Nenden Octavarulia Shanty

This paper talks about the learning about making full pack in order to introduce a part of place value concept.

INTRODUCTION

Teaching mathematics through mathematizing might help children to get a better understanding about mathematics itself. Mathematizing is the activity of interpreting, organizing, and constructing meaning of situation with mathematical modeling (Fosnot & Dolk, 2001).

Place value is a basic and an important concept in mathematics. The invention of place value in the history of human kind has taken a long time. Giving children an understanding of place value will take a long time too, therefore a context needs to be designed so that student will be engaged in the process of the invention. Through this context students are challenged to find a way of counting big numbers. This context gives students an opportunity to explore their thinking. They have plenty of time to discover different strategies. This is very important in students’ learning process. Discovering something new needs a process of thinking, in this stage, students analyze the problems, then they think of a way to solve it, there’s when strategy occur.

Starting from a quotation: “mathematics for all”, mathematics should be taught no longer in school just as a tool, but should be taught as a subject which possesses several mathematical goals that reflect the diverse roles of mathematics which plays in the society. The process of how mathematics is learned is as important as what a mathematical product is learned. Freudenthal said that mathematics is a human activity [Freudenthal, 1991]. It means that mathematics itself becomes a part of the learner’s asset if we can let the learner to appreciate mathematics as an activity through a learning process and not just mathematics as an end product.To gain such a broad perspective of the mathematics subject as a whole, we feel that an acquaintance with the history of mathematics is indispensable. As stated in Swetz, the history of mathematics can give students an awareness of tradition, a feeling of belonging, and a sense of participation [Swetz, 2000]. By incorporating some historical aspects into teaching and learning processes, teaching can reduce something mistique and abstract.

From Wikipedia, the free encyclopedia

Hans Freudenthal

Hans Freudenthal (September 17, 1905 – October 13, 1990) was a Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.

Freudenthal was born in Luckenwalde in Germany into a Jewish family and completed his thesis work with Heinz Hopf at the University of Berlin, and defended a thesis on the ends of topological groups in 1930. He was officially awarded a degree in October 1931. He then went to Amsterdam to serve as assistant to Brouwer. In 1937 he proved the Freudenthal suspension theorem.

In 1941 Freudenthal was suspended from duties at the University of Amsterdam by the Nazis. His wife, however, was not Jewish, so he was not sent to a concentration camp in eastern Europe but he was deported to a labor camp in the village of Havelte in the Netherlands. At the end of 1944 he was able to escape and join his family in occupied Amsterdam.

Later in his life, Freudenthal focused on elementary mathematics education. In the 1970s, his single-handed intervention prevented the Netherlands from following the worldwide trend of “`new math“‘.^[1] He was also a fervent critic of one of the first international school achievement studies.^[2]

In 1971 he founded the IOWO at Utrecht University, that after his death was renamed Freudenthal Institute, the current Freudenthal institute for science and mathematics education. He was awarded the Gouden Ganzenveer award in 1984, and died in Utrecht in 1990, sitting on a bench in a park where he always took a morning walk.

Guys, if you want to join IMPoMe scholarship as I ever inform you about that, you can download the application form and also CV that you have to fulfill in the link below:

www.p4mri.net

This program, a consortium among University of Utrecht, the Netherlands and Surabaya University (UNESA) and Sriwijaya University (UNSRI) in Palembang, provides an opportunity for the Lecturers of the Candidates of New Academic Staff or (CTAB), and the teachers of Mathematics with a sarjana degree in mathematics education or sarjana degree in mathematics to join International Master Program in Mathematics Education.

The program will be carried out for a period of 2 years and 2 months which is divided into 3 stages, namely 8 months in Indonesia (UNESA or UNSRI), 1 year in Netherlands (University of Utrecht), and 6 months for research and thesis writing in Indonesia.

The scholarship for the period of studying in Indonesia for the Lecturers or CTAB will be provided by Ditjen Pendidikan Tinggi Depdiknas (BPPS), while the period in the Netherlands will bee funded by StuNed.

The requirements to be the candidates are as follows.

In September 7^th to September 9^th, IMPoME’s (International Master Program on Mathematics Education) students had some work sessions on mathematics and the didactics of the RME (Realistic Mathematics Education) with Jaap den Hertog – Coordinator of the IMPoME program and lecturer from Utrecht University and Aad Goddjin – lecturer from Utrecht University. The central issues of these sessions were mathematizing and didactizing. Every day we had three sessions, four hours for didactics about ratio and proportions (Jaap den Hertog) and two hours for mathematics about Geometry of Vision (Aad Goddijn).

IMPoMe students, Aad Goodjin, Jaap den Hertog, and Prof. Zulkardi

1. INTRODUCTION

A progressive innovation program, i.e. PMRI (Pendidikan Matematika Realistik Indonesia), that has been running for more than seven years, has a primary aim to reform mathematics education in Indonesia. This innovation program is adapted from RME (Realistic Mathematics Education) in the Netherlands that views mathematics as a human activity (Freudenthal, 1991) in which students build their own understanding in doing mathematics under the guidance of the teacher.

As implementation of PMRI, there are four schools that have become KKG PMRI schools since 2004 in Palembang, i.e. SDN 117, SDN 98, MIN 1, and MIN 2. My observation’s object is SDN 98 Palembang. Since May 2009, I had observed this school together with Nasrullah, Yeka, and Farid. We observed in different classes. The teacher in my classroom observation actually had not joined workshop and seminar PMRI yet. But, I invited her to join PMRI by practicing directly PMRI in her class, and she was very welcome with it. Her name is Mrs. Nurhayati. Two weeks I observed class before implemented PMRI in class. Together with the teacher, we made lesson plan and prepared material and visual aids for teaching and learning process.

2. PMRI IMPLEMENTATION IN CLASS

The material is about numbers up to thousand in grade three. Based on curriculum, Grade 1 to grade 3 is using ‘tematik’. ‘Tematik’ means that one theme integrate to all subject such as mathematics, social, science, etc. For this meeting the theme was about ‘Public Place’. First, the students are given a context about football court (the picture is given in students’ handout). The students needed to guess how many spectators in there and then explain the way they found their answer. Then we go to the next problem, still about guessing (we don’t need the correct answer here), they need to count how many seats for spectators are available in a side of football court (the picture is given). There is an interesting answer from a student whose name is Cahya Yunzilla. She said that the quantity of seats is less than the quantity of spectator. She explained that maybe there are spectator who didn’t have a seat, so they need to stand up for watching football game. From this problem, we can explore more about the capacity of stadium and give a cross question to the students.

As the students knew about the large quantity (such as the people or the seats in stadium), we try to make a concrete how much 1.000 is it. In this activity, we use straws as visual aids. They have to bind 10 straws using a rubber. So, the straws are in 10 – 10 now. Next, they need to bind again the 10 of bind-10 straws (each bind consists of 10 straws).

Students work with straws

SUMMARY

A Learning-Teaching Trajectory for Grade 4, 5, and 6

Frans van Galen, Els Feijs, Nisa Figueiredo, Koeno Gravemeijer, Els van Herpen and Ronald Keijzer

Core Insight for Proportion

There are many forms of mathematical descriptions with fractions, percentages, decimals and proportions, and they all have their own rules and procedures. Learning all these arithmetic rules requires a lot of practice, and experience shows that students quickly forget rules and procedures when the practice stops. The emphasis is shifted from skill-carrying out procedures-towards understanding. Core insights indicate what the teaching should pay particular attention to.

Proportions are Everywhere

• Enlarging and reducing: photos, copiers, models, maps, etc
• Money: price comparisons, get 4 for the price of 3, telephone rates, etc.
• Recipes for 4 or  people, making coffee
• Comparing probabilities.
• Gears on a mountain bike, how step the hill is
• Graphs and diagrams

SUMMARY

DAVID BEN-CHAIM, JAMES T.FEY, WILLIAM M. FITZGERALD, CATHERINE BENEDETTO and JANE MILLER

I. INTRODUCTION

One of the new middle grades curriculum projects, the Connected Mathematics Project (CMP), was funded to develop a complete mathematics curriculum with teacher support materials for the middle grades six, seven, and eight. This curriculum is structured to develop students’ knowledge and understanding of mathematics that is rich in connections – connections among the core ideas in mathematics and its applications. The environment of students who experience the CMP curriculum is different than the environment of students in the traditional curriculum in terms of the textbooks they are using, the classroom organization, and the methods by which they are being taught. This report concern regarding attainment of proportional reasoning in reform and traditional curricula, by comparing work of seventh grade CMP and non-CMP students on a variety of tasks.