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Etnomatematika

10 November 2013

ETNOMATEMATIKA:

KETIKA MATEMATIKA BERNAPAS DALAM BUDAYA

 

(Oleh: I Nengah Agus Suryanatha & Ratih Ayu Apsari)

 

APA ITU ETNOMATEMATIKA?

Etnomatematika merupakan matematika yang tumbuh dan berkembang dalam kebudayaan tertentu (Yusuf dkk, 2010). Budaya yang dimaksud disini mengacu pada kumpulan norma atau aturan umum yang berlaku di masyarakat, kepercayaan, dan nilai yang diakui pada kelompok masyarakat yang berada pada suku atau kelompok bangsa yang sama (Hammond, 2000).

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Istilah etnomatematika berasal dari kata ethnomathematics, yang terbentuk dari kata ethno, mathema, dan tics (Yusuf dkk, 2010) Awalan ethno mengacu pada kelompok kebudayaan yang  dapat dikenali, seperti perkumpulan suku di suatu negara dan kelas-kelas profesi di masyarakat, termasuk pula bahasa dan kebiasaan mereka sehari-hari. Kemudian, mathema disini berarti menjelaskan, mengerti, dan mengelola hal-hal nyata secara spesifik dengan menghitung, mengukur, mengklasifikasi, mengurutkan, dan memodelkan suatu pola yang muncul pada suatu lingkungan. Akhiran tics mengandung arti seni dalam teknik.

Oleh karena tumbuh dan berkembang dari budaya, keberadaan etnomatematika seringkali tidak disadari oleh masyarakat penggunanya. Hal ini disebabkan, etnomatematika seringkali terlihat lebih “sederhana” dari bentuk forma matematika yang dijumpai di sekolah. Masyarakat daerah yang biasa menggunakan etnomatematika mungkin merasa tidak percaya diri dengan warisan nenek moyangnya, karena matematika dalam budaya ini, tidak dilengkapi definisi, teorema, dan rumus-rumus seperti yang biasa ditemui di matematika akademik.

 

CONTOH ETNOMATEMATIKA

Nenek-nenek kita di Bali mungkin tidak mengenal definisi lingkaran sebagai himpunan titik-titik yang berjarak sama. Mereka juga bisa jadi tidak tahu bagaimana membuat gambar lingkaran dengan menggunakan jangka seperti yang biasa kita lakukan. Mereka mungkin tidak tahu jumlah sudut dalam lingkaran sebesar 3600. Tapi dengan jelas mereka bisa membuat bentuk lingkaran dengan menggunakan peralatan sederhana, hanya dengan busung (janur/daun kelapa yang masih muda), semat (lidi tajam yang berguna untuk merekatkan bagian-bagian busung), dan pisau.

Bagaimana caranya?

Potong janur dalam ukuran yang sama. Pertemukan tengahnya kemudian semat ujung-ujungnya.

Ilustrasinya begini:

 

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Begitu pula dengan tradisi otonan (lihat penjelasan matematis yang lebih lengkap di: https://p4mriundiksha.wordpress.com/2013/10/18/masalah-matematika-dengan-konteks-lokal-1/ )

Konsep kelipatan persekutuan dengan sangat baik diterapkan dalam perhitungan otonan tersebut, dimana penanggalan kelahiran seseorang (menurut perhitungan wewaran dan pawukon) akan berulang setiap 210 hari sekali.

Belum lagi konsep modulo yang dapat kita lihat daam sistem pemberian nama di Bali. Anak pertama memiliki nama yang mengandung unsur Wayan/Putu, anak kedua Nengah/Made/Kadek, anak ketiga Nyoman/Komang, dan anak keempat Ketut. Apabila seseorang memiliki anak lebih dari empat, pemberian namanya akan berulang kembali dari satu, yaitu Wayan/Putu, dan seterusnya. Dengan kata lain, pemberian nama di Bali memiliki dasar modulo 5, yang hanya memiliki 4 orang anggota.

 

CONTOH LAINNYA

Semadiartha (2011) mengajukan konsep refleksi yang digunakan pada bangunan-bangunan di Bali.

Misalnya:

 

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(dokumentasi Semadiartha, 2011)

 

Mertayasa (2011) juga memiliki pengamatan yang tak kalah menarik. Ia menyelidiki tentang bagaimana seorang penjual nasi sebenarnya mengenal konsep ke-simetris-an pada bangun datar, dimana ia mampu mentransformasi kertas minyak yang berbentuk persegi panjang, nejadi sebuah lingkaran yang memiliki bentuk melengkung dibagian atasnya, dengan menggunakan teknik melipat dan menggunting.

 

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(dokumentasi Mertayasa, 2011)

 

Sepertinya akan banyak etnomatematika yang membuat kita terkagum-kagum akan sifat universal matematika. Terlebih lagi di Indonesia, yang memiliki keragaman budaya dengan kearifan lokalnya masing-masing. Kemunculan etnomatematika dalam diskusi tentang ilmu matematika nampaknya akan menjadi sangat menarik. Di satu sisi memperkaya ilmu pengetahuan, di sisi lain melestarikan budaya. 🙂

 

 

 

Referensi:

Mertayasa, Dewa Made. Etnomatematika Pada Pedang Nasi dan Kaitannya dalam Pembelajaran Matematika. Makalah Seminar Matematika[*]. Program Pasca Sarjana Pendidikan Matematika Universitas Pendidikan Ganesha

Semadiartha, I Kadek Sembah. 2011. Etnomatematika Ukiran Bali dan Implementasinya Dalam Pembelajaran Matematika. Makalah Seminar Matematika[*]. Program Pasca Sarjana Pendidikan Matematika Universitas Pendidikan Ganesha

Suryanatha, I Nengah Agus. 2011. Etnomatematika: Permainan Teka-Teki Wasakwakwalwa dalam Kebudayaan Hausa. Makalah Seminar Matematika[*]. Program Pasca Sarjana Pendidikan Matematika Universitas Pendidikan Ganesha

Hammond, Tracy. 2000. Ethnomathematics: Concept Definition and Research Perspectives. Thesis for Degree of Master of Arts, Columbia University. http://srlweb.cs.tamu.edu/srlng_media/content/objects/object-1234476000-b6fdd344454299ac478700e4deb6e040/2000HammondEthnoma thematics.pdf

Yusuf, Mohammed Waziri, dkk. 2010. Ethnomathematics (a Mathematical Game in Hausa Culture). International Journal of Mathematical Science Education Technomathematics Research Foundation.  http://www.tmrfindia.org/sutra/v3i16.pdf

 

[*] serangkaian mata kuliah seminar matematika untuk mahasiswa semester 3 program pasca sarjana Undiksha tahun 2011, dengan dosen pengampu Prof. Dr. I Gusti Putu Suharta, M.Si.

 

Metode Representasi Visual

9 November 2013

REPRESENTASI VISUAL:

SALAH SATU METODE MENYELESAIKAN MASALAH YANG BERKAITAN DENGAN SISTEM PERSAMAAN LINIER

(Oleh: Ratih Ayu Apsari*)

Membelajarkan Sistem Persamaan Linier Dua Variabel (SPLDV) pada siswa sekolah dasar?

Beberapa bulan yang lalu, salah seorang rekan saya pernah mendiskusikan masaah yang ia temui ketika mengajar seorang siswa SD yang sedang mempersiapkan diri untuk mengikuti olimpiade matematika. Dalam soal-soal olimpiade tahun-tahun sebelumnya yang sedang siswa itu pelajari, ternyata ada soal yang konsepnya tentang sistem persamaan linier. Teman saya panik. Siswanya masih terlalu dini untuk belajar SPLDV secara formal. Tapi ia tetap mencoba, memberi penjelasan perlahan-lahan tentang dasar-dasar SPLDV. Tapi semakin dijelaskan semakin siswanya tidak mengerti. Apa itu variabel, apa itu metode substitusi, eliminasi, grafik, dan sebagainya. Siswa galau. Guru (teman saya itu) lebih galau lagi.

Pernahkah Anda mengalami kejadian serupa?

Saya menyimpan pertanyaan tentang cara menyelesaikan SPLDV ini dalam waktu yang cukup lama sampai suatu hari, di mata kuliah Problem Solving, dosen saya yaitu Dr. Yusuf Hartono, mendiskusikan pertanyaan serupa.

Berikut adalah soal yang dilontarkan dosen saya:

1

Saat itu, saya dan sembilan orang lainnya (teman sekelas saya) serentak menggunakan metode campuran eliminasi dan substitusi..

Dosen saya tertawa, “Sini saya tunjukkan cara yang lain”, katanya.

Beberapa minggu setelahnya akhirnya saya tahu cara yang beliau gunakan saat itu disebut sebagai “making a visual representation” atau membuat representasi visual alias membuat gambarnya.

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  • Pertama, karena sudah jelas baik setiap kelinci maupun ayam punya sebuah ekor, berarti total hewan di kandang tersebut adalah 32. Untuk itu, kita gambarkan 32 lingkaran sebagai perwujudan badan ayam dan kelinci.

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  • Kedua, karena setiap kelinci dan ayam minima punya dua buah kaki, kita gambarkan dua buah garis pada setiap lingkaran sebagai wujud dari kaki.

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  • Hitunglah banyak “kaki” yang telah digunakan dan bandingkan dengan kaki yang tersedia. Karena kita sudah menggunakan 64 kaki sementara yang tersedia 70 kaki, berarti ada 6 kaki yang belum digunakan. Sisa kaki ini akan ditambahkan masing-masing 2 ke beberapa buah lingkaran. Dengan demikian ada beberapa lingkaran yang punya empat buah garis.

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  • Hitunglah banyak lingkaran yang punya dua buah garis, itu adalah representasi banyaknya ayam.
  • Hitunglah banyak lingkaran yang punya dua buah garis, itu adalah representasi banyaknya kelinci.

 

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Jadi,

Bagaimana metode ini menurut Anda?

Saya harap ini dapat membantu Anda dalam membantu siswa yang ingin menyelesaikan masalah yang berkaitan dengan persamaan linier meskipun mereka belum pernah belajar konsep formalnya 🙂

*)

Mahasiswa Program Pasca Sarjana Pendidikan Matematika

International Master Program on Mathematics Education (IMPoME)

Universitas Sriwijaya

temukan artikel asli (dalam Bahasa Inggris) di:

http://ratiihayu.blogspot.com/2013/11/visual-representation-method.html

Masalah Matematika dengan Konteks Lokal [3]

18 October 2013

CARA MEMBUAT BENTUK DASAR “SAAB”

(Oleh: Ratih Ayu Apsari)

 

Dalam tradisi Bali, ketika ada kerabat/tetangga kita yang mempunyai acara keagamaan, kita akan berkunjung kesana dan membawa hadiah yang diletakkan dalam sebuah wadah berukuran cukup besar yang disebut dengan saab. Saab adalah suatu kerajinan tangan yang terbuat dari ental (daun lontar), yang ketika sudah jadi nantinya dilapisi dengan beludru dan manik-manik (atau bisa juga hanya diwarnai dengan pewarna). 

 

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Gambar 1: Saab

Seperti yang dapat Anda perhatikan, bagian dasar dari saab berbentuk lingkaran. 

 

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Gambar 2: Dasar Saab yang Berbentuk Lingkaran

 

Zaman sekarang, para perajin saab membuat pola berbentuk lingkarannya dengan jangka. Kira-kira bagaimana ya cara membuat bagian dasarnya kalau tidak ada jangka seperti jaman dahulu? 

Pada Gambar 3 berikut terdapat bahan-bahan dasar untuk membuat saab. Dengan bahan-bahan tersebut, dapatkah Anda membayangkan apa yang digunakan para pendahulu kita dalam membuat bentuk lingkaran? Jelaskan dan gambarkan ide Anda!

 

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Gambar 3: Peralatan untuk Membuat Badan Dasar Saab

 

 

Masalah Matematika dengan Konteks Lokal [2]

18 October 2013

SISTEM IRIGASI TRADISIONAL BALI “SUBAK”

(Oleh: Ratih Ayu Apsari)

Subak adalah kearifan lokal milik masyarakat Bali yang mengatur sistem irigasi di areal persawahan pada daerah tertentu. Subak dikepalai oleh Kelihan Subak dan terbagi atas beberapa bagian yang lebih kecil yang disebut dengan tempekan. Setiap subak memiliki banyak tempekan yang berbeda dan besar tempekan tersebut juga berbeda. Kapasitas air yang dialiri ke setiap tempekan disesuaikan dengan luas tempekan itu sendiri sehingga seringkali terjadi perbedaan banyak air yang dialiri ke masing-masing tempekan.

Desa Tukadsumaga adalah salah satu daerah pertanian di Kabupaten Buleleng, Provinsi Bali. Di daerah ini ada suatu subak yang disebut Subak Anyar, yang memiliki enam buah tempekan bernama tempekan Bukit Taman, Jambul Ilang, Banjar Buluh, Dajan Munduk, Dauh Tukad, dan Dangin Tukad. Setiap tempekan ini memiliki luas daerah berbeda.

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Suatu hari seorang Kelihan Subak yang baru yaitu Pak Nengah, penasaran dengan banyak air yang dialirkan ke masing-masing tempekan. Ia kemudian mengumpulkan data dan menemukan bahwa jika Subak Anyar mengaliri: (1) seluruh tempekan, maka banyak air yang diperlukan adalah 50.000 liter, (2) Bukit Taman, Jambul Ilang, dan Banjar Buluh, maka banyak air yang diperlukan adalah 24.968 liter, (3) Jambul Ilang dan Dauh Tukad, maka banyak air yang diperlukan adalah 14.84, (4) Banjar Buluh, Dajan Munduk, dan Dangin Tukad, maka banyak air yang diperlukan adalah 26.399 liter, dan (5) Dajan Munduk, Dauh Tukad, and Dangin Tukad, maka banyak air yang diperlukan adalah 25.032 liter.

Berdasarkan data di atas, dapatkan Pak Nengah mencapai tujuannya? Jika iya, tuliskanlah solusi yang menurut Anda berhasil ia peroleh terkait porsi air untuk setiap tempekan !

Masalah Matematika dengan Konteks Lokal [1]

18 October 2013

“OTONAN”: PERINGATAN HARI KELAHIRAN BERDASARKAN WEWARAN dan PAWUKON
(Bidang Materi: Bilangan)

 

Oleh: Ratih Ayu Apsari [06022681318077]
International Master Program on Mathematics Education (IMPoME)

 

Dalam kepercayaan umat Hindu di Bali ada suatu ritual yang disebut dengan otonan yang SONY DSCmerupakan peringatan hari kelahiran berdasarkan penanggalan wewaran dan pawukon pada Kalender Saka.

Wewaran terdiri atas beberapa jenis, yaitu ekawara, dwiwara, triwara, caturwara, pancawara, sadwara, saptawara, astawara, sangawara, dan dasawara. Dari kesepuluh wewaran tersebut yang biasa dijadikan patokan dalam menentukan otonan adalah pancawara dan saptawara (bersama-sama dengan pawukon). Adapun pawukon merupakan siklus yang terdiri atas 30 wuku dan berganti setiap 7 hari sekali.

Berikut ini adalah daftar pancawarna, saptawarna, dan wuku.

Tabel 1: Pancawarna

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Tabel 2: Saptawara

Saptawara indo

 

 

 

 

 

 

 

 

Tabel 3: Wuku

Wuku

 

 

 

 

 

 

Jika Gede Yudhistira merayakan otonannya yang ke 54 pada tanggal 3 November 2013 dimana hari tersebut menurut penanggalan Saka Bali jatuh pada Redite Umanis Langkir, dapatkah kamu menentukan tanggal lahirnya?

INTRODUCING LINEAR EQUATION SYSTEM FOR GRADE 8 STUDENTS

15 September 2013

INTRODUCING LINEAR EQUATION SYSTEM FOR GRADE 8 STUDENTS

by: Ratih Ayu Apsari
Student of International Master Program on Mathematics Education (IMPoME)

Many educators usually use a formal approach to teach about linear equation system. We might invoke the real life experience problem, but we will tell their pupils to do standard strategies to solve it. For example, let considering a beautiful “T-Shirt and Soda” problem given by Romberg and de Lange (1998) on Zulkardi (2002).

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Figure 1: T-Shirt and Soda Problem

In what way you will solve that problem?
It might be true that most mathematics teachers will directly use one of three most common use strategies to solve linear equation system, such as by sketch a graph, elimination, or substitution. They will represent the T-Shirt and Soda as the mathematical symbol, let say x and y and start their formal method.
However, why we are not trying to see the problem in different point of view? Assume that we are the grade 8 students who have no experience whit this kind of problem. What will we do?
It is something amazing that our students may solve this problem without knowing anything about x, y and any standard method. Consider this possible strategy.

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Figure 2: Example of Non-formal Strategy

This is my strategy:
Because I omit several item, the remainder is one T-Shirt on the first expenditure and one Soda on the second expenditure. From that situation, I can infer that the price for T-Shirt is $14 higher than Soda.
After knowing that fact, I can find the price of each. For instance, I would like to find the price for Soda using the second expenditure. Since I know the price for Soda is $14 cheaper than T-Shirt, I can say that I spent $16 for 4 Soda. Therefore, the price for one Soda is $4. Since the T-Shirt is $14 more than Soda, then the price of T-Shirt should be $18.
What do you feel when your students can answer the question through a creative way like what I have done? It is actually applied the concept of substitution and elimination, but not in a formal scheme.
Feel curious for other creative strategy that might be emerge in your class try to give the similar problem to your students!
Here you can improve the problem into something that experimentally real to the Balinese students. How if you use the context of Sukawati Market? You can change the T-Shirt as the Sukawati Pants with flower pattern and the Soda with the Sukawati Necklace. Change the price from US Dollar ($) to Rupiah (Rp).

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Figure 3: Modifying T-Shirt and Soda Problem into Sukawati Market Problem

 

Enjoy your class!

Note for the readers who doesn’t familiar with the name of Sukawati:
Sukawati is a famous handicraft market located in Gianyar, Bali. It is well-known place to buy a traditional clothes, accessories, statue, painting, and other local industries.

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS (Part 3)

5 September 2013

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS

(Part 3)

Composed by : Ratih Ayu Apsari

The content is summarized from seven articles of National Conference of Mathematics XIV (2008), Sriwijaya University.

[6] Puspita Sari : Empty Number Line Model in The Addition and Subtraction Learning.

This study is conducted for second graders students, which purposed to help children develop a framework of number relations to construe flexible mental arithmetic strategies and to make students use to solving addition and subtraction problems up to 100 both in context and in a bare number format using mental arithmetic strategies.

The researcher use the empty number line—a number line which has no numbers or markers on it— as a model to represent students’ strategies during mental computation. She also claimed that a empty number line allows the students to track their errors, because each step in students’ thinking can be recorded.

The empty number line could be introduced through a string of beads which alternate in colour for every ten of it, to help the students doing measurement activities. The empty number line is emerged first as model of situation and then it develops as the model for situation.

In the Picture 7 below, the example of empty number line is showing.

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Picture 7: The emergence of an empty number line (Picture Modified)

[7] Rooselyna Ekawati : ‘Lapis’ Cake Problem as The Contextual Situation in Learning Fraction.

One of some goal of this research was to help students understanding the equivalence fractions. To encourage students in learning, the researcher use the question about “Lapis Surabaya” which is familiar with the subject experiments.

Kirana is given a challenge by hher father to divide the cake fairly. Under the bread, there is usually a paper which has equal size to the cake. Based on the paper, can you help Kirana to complete her father’s task?

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Picture 8: Lapis Surabaya

From this context, the teacher guide the students to folding strategy using paper strip folding model. The researcher note that paper string folding is very good model to develop students understanding in comparing fraction and doing some operation, such as addition and find the difference between fraction.

In the first activity, students use basic paper fold strategy to divide cake in equal size. However, this strategy will be quite difficult when the students want to divide the whole cake into odd pieces. As the bridging to accomplish the equality task, the teacher can introduce the use of rubber band in the dividing paper process.

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS (Part 2)

5 September 2013

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS

(Part 2)

Composed by : Ratih Ayu Apsari

The content is summarized from seven articles of National Conference of Mathematics XIV (2008), Sriwijaya University.

[3] D.N. Handayani: Butterfly-Wing Context to Support The Earlier Development of Number Sense.

One of mathematical phenomenology that deal with the early number sense, specially in first grade students of primary school is the cardinality. In the formal mathematics, cardinality of a set is a measure of the number of element of the set. The problem is, the beginner students often not realize the aim of counting. For instance, when they aregiven five candies and asked to count how many candies is it, they might start counting as “one, two, three, four, five”. However, even though they stop at “five”, the teacher should investigate it carefully: are they allready understand that 5 means five objects or they think that the fifth object is 5.

To help the students reach the basic understanding in number sense, the butterfly-wing context had been choosen in this research, because it has pattern which similar in the left and right side. The students were asked to observed the pattern in the butterfly wings and guided to recognize the pattern. At the end of lesson, the students are expected to count “how many” in sets of objects using various structures.

[4] Meiliasari: The Context of Structured Candy on Earlier Addition and Substraction Up to 20.

At the earlier phase of learning, children generally use many kind of counting strategies, such as count all objects one by one and count from larger addend, which usually use their fingers to keep the track. When deal with larger number, some students might realize that the counting method seems to be no longer effective. The children will develop new strategies, such as doubling (i.e., 6+8 = 6+6+2)  and splitting (i.e., 6+8 = 6+4+4=10+4). The development of this process may take quite long time.

In order to help te students working in addition in easier and quicker way – and less possibility to do computational error, this study was conducted using the context of candies, which is very familiar in student’s daily live. It is had been tested that the question such as; Dinda as 4 candies and then her mother give another 3 candies. How many candies does Dinda has?  Is more acceptable in low class students rather than directly use the abstract symbol as 3+4 = …?

The lesson activity is organize as follow. At the first time, teacher told students to count a number of candies. They can manually count it (unstructured way) or they can arrange it first, suc as by making two rows of candies which has some number for each row, and then count it (structured way). The purpose of this activity is to make students realized that structure helps them to counting faster.

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Picture 4: Illustratation of Unstructured and Structured Candies (Picture Modified)

The next activity is purpose to guide the students to recognize the double structure. Before enroll the worksheet phase, the students are invited to sing the “double song” (satu ditambah satu sama dengan dua, dua ditamba dua sama dengan empat, etc.) which is populer in Indonesia. This song is purpose to stimulate the students’ understanding in double sum. In this stage, the worksheet still use the context of candies which are arranged in one or two packs of two rows of five.

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Picture 5: Illustration of Question in Worksheet 2

The third activity is illustrated on the following picture.

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Picture 6: Illustration of 5+2=7

The task is about a candy box which just fullfil by 7 canies (the white circles is means the place is not covered by candy). At first, the students expected can tell that it all 7 candies on the box. Second, they can explain that since there are 5 candies in first row and 2 candies in second rows, te total is 7. In mathematical sentence, they can write the mathematical sentence 5 + 2 = 7.

 To help the students construct their understanding in subtraction, the researcher embeded the concept on the subtraction as the invers of addition, rather than using counting strategies, such as counting up (such as (5 – 3 = 4,5 so 5-3=2) or counting backward (5 – 3 = 5,4 so 5 – 3 = 2). That’s why, the students will make the correlation between addition and subtraction. For intance, 6 + 4 = 10, so that 10 – 6 = 4 and 10 – 4 = 6.

[5] Neni Mariana : School Building Context to Develop Spatial Ability.

Spatial ability is the skill to mentally manipulate, understand, reorganize, or interpret relationships of shapes and space. This comprehension is related to matematics, specially geometry achievement for the students (Casey et.al., 2008; Melancon, 1994; Tartre, 1990; Tracy, 1987).

The researcher actually designed for nine activities for learning, but for this chance, the disscussion will just about five of it. The activities are set as the following step.

Activity 1 : My School Building

The goal of this activity is the children are able to localize for main buildings of the school on a grid paper. This activity use several cube with same size.

Activity 2 : Where Our Classroom Is

The goal of this is activity is the children are able to localize their alssroom position on a grid paper. Through this activity, children are expected to gradually emerge 2-dimension scale model. The previous activity is just use the same-size cube. This condition not match with real situation, because in the school some building have different weight, height, and even the shape. By starting tis activity, a conflict will appear about the shape of the school. Consequently, the pupils will come up with a conclusion that not all buildings can be represented by one cube since some of them higher, wider, etc.

Activity 3 : Removable Buildings

The purpose of this activity is to make sure that children are able to: (a) localize all rooms by making a map of the basements on a grid paper, and (b) connect between 3D constructions and 2D shapes of their basements.

Activity 4 : Make a Route to an Important Place in the School

The goal for this activity is the students are able to spatially explain routes to some important places using directions, such as to the left, straight ahead, to the right, and so forth.

Activity 5 : A Mini Lesson – Where Do You Have to Stand?

The aim for this activity is to help the students to denote one-to-one correspondence between a certain point of standing viewer and a certain point of a part of the school buildings.

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS (Part 1)

5 September 2013

7 INSPIRING CLASSROOM ACTIVITIES USING REALISTIC MATHEMATICS

(Part 1)

Composed by : Ratih Ayu Apsari

The content is summarized from seven articles of National Conference of Mathematics XIV (2008), Sriwijaya University.

[1] Al Jupri : Supermarket Context in Learning Estimation Problems.

The study was caused by the minimum attention given by the mathematics curriculum in term of the importance of computational estimation skill. However, many experts in mathematics education believe that this comprehension is needed by the children to solve their daily problem experience, since most of it use non-exact calculation (Carpenter et all (1976), Driscoll et all (1981)). There are several kind of question which is appear in daily life, such as are there enough ?, could this be correct ?, and approximately how much is it ?. This kind of question, tend to be easier to solve with estimation strategies rather than the exact one. The researcher use supermarket as the context in teaching estimation for fifth grader students since it is familiar and easy to imagine by the Indonesian pupils. One example of its problem given in the class is:

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Picture 1: Illustration of Problem Given on the Research (Picture Modified)

This kind of question can stimulated students to try other way (estimation strategy) to find the answer, since it will quite complicated to do an exact calculation like what they use to.  However this context might be helpful for students either teachers, the researcher himself realize that many students still doubting the result they get through estimation strategy since their prior paradigm told them that mathematics should not be answered by approximately answer. That’s why the researcher suggest to do class discussion after doing students’ worksheet.

[2] Ariyadi Wijaya : Indonesian Traditional Games in Learning Measurement of Length.

The researcher use Gundu and Benthik (Javanese traditional games) as his context to encourage the basic concept understanding in measurement for second grade elementary school’s students. This research conducted since the measurement topic usually teach directly in formal level. Even though children engaged in a number of daily activities which use measurement context, it not guaranteed that they can make a relation between what they use to do and what they learn in the class.

The idea behind applied the gundu game is to emerge the concept of indirect comparison. In this game, each player should throw their marbles from starting point to a pole on the ground. The winner determined by compare the distance of the marbles from the pole.

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 Picture 2: Illustration of Gundu Game

The Benthik game itself is doing on this way: all players in each team have to hit a short stick and then the distance of the fallen stick is measured. The winner determined by the team which has the longer distance of the stick. Students are free to choose measurement tools either the unit which use to compare the length of distance. The conjecture for this activity is the students, while measure the distance of their stick, may use different tool and unit, such as their footsteps. It will lead them to different result since every students have different size of step. From this situation, they will realize that they need to use same measurement to obtain same result for same distance. This basic concept can be used as the first step in introduce the standard measurement for the students.

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Picture 3: Illustration of Benthik Game

The report of a small study on percentages

5 October 2012


  1. Introduction

This paper is the report of a small study on percentages conducted in a seventh grade of one international secondary school in Rotterdam from September until October 2011. The study was conducted as a part of one course the researcher took, namely Integrative Practical (IP). The course aims at giving experience to master students in doing a design research. The study aims at supporting seventh graders in developing their understanding on percentages. In the light of it, the general research question posed in this study is how can we support pupils in developing their understanding of percentages? This general research question can be elaborated into three specific sub questions: Read more…