EARCOME 7

EARCOME

Scientific Programme

The theme of EARCOME 7 is “In Pursuit of Quality Mathematics Education for All.” 
This resonates with the need for good quality mathematics education to be inclusive of all students regardless of their gender, background and contexts.
EARCOME 7 will consist of the following activities: Plenary Lectures (PL), Regular Lectures (RL), Topic Study Groups (TSG), Workshops (W), Special Sharing Groups (SSG), Plenary Panel Discussion (PD) and Poster Presentations (PP).
The TSG themes are:
TSG 1: Quality Mathematics Curriculum and Materials
TSG 2: Quality Mathematics Classroom Practices
TSG 3: Quality Mathematics Assessment
TSG 4: Quality Mathematics Teacher Education and Development
TSG 5: Quality Use of ICT in Mathematics
TSG 6: Quality Use of Language and Discourse in Mathematics
TSG 7: Quality Early Childhood and Lower Primary Mathematics Education

Call for Papers and Important Dates

We invite the mathematics education community to submit abstracts of papers for presentation at the Topic Study Groups. Research papers that reflect well thought out studies related to the TSG themes, particularly those that have significant practical implications for teaching and learning, are most welcome.We also invite the mathematics education community to submit abstracts for poster presentations.
Submit the abstracts by email to: earcome7sec@gmail.com
For TSG proposals, use the following format for the filename and the subject line:
TSG [No.]_[Complete Name of Corresponding Author]_[Country].
The maximum number of words is 500.
For Poster proposals, use the following format for the filename and the subject line:
Poster_[Complete Name of Corresponding Author]_[Country].
The maximum number of words is 200.
All abstracts will be reviewed, after which corresponding authors will be informed of the decisions. The full papers for accepted TSG proposals will be peer-reviewed and published in the conference proceedings.
Important dates:
April 30, 2014 – Deadline for TSG proposals
June 16, 2014 – Release of decisions on the TSG proposals
September 1, 2014 – Deadline for poster proposals
October 3, 2014 – Release of decisions on the poster proposals
December 1, 2014 – Deadline for full papers for TSG proposals
January 5, 2015 – Feedback to authors
February 6, 2015 – Deadline for revised full papers for TSG proposals
For more information, click…http://earcome7.weebly.com/programme.html
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ICT and Introduction to RME Tasks

1. Reflection Paper

a. Reflection Paper 1, https://umipuji.wordpress.com/2013/09/02/reflection-paper-1/
b. Reflection Paper 2, https://umipuji.wordpress.com/2013/09/08/reflection-paper-2/
c. Reflection Paper 3, https://umipuji.wordpress.com/2013/09/15/reflection-paper-3-2/
d. Reflection Paper 4, https://umipuji.wordpress.com/2013/09/21/reflection-paper-4/
e. Reflection Paper 5, https://umipuji.wordpress.com/2013/10/02/reflection-paper-5/
f. Reflection Paper 6, https://umipuji.wordpress.com/2013/10/07/reflection-paper-6/
g. Reflection Paper 7, https://umipuji.wordpress.com/2013/10/14/reflection-paper-7/
h. Reflection Paper 8,

https://umipuji.wordpress.com/2013/10/23/building-blocks-to-develop-students-spatial-visualisation-ability/

i. Reflection Paper 9,

https://umipuji.wordpress.com/2013/11/27/percentage-bar-as-the-powerful-model-for-learning-percentage/

j. Reflection Paper 10,

https://umipuji.wordpress.com/2013/11/28/common-sense-for-concreting-abstract-mathematics/

2. Lesson,

https://umipuji.wordpress.com/2013/10/10/application-of-pmri-on-persentage-in-class-5a-sd-iba-palembang/

3. Video (it is tagged in a powerpoint),

https://umipuji.wordpress.com/2013/10/30/penyelesaian-soal-persentase-oleh-siswa-kelas-5-sd-iba-palembang/

4. Powerpoint

a. Powerpoint 1,

https://umipuji.wordpress.com/2013/10/20/intelligent-guessing-and-testing-including-approximation/

b. Powerpoint 2,

https://umipuji.wordpress.com/2013/12/03/introduction-to-rme/

5. Contextual Problems

a. Bahasa Indonesia,

https://umipuji.wordpress.com/2013/10/17/contoh-soal-statistik-geometri-dan-bilangan-dengan-konteks-purworejo/

b. Bahasa Inggris,

https://umipuji.wordpress.com/2013/10/20/the-example-statistic-geometry-dan-number-problems-with-the-context-of-purworejo/

6. Applet, https://umipuji.wordpress.com/2013/11/09/how-fast-your-multiplication-ability/

Apakah ini Sekedar Ketidaktelitian Siswa?

Materi pengukuran waktu merupakan materi yang sangat penting. Hal ini karena dengan mempelajari materi ini siswa diharapkan memiliki bekal yang cukup untuk menyelesaikan masalah kehidupan sehari-hari mereka yang berkaitan dengan waktu. Sayangnya, pembelajaran matematika, khususnya tentang pengukuran waktu, masih jarang yang mampu mengkaitkannya dengan dunia siswa yang sesungguhnya. Sejalan dengan apa yang disampaikan oleh Gravemeijer dalam reflection paper saya sebelumnya, pembelajaran ini masih sering disampaikan dalam angka-angka dan rumus-rumus kurang bermakna yang sering menggiring siswa pada dunia yang berbeda dengannya.

https://umipuji.wordpress.com/2013/11/28/common-sense-for-concreting-abstract-mathematics/

Ketika saya dan rekan saya memberikan sebuah soal pengukuran waktu kepada siswa kelas 5, kami mendapati kasus yang hampir sama. Dari kelima kelompok siswa, tiga kelompok belum mampu menggunakan pengalaman sehari-harinya untuk menyelesaikan soal yang pada dasarnya merupakan soal yang biasa mereka temukan dalam kehidupan sehari-hari. Ketika ketiga kelompok ini sampai pada penentuan “Pukul berapakah yang menunjukkan 115 menit sebelum pukul 14.00?” Ketiga kelompok mendapatkan jawaban yang sama, yaitu 12.45. Mengapa demikian? Mari perhatikan uraian jawaban mereka berikut ini.

  • 115 menit = 1 jam 55 menit
  • Siswa menulisnya menjadi 1.55
  • Siswa mengurangkan 1.55 dari 14.00 seperti pada gambar berikut.

time ok 2

Seperti ditunjukkan pada gambar, hasilnya terlihat bahwa 14.00 – 1.55 = 12.45. Pernahkan teman-teman menemukan jawaban siswa yang demikian?

Awalnya saya pikir ini hanya masalah ketidaktelitian. Tetapi setelah saya cermati, nampaknya hal ini tidak demikian. Perhatikan uraian saya berikutnya.

Ketika kami meminta siswa untuk mengecek dengan cara menghitung dari depan (apakah 115 menit setelah pukul 12.45) menunjukkan pukul 14.00? Kali ini siswa mampu mengkaitkan pengalaman sehari-harinya untuk menghitung 115 menit setelah pukul 12.45. Mereka dapat menyadari bahwa 115 menit setelah pukul 12.45 itu lebih dari 14.00, yang berarti jawaban mereka kurang tepat.

Mereka pun mengecek perhitungan mereka (dengan cara susun seperti pada gambar di atas) berkali-kali dan tidak pula menemukan titik kesalahannya. Mereka yakin kalau perhitungan mereka benar. Namun, mengapa ketika di cek jawabannya salah????

Ketika kami menanyakan dalam satu jam ada berapa menit, mereka dengan cepat, tepat, dan kompak menjawab 60 menit. Tetapi mengapa mereka belum mampu mengkaitkan hal ini untuk menyelesaikan persoalan di atas? Mereka menyamakan perhitungan 1.400 – 155 dengan  perhitungan pukul 14.00 dikurangi 1 jam 55 menit. Bukankah ini berarti bahwa siswa belum mampu memaknai angka-angka yang mereka tulis???

Saya pun teringat dengan materi operasi hitung pada pengukuran waktu yang diajarkan mulai kelas empat. Siswa diajarkan tentang tambah kurang pada satuan waktu. Di beberapa buku paket diajarkan cara penyelesaian sebagai berikut.

Contoh soal :

7 jam 20 menit – 2 jam 45 menit =…………..

Caranya :

time ok 1

Dari situ, kita bisa melihat bahwa apa yang diajarkan dalam buku paket adalah tentang lama waktu. Sedangkan soal yang kami berikan berkaitan dengan notasi jam (14.00) dan lama waktu (1 jam 55 menit). Namun, sepertinya siswa menggunakan ingatannya yang parsial tentang operasi tambah kurang pada lama waktu diatas untuk menyelesaikan persoalan yang kami berikan. Selain penggunaan notasi yang kurang tepat (1 jam 55 menit ditulis 1.55), siswa belum mampu mengkaitkan 1 jam yang terdiri atas 60 menit untuk menyelesaikan persoalan di atas. Bukankah ini tidak hanya masalah ketelitian? Bukankah kesalahan seperti ini bisa dihindari jika pembelajaran tidak hanya mengingat tetapi penuh makna?

Menjadi guru memang tidak mudah. Ketika saya mengajar di sebuah SD, saya pun mengalami hal demikian. Inginnya mengajar begini dan begitu. Tetapi, tidak jarang idealita kita terbentur dengan target-target materi yang begitu banyak atau pun waktu yang serasa tidak cukup untuk mempersiapkan bahan ajar dengan maksimal. Namun, marilah kita belajar untuk pantang patah arang. Belajar bersama untuk menjadi guru yang lebih baik. Belajar bersama untuk mendidik anak-anak Indonesia menjadi anak yang lebih cerdas.

Carpediem. Majulah Pendidikan Indonesia !!!

Common Sense Concrete for Concreting Abstract Mathematics

This paper is the reflection of the article of Koeno Gravemeijer that titles How Concrete is Concrete?  Koeno Gravemeijer is a realistic mathematics education expert from Freudenthal Institute, Utrecht University, Nederland.

Mathematics is abstract, so most of the students think that mathematics is not easy. For making the learning of mathematics easier, the teachers introduce tactile or visual models. They think it is able to make the abstract mathematics concrete. However, Gravemeijer will show that our common way of making things concrete for the students does not work because we help students to make a connection with what we know, not what they know.

The first example that will be shown by Gravemeijer is about how the student of grade 6 solved the comparing fraction problem. The context is about a bakery that would cut banquet bars (a sort of large cookies) to order. They were given paper strips of a given length to enact the cutting process. Then they were asked to cut the banquet bars into eight equal pieces, or six, or ten, and so forth. After they asked to use similar strips to compare 1/3 and 2/6, they solved this problem by comparing the lengths of pieces produced in the two different divisions-either dividing by three or dividing by six. However, students concluded that 1/3 was not equal to 2/6.

Gravemeijer analized the answer of the students then he found that the way students cut the strips was not very precise. It made the answer of the student is like that. It means that the tactile representations do not support an insightful solution. Furthermore, in this case, we may denote the two ways in which ‘concrete’ can be understood as either “material concrete” or as “common sense concrete”. The students’ point of view is sometimes different with teacher’s point of view. In this case, the teacher see the relation between 1/3 and 2/6 in the paper cutting, but the students just see the blocks with various sizes.

So, how is the better one? We prefer to help students to reason how 1/6 relates to 1/3. First, a bar is divided into three parts and each piece into halves next, to get six equal pieces. Then, they will understand that 1/6 is a half of 1/3 and they able to concluse that 2/6 equal to 1/3.

equality

The second example is about addition tasks for the student of grade 1. She is Auburn. When Auburn counting on 16 + 9, she got 25. She also know that if she had 16 cookies and another 9 added, she would have 25 cookies. But, when she filled the worksheet, she wrote 15. When she was interviewed why the answers are different, she said that she didn’t know. Lets look at a part of that worksheet below.

concrete

If we analize the worksheet, we able to know why Auburn’s answer is 15. She just imitated the example from the worksheet. She thought that the mathematics of the worksheets seem different with the world of everyday-life experience. She will not be inclined to use everyday-life knowledge to make sense of ‘school math’ problems. Gravemeijer argue that the knowledge gap between teachers and students is too big to make this work. And manipulatives cannot bridge this gap.

So, what is the better? We could use arithmetic rack to fasilitate the students for communicating and scaffolding.

artmtk rck

In conclution, we may try to follow Freudenthal’s adagio that ‘mathematics should start and stay within common sense’ by trying to foster the growth of what is common sense for the students.

Percentage Bar As The Powerful Model for Learning Percentage

This article is the reflection paper of the article of Frans van Galen and Dolly van Eerde that titles Solving Problems with The Percentage Bar. It was publised in IndoMS JME, Volume 4 Number 1, 1 January 2013, page 1-8.  Frans van Galen and Dolly van Eerde are realistic mathematics education experts from Freudenthal Institute, Utrecht University, Nederland.

Percentage is one of the matematics material that is taught from grade 4 until 6 in primary school. We can imagine, how often this material is taught. However, when a group of IMPOME students carried out a study in grade 7 on students’ understanding of percentages, they were surprised because there are only four students from 14 students who they tested were able to give a correct answer on the following problem :

bike problem

Although the students had a certain area to be a scrap paper, they just used it to wrote calculation. None of them used it to draw model to clarify the relation between the given numbers. It was obvious that most of the students didn’t know a systematics procedure for working with percentages.

A week later, they interviewed the students about the way they solved some of these problems. They find that there are four students’ ways to solve the problem.

  • Converting the percentage into a decimal number and multiplied, for example : 0,15 x 600
  • Multiply with fractions, for example :

soal 1

  • Trying to make proportions equal, for example :

soal 2

  • Guided by the numbers in the problem, for example : 600 is divided by 15

Eventhought two first solutions are true, but they were not consistent and made calculation error. While, the way solution number 3 made the students were confused.

In a teaching experiment, the students were taught the use of the percentage bar.The researchers has 2 approaches.

  • Calculating via 10%. The problem is like that “if the price of the handphone is € 300 and you just pay € 240, how much the percentage of the discount?” The answer of the student is shown below.

PBar

First, student calculated 50% and 25% of € 300, but that didn’t lead to a discount of € 60. As a next step, she started with 10% and found € 60 by doubling.

  • Calculating via 1%. The problem is about the downloading the computer file. “How many Mb if someone download 11% of 600Mb?” The student answer is shown below.

PBar 2

Student’s strategy is 50% equals 300, 25% equals 150 and 10% equals 60. 11% as 10% + 1%.

Although teaching experiment by percentage bar was carried out just one lesson, the result confirm that the percentage bar is a powerful model that deserves a central place in the teaching of the percentage. It helps the students to make a representation for themselves of the relations between what is given and what is asked, offers scrap paper for the intermediate steps in the calculation process, and offers a natural entry to calculating via 1%.