu sifat-sifat seorang anak. Terlepas dari itu semua tetap saj aitu merupakan modal untuk pengabdian yang selanjutnya.

See you in my class!!! Easy Math not Dizzy Math we learn

Flash Matematika

Gambar Bangun Ruang

Bangun Ruang1

Fungsi Kuadrat

Mengajar Les Pada Sebuah Bimbingan Belajar – Suatu Refleksi Diri

Sudah hampir lima bulan saya menjadi fasilitator matematika (a.k.a tentor/guru les) di sebuah bimbingan belajar 3A Children Center di Jl.Colombo no 8 Yogyakarta (Sekalian Promosi). Tapi, bukan itu yang akan dibahas disini. Tapi tentang bagaimana proses belajar-mengajar yang terjadi dalam ruangan kelas saya itu. Konsep pendidikan untuk anak-anak telah membatasi kelompok umur yang masuk dalam lembaga bimbingan belajar tersebut. Jika selama ini lazimnya anak-anak yang ikut les itu mulai dari SMP atau minimal SD kelas V dan VI dalam rangka menghadapi UNAS maka kondisi berbeda mulai marak. Di 3A Children Center, banyak murid yang berasala dari kelas 0 hingga kelas V . Hal ini membuat kesulitan tersendiri dalam mengajar. Bukan hanya harus sabar namun harus memiliki kearifan, dan perilaku yang sehat. Bayangkan saja, jika anda ditanyai oleh anak TK tentang apa itu tornado atau katrina? Bagaimana anda menjelaskannya? Atau pernah suatu ketika mereka bertanya tentang apa itu menit, apa itu detik? Pernah memikirkan cara menjelaskan satuan waktu seperti menit dan detik pada anak yang bahkan belum duduk di bangku SD?
Meski banyak ahli berpendapat bahwa mengajarkan anak tentang suatu konsep abstrak terlalu dini tidak baik bagi perkembangan anak itu sendiri, toh banyak orang tua yang “melanggar” hal itu. Meski perbuatan itu tidak dapat disalahkan mengingat syarat untuk masuk ke sekolah ‘favorit’ memang mengharuskan kemampuan itu. (Baca juga menghindari kekerasan pada anak )
Back to the topic. Saya pernah membaca suatu pendapat dalam suatu buku (kalo ga salah time life seminggu belajar matematika) anak-anak sebaiknya tidak diajarkan matematika dengan cara yang rumit. Memang jika kita lihat buku-buku pelajaran saat ini memang bukan main rumitnya bagi anak-anak yang baru mulai mengenal ilmu hitung(matematika). Bagaimana tidak, anak-anak dituntut untuk dapat menghafal angka. Setelah dirasa hafal, mereka harus mengucapkan angka secara benar balam urutan yang acak sebelum mereka diharuskan mengurutkan suatu susunan angka acak menjadi suatu susunan yang diharapkan. (mirip-mirip cari integral ganda gitu deh kalo buat mahasiswa).
to be continued……….

Everyday Mathematics is one of a number of relatively new math programs developed around the NCTM standard. Although it has been widely adopted, and praised by education innovators, it has also been criticized as one of the worst math texts introduced in recent years. A 2007 web video produced by Where’s the Math singled out Everyday Mathematics for emphasizing unusual and inefficient computation methods, statements that it is a waste of time to teach traditional computation methods to proficiency, and instead spend “precious class time” on activities such as planning a trip across the country with colorful maps. However, unlike TERC, this program does cover many traditional computation methods, along with several alternatives.

1 Description of the program
2 Application in the classroom
3 Evidence of effectiveness
4 Critics and their rationale
5 Notes
6 External links
7 References

Description of the program
Scope and sequence:
According to the developers, “…[t]he developers of Everyday Mathematics believe that the groundwork for mathematical literacy should begin at a much earlier age than offered by traditional mathematics programs…”(Current Curriculum 2002).
Everyday Mathematics is based on a “spiral” curriculum, where mastery is not required before the introduction of new topics. This is contrasted to seeing an obvious progression of skill build-up occur (student masters one digit addition and moves on to two digit addition) In opposition to this view, however, “…Everyday Mathematics was designed to take advantage of the spacing effect…” (Braams 2003). It relies on the notion that regular reinforcement of important skills is necessary, emphasizing that skills should appear multiple times and throughout a course of study. The key principle in regards to spiraling and distributed practice is that mastery and fluency in basic skills are goals that should be achieved long after they are first introduced (Braams 2003).
In accordance with this belief, the Everyday Mathematics program is set up around seven mathematical strands. Those seven are as follows:
• Algebra and Uses of Variables
• Data and Chance
• Geometry and Spatial Sense
• Measures and Measurement
• Numeration and Order
• Patterns, Functions, and Sequences
• Operations
• Reference Frames (About Everything Mathematics 2003)
Features of the program:
Beyond the scope and sequence, EM has several other discerning features. The following is a listing of them, as well as an explanation for how the program incorporates them.
• Real-Life Problem Solving-
EM places a great deal of focus on real-world problems. A great deal of instruction revolves around application of mathematical concepts in everyday situations.
• Balanced Instruction-
“…Learning is conducted in whole group, small group, and individual settings. Students experience open-ended questions, hand-on explorations, supervised practice, and long term projects…” (Current Curriculum 2003).
• Multiple Methods for Basic Skills Practice-
Students practice basic skills through daily review problems, mental math activities, flash cards, games, homework, etc.
• Emphasis on Communication-
Discussion is very important to the program. Students are asked to explain their problem solving strategies. Students are also expected to listen and learn from other students.
• Enhanced Home/School Partnerships-
Information is sent home to help parents work with their children. Homework is structured so that students are meant to rework problems from previous lessons with adults in the home.
• Appropriate Use of Technology-
Technology is used within the program in a way that is meant to instruct children when and where it is appropriate to use it. This is especially true when it comes to calculators.

Application in the classroom
Below is an outline of the components of EM as they are generally seen throughout the curriculum.
Lessons:
A typical lesson outlined in one of the teacher’s manuals includes 3 parts.
1. Teaching the Lesson- This is where the new content is introduced.
2. Ongoing Learning and Practice-In this section, material is reviewed for maintenance purposes.
3. Options for Individualizing- Here is where options for extending or reteaching concepts are presented.
(Click link to view a sample of a lesson http://everydaymath.uchicago.edu/samplelessons/2nd/index.html)
Daily Routines:
Everyday, there are certain things that each EM lesson requires the student to do routinely. These components can be dispersed throughout the day or they can be part of the main math lesson.
• Math Messages- These are problems, displayed in a manner chosen by the teacher, that students complete before the lesson and then discuss as an opener to the main lesson.
• Mental Math and Reflexes- These are brief (no longer than 5 min) sessions “…designed to strengthen children’s number sense and to review and advance essential basic skills…” (Program Components 2003).
• Math Boxes- These are pages intended to have students routinely practice problems independently.
• Home Links/Study Links- Everyday homework is sent home. Grades K-3 they are called Home Links and 4-6 they are Study Links. They are meant to reinforce instruction as well as connect home to the work at school.
Supplemental Aspects
Beyond the components already listed, there are supplemental resources to the program. The two most common are games and explorations.
• Games – These are counted as an essential part of the EM curriculum. “…Everyday Mathematics sees games as enjoyable ways to practice number skills, especially those that help children develop fact power…” (Program Components 2003). Therefore, authors of the series have interwoven games throughout daily lessons and activities.
• Explorations- One could, perhaps, best describe these as mini-projects completed in small groups. They are intended to extend upon concepts taught throughout the year.
Implementing all of these components is a challenge, as it requires time, and a change of attitudes from students and teachers, can also be a problem. “…Instead of fostering a competitive environment and teaching students through logical deduction, Everyday Mathematics uses a collaborative milieu and allows students to draw their own conclusions after seeing recurring math patterns. Teachers facilitate the process instead of teaching it… (Knight 2005). Teachers must also have faith in the spiral curriculum in order to implement and assess student work. Teachers who have been trained on grading for mastery, may become frustrated in application of EM.

Evidence of effectiveness
“[d]espite its critics, Everyday Mathematics has 13 years of university research behind it …” (Knight 2005).
Among positive evidence, “The research evidence about Everyday Mathematics (EM) almost all points in the same direction: Children who use EM tend to learn more mathematics and like it better than children who use other programs.” (University of Chicago 2005).
It was originally developed as a research project for the University of Chicago. “Each grade level of the Everyday Mathematics program went through a three-year development cycle that included a year of writing, a year of extensive field-testing in a cross-section of classrooms, and a year of revising…” (University of Chicago 2005).
Few other programs have been through so much testing and research, nevertheless, the program has been challenged by critics

Critics and their rationale
Criticism of EM has come from all directions. Many internet sites and web pages and even internet videos have been dedicated to countering the position of many school districts and education professionals that EM is an effective mathematics program. Many believe that EM is not just innovative, but a severely deficient and radical approach to math that should be abandoned.
One direction from which criticism comes is from parents. “..[S]uch programs as Everyday Mathematics raise the eyebrows and sometimes the ire of parents simply because they don’t use the traditional methods parents are accustomed to…” (Knight 2005). It is difficult for some to trust EM because it seems to differ so much from the math they grew up with. Many parents complain that the methods used in homework are so different from traditional methods, they are unable to assist in homework assignments. Other parents claim that their children are unable to master simple arithemetic problems. Methods such as the “lattice” multiplication method are far more tedious, and require more drawing and effort with no real advantage over traditional methods. By 2007, school districts that were considering adopting EM were encountering very negative reactions from parents when asked about the choice of EM [1]
Many professional mathematicians consider EM to be an inferior curriculum. Like many parents, they believe that overlooks or underplays basics. It does not promote the use of standard algorithms that have been tested and used for a long time by professionals who use math every day.
However, Wertheimer (2002) points out that “…[t]he mathematicians are among the few survivors of the traditional mathematics program. They are trying to apply what they know to the entire population”. He also has a great deal of reservations about the ability of these mathematicians to evaluate the complexity of educational methodology that can help everyone achieve. Mathematics education should help promote the success of everyone not just those naturally successful at math. (Wertheimer 2002). Others questioned the assumption that groups such as women and minorities cannot be expected to learn basic math facts in a traditional way, and that only “successful” groups should be learning “real math”.
Beyond parents and professional mathematicians, even teachers have joined in the argument. Teachers who have encountered problems with such a radical approach have also dissented.
A common argument is that the program was not the problem, but implementation was. Critics claimed that the content was difficult for teachers to teach without a great deal of training. Much of the content in geometry and statistics goes far beyond the traditional 5th grade math most parents and elementary teachers are proficient in, because of the belief that students in early grades should be studying advanced math concepts rather than only basic facts and methods.

taken From Wikipedia.com

Math Wars

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 curricula
Examples 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 reform
Critics 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 textbooks
Critics 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 recommendations
In 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