Introduction What Students’ Thinking about Contextual Problems is.

This paper has been presented at International Seminar on Innovation in Mathematics and Mathematics Education 1 st ISIM-MED 2014 Innovation and Technology for Mathematics and Mathematics Education Department of Mathematics Education,Yogyakarta State University Yogyakarta, November 26-30, 2014 E – 33 What Students’ Thinking about Contextual Problems is Ekasatya Aldila Afriansyah Program Studi Pendidikan Matematika STKIP Garut Indonesia e_satyayahoo.com Abstract There were some studies which had been investigated how students think when facing contextual problem; the case of decimal numbers problems. Some of them observed it in detail. The goal is to scaffold students’ thinking and to help them be motivated in practice. The idea was an understanding of place value and relationship between numbers and decimal numbers using contextual problems. Realistic Mathematics Education underlies the design of the activities and the contexts; design research was done in two cycles. It was conducted in three phases: preliminary design, teaching experiment, and retrospective analysis. Six students and 34 students of fifth grade were involved as data; each group of students was divided into two cycles. It was held at MIN 1 Palembang, one of PMRI participant school in Palembang. Students would enable to work with contextual situations within measurement activities; number line is used as a model for supporting their understanding and reasoning. In the analysis, their reasoning was used to develop the new one of learning trajectory. The result of this study could show that the activities could bring students’ understanding from the contextual situation to the formal situation. Students would not use integer number system when doing decimal number problem. Learning trajectory on this study can be used for elementary school. Keywords: contextual problems, decimal numbers, design research Realistic Mathematics Education.

1. Introduction

The extensive studies from around the world on decimals have documented students’ difficulties and weak conceptual understanding of decimals from elementary to college levels, Steinle dan Stacey [1]. Ubuz dan Yayan [2] explained about the knowledge in the domain of decimals and investigated students’ performance, and also observed their difficulties in reading scales, ordering numbers, and the operation of decimals. Because of those difficulties, the teaching and learning process on decimals needs more attention. Much of the research literature on teaching learning process about decimals separated decimals from meaningful contexts, often in order to teach students about place value, Irwin and Britt [3]. One level of knowledge involved in processing decimal numbers consists of position knowledge involving place number names, the base ten system, and order of the places hundredths are larger than tenth, etc., Widjaja [4]. Practically, some students use the meaning of whole numbers and apply this knowledge on decimal number concepts when they try to solve the problem of decimals. There are some studies investigated how students might be thought the sense of decimals which requires the application of four basic arithmetic operations. The fact that there are current studies which are provide the misconceptions of students in doing decimals without further investigation, has established a need to conduct this topic deeply. Based on what present studies have found, researcher hopes that this study can International Seminar on Innovation in Mathematics and Mathematics Education 1 st ISIM-MED 2014 Department of Mathematics Education,Yogyakarta State University,Yogyakarta, November 26-30, 2014 EP - 280 extend previous knowledge in some way and give a contribution continuing the research about decimal number. Although previous studies have addressed students’ difficulty on decimals addition, none of them have described explicitly the way to solve it. For example, in his research, Irwin [5] stated that when you do something to one side of the point or comma, you also do it to the other side e.g., 2,5 + 1 = 3,6. Another example, Ubuz and Yayan [2] stated that the most common errors in the addition tasks were adding the last digit of number behind the comma adding up 0,1 to the number 4,256 and 6,98, students gave the answers of 4,257 and 6,99 instead of 4,356 and 6,98. In order to overcome the difficulty, this study presents a sequence of classroom activities aimed at constructing the understanding of place value in decimal numbers. Furthermore, according to the approach of some Indonesian textbooks, the way of teaching and learning decimals is conducted directly using algorithm. It does not present any concrete models. It is in line with the previous research from Zulkardi [6]. He stated that the topic of decimals in Indonesian textbook mainly contains sets of rules and algorithms and it lacks applications that are experientially real to the students. The meaningful situation is important in order to avoid students’ misconception about decimals, Pramudiani [7]. Supporting students with a model e.g. number line can engage them to find some strategies which lead them to the meaningful learning situation. So, this study provides some classroom activities which are related to the experiential world of the students, it is purposed to bring students’ informal knowledge or out of school reasoning experiences into school mathematics or formal knowledge. Considering the misconception of students and also the approach of the textbook in Indonesia, this research has an aim to investigate the development of students’ thinking about contextual problems in decimals through the activities. The research question is: “How can contextual problems support students ’ thinking to understand decimals?”

2. Research Method