Critical Analysis of Roth and Bowen’s Paper: “When Are Graphs Worth Ten Thousand Words? An Expert-Expert Study”

Purpose and Question of the Research

The authors present the research purpose very explicitly in the paper. It can be found on the page 430, second paragraph, in which they state that: “this study was conducted to better understand graphing expertise. We were particularly interested in understanding the contributions of experience (content represented, laboratory experience, and understanding of conceptual frameworks) to the particular readings provided by scientists”. The research purpose is also written explicitly in the discussion (see p. 466, first line of the first paragraph): “… to better understand readings of familiar and unfamiliar graphs by professional scientists”.

The research question is not formulated explicitly in the paper. As the reader, I do not know exactly whether the authors forgot to mention the research question intentionally or not. But, the title of the paper is written in the form of a question, when are graphs worth ten thousand words. Later, in the conclusion (see p. 470, the last paragraph), the authors say that this title is their initial question, but not the research question. In my perspective, this initial question cannot be categorized as the research question or even as a good research question. Although it is researchable, this initial question does not provide any clear explanation about the things that the study wants to investigate. There is no any explanation in the question about the kinds of graphs that are going to be used. The word ‘when’ is also somewhat ambiguous. What does the term when means? Does it mean the time of presenting the graphs, or the kinds of graphs? But, this initial question is worthwhile to investigate. The researchers formulate the reason for it (see p. 430, paragraph one): “… there is little work on the actual use of graphs in everyday science, or on scientists’ reading of unfamiliar graphs”. Continue reading

Critical Analysis from Methodological Perspective: A case of Lederman’s Research Paper

Regardless of methodology, almost all researchers engage in a number of similar components in conducting their research. All of these components include, purpose and question of the research, research approach and methods, population and sample of subjects, data collection (e.g. tests or other measuring instruments, a description of procedures to be followed), a description of intended data analysis and interpretation, and conclusions. Those components are also considered as the key elements in doing critical analysis of research papers based on methodological perspective. In this text, I shall present my own critical analysis from methodological perspective of Lederman’s research paper titled Teachers’ understanding of the nature of science and classroom practice: factors that facilitate or impede the relationship.

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An Analysis of Misunderstanding in Mathematics: The Case of Meanings of Equal Sign

Introduction

Many mathematical symbols and notations are figured routinely by students in learning mathematics in the school contexts. Those symbols and notations are mostly faced by students, especially when they learn about arithmetic and algebra. In fact, many students are struggling to understand the meaning of those mathematical symbols and notations, and sometimes lead them to the misunderstandings (e.g. Kiran, 1981). Realizing this issue, many researchers and experts from many different fields and backgrounds have been trying to find out what kinds of misunderstandings that happen in the students’ thinking in learning mathematics and how to deal with them.

Furthermore, misunderstandings about mathematical symbols and notations are also happened in the case of equal sign (or more holistically, equality). Question about how students understand the equality symbol have largely been discussed by many researchers and experts from many different fields persist through elementary schools to high schools and colleges (e.g. Jones and Pratt, 2007; Hattikudur and Alibali, 2010). Based on those extensive researches focusing in this issue, many students do not interpret the equal sign, as an equivalence symbol. They misunderstand about the meaning of the equal sign. Moreover, as will be seen, understanding the equal sign as an equivalence relation does not seem to come easily to the students. The purpose of this essay is to analyze about misunderstandings of the equal sign among elementary and secondary school children.

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Teaching and Learning The concept of Adding and Subtracting of Whole Numbers up to Nine Hundreds Using RME Approach in Indonesian Primary School

A.    INTRODUCTION

This observation report explains about the process of teaching and learning adding and subtracting up to nine hundreds without saving at SD Negeri 98 Palembang, South Sumatera, Indonesia by using Realistic Mathematics Education Approach with stone and arrow cards as a model of and model for respectively. This activity involved 35 pupils.

In this observation, I was a teacher in the classroom. The teaching and learning activities ran about 60 minutes. When I was teaching, I also did documentation and guided the students to follow the instruction. In this meeting, I introduced the concept of addition up to nine hundreds to the students through telling the story titled “Perjalanan Si Bolang”.

 

B.     DISCUSSION FINDINGS

I conducted my observation in SD Negeri 98 Palembang, a public primary school located at K.H.A. Azhari street, 14 Ulu, Palembang on the 8th of October, 2011. It is one of the public primary schools in Palembang that has been applying PMRI in the classroom.

When I met with Mrs. Ningcik, as she called, she said that the students at grade III start their lesson in the noon, around 1.20 p.m. Presently, the topic for mathematics subject is adding up to one thousands. But than, she suggested me to start with adding without saving. By discussion with her, either by phone or message, I also told her that I am planning to use story as a context in teaching the concept of adding up to one thousands and she agreed with it.

 

C.    GOAL OF OBSERVATION

The goal of this research is to make students understand the concept adding up to nine hundreds without saving by using Realistic Mathematics Education Approach.

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“pempek” Story, Straws and Arrow Cards in Teaching and Learning Place Value Concept at Grade II

 A.    INTRODUCTION

This observation report explains about the process of teaching and learning place value at SD Negeri 98 Palembang, South Sumatera, Indonesia by using Realistic Mathematics Education Approach with straws and arrow cards as a model of and model for respectively. This activity involved 32 pupils.

In this observation, Mrs. Mariani was a teacher in the classroom. The teaching and learning activities ran about 60 minutes which was helped by Novita Sari and me for documenting and guiding the students to follow the instruction. In this meeting, we introduced the concept of place value to the students through telling the story titled “Ibu Ros dan Pempek”.

B.     GOAL OF RESEARCH

The goal of this research is to make students understand the concept of place value by using Realistic Mathematics Education Approach.

C.    RESEARCH FINDING

1.      Discussion Result

This research conducted in SD Negeri 98 Palembang, a public primary school located at K.H.A. Azhari Street, 14 Ulu, Palembang on the 23th of September, 2011. It is one of the public primary schools in Palembang that has been applying PMRI in the classroom. Before my friend Novita sari and I, went to this school for conducting our research, we had had discussion with Mrs. Mariani as a teacher at grade II. From the discussion, we have a deal that Mrs. Mariani will be a teacher in the class and Novita sari and I will help her to guide the students in the group.

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Four-D Model (Model Pengembangan Perangkat Pembelajaran dari Thiagarajan, dkk)

Model pengembangan perangkat Four-D Model disarankan oleh Sivasailam Thiagarajan, Dorothy S. Semmel, dan Melvyn I. Semmel (1974). Model ini terdiri dari 4 tahap pengembangan yaitu Define, Design, Develop, dan Disseminate atau diadaptasikan menjadi model 4-D, yaitu pendefinisian, perancangan, pengembangan, dan penyebaran.

 

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Developmental Research (Penelitian Pengembangan)

Penelitian pengembangan atau dalam bahasa Inggris developmental research merupakan salah satu paradigma penelitian yang tergolong baru di Indonesia. Namun demikian, di negara-negara maju paradigma penelitian tersebut sudah lama diterapkan guna merancang dan mengembangkan suatu model tertentu sesuai dengan tujuan yang diharapkan, termasuk dalam pengembangan model penelitian pendidikan (Upu, 2005).

Freudenthal (1991: 161), mengemukakan makna “developmental research” yakni:

experiencing the cyclic process of development and research so consciously, and reporting on it so candidly that it justifies itself, and that this experience can be transmitted to others to become like their own experience.

 

Penelitian pengembangan bertujuan menghasilkan dan mengembangkan produk berupa prototipe, desain, materi pembelajaran, media alat atau strategi pembelajaran, untuk mengatasi masalah. Penelitian pengembangan bukan untuk menguji teori, namun menguji dan menyempurnakan produk.

Menurut Sudjana (dalam Trianto, 2007), untuk melaksanakan pengembangan perangkat pembelajaran diperlukan model-model pengembangan yang sesuai dengan sistem pendidikan. Model adalah seperangkat prosedur yang berurutan untuk menunjukkan suatu proses, seperti penilaian suatu kebutuhan, pemilihan media, dan evaluasi. Sesuai dengan pengertian tersebut, maka model pengembangan adalah seperangkat prosedur yang berurutan untuk melaksanakan pengembangan pembelajaran.

References:

Freudenthal, H. 1991. Revisiting Mathematics Education. Netherlands: Kluwer Academic Publishers.

Trianto. 2007. Model Pembelajaran Terpadu dalam Teori dan Praktek. Surabaya: Prestasi Pustaka.

Upu, H. 2005. Karakteristik Research and Development(R & D). Eksponen Jurnal Pendidikan Matematika Matematika Edisi Khusus, Januari 2005 FMIPA UNM, halaman 1-3.