RSS
Tampilkan postingan dengan label design research. Tampilkan semua postingan
Tampilkan postingan dengan label design research. Tampilkan semua postingan

Design Research on Mathematics Education: Investigating The Progress of Indonesian Fifth Grade Students’ Learning on Multiplication of Fraction with Natural Numbers

posted by harpenidewantara | Label: ,

Nenden Octavarulia Shanty (2008)

IndoMs. J.M.E
Vol.2 No.2 July 2011
 
The research written by Nenden was done under design research methodology, with thirty-seven students of fifth grade at SDN 17 Palembang as the research subject. In this study, researcher concerned about multiplication of fraction with natural numbers by applying Realistic Mathematics Education.
This study aims at investigating the progress of studetns’ learning on multiplication fractions with natural numbers through the five activity levels based on RME proposed by Streefland. There are four activities designed by researcher in this study; those are:
  •  Locating flags and water posts on the running route with an expectation that students are able to make a construction of partitioning, part of a whole. The running race route context was chosen as the context to provoke the students in producing their own fractions within measurement (length) activity.
  • Notating fractions in the empty fractions cards, putting the fraction cards on the string of yarn, and describing the relations among fractions. Through this activity, students could symbolize the result of partitioning and show it on the string of yarn. Furthermore, they also could describe the relations among fractions such as equivalent fractions.
  • Math congress 1. In this activity, students shared their activities in activities 1 and 2, about their experiences in partitioning the track, symbolizing the result of partitioning, and describing the relations among fractions. Students, furthermore, came up with the use of number line as a model-of measuring situation. Such number line was proven as a powerful model to encourage students in generating equivalencies of fractions.
  • Determining who is running farther. Through this activity, students could compare fractions within a certain length. In this case, students informally use fractions as multipliers.
  • Math congress 2. In the second congress, students shared their ideas and experiences in informally using fractions as operator. Teacher guided students to discuss about different strategies and lead students come to the idea about a more efficient way to solve problem involving multiplication of fraction by natural number, e.g  .to find the answer of 4/6 of 6 kilometres by multiplying 4 by 6 kilometres then divided it by 6 (the denominator of 4/6). Through the use of students’ own creations and contributions, the use of number line as model-of has been transformed into a model-for more formal reasoning.
  • Conducting mini lesson about fraction as operator. In this activity, students were given the opportunity to use their strategies in solving the problems from the previous activity.
In conclusion, this research has shown students learning about multiplication fractions with natural numbers by conducting the five activity levels proposed by Streefland  (1991) as the steps of learning with fractions.

  • Digg
  • Del.icio.us
  • StumbleUpon
  • Reddit
  • RSS
Read User's Comments(0)
posted by harpenidewantara

Developing Students’ Spatial Visualisation Ability

posted by harpenidewantara | Label: ,

Dwi Afrini Risma, Ratu Ilma Indra Putri, & Yusuf Hartono

International Education Studies; Vol.6, No. 9; 2013; ISSN 1913-9020; E-ISSN 1913-903
Published by Canadian Center of Science and Education

The research written by Dwi Afrini Risma aims at studying on how the building block activity supports the development of students’ spatial visualisation. In addition, the researcher was also interested to explore how students visualise and interpret the building blocks and teacher’s roles in developing the way students interpret and visualise the building blocks.
This research was done under design research methodology, conducted at grade 3 SDN 117 Palembang by involving 39 students whose ages ranging from 9 to 10 years and a teacher as research subject. The learning activities in this study were generally designed to help students develop their spatial visualisation ability. There were five instructional activities designed by researcher in this study.
However, in journal (International Education Studies; Vol.6, No. 9; 2013, published by Canadian Center of Science and Education) researcher merely presented one of those activities which conducted in a second cycle of an explanatory teaching experiment. In such activity, called building block activity, students worked on spatial visualisation task by exploring building blocks. Students were provided with wooden cubes and worksheet. Then, they should construct the cubes to be some buildings which were appropriated with the instruction given in the worksheet.  The purpose of this activity is to enable the students to make connection between different views of the building blocks and to identify the side views (front view, back view, and right view) and the top view of the building blocks.
The researcher conducted this activity in two meetings (2x35 minutes).  The students worked in small groups, consisting 3-4 students in each group, to solve three problems. The first given problem as follows:
                                  
In the first meeting, the researcher started the learning by introducing the context and problem that should be solved by the students. In the first problem, students were asked to construct a building blocks from small blocks as shown in worksheet (as the following figure) and then drew its side views and top view. In the second problem, students have to construct their own building blocks consisting 5 wooden cubes and then drew its side and top views. Whilst the third problem was presented in the second meeting conducted ten days later. In this problem, students should work individually to construct their own building blocks from four blocks and then drew its side and top views. 
After conducting the instructional activities, the researcher observed that the way students visualized and interpreted the building blocks were increased. The researcher, therefore, concluded that spatial visualisation activities such as visualize the building blocks support the development of students’ spatial ability.

  • Digg
  • Del.icio.us
  • StumbleUpon
  • Reddit
  • RSS
Read User's Comments(0)
posted by harpenidewantara

A Concrete Situation for Learning Decimals

posted by harpenidewantara | Label: ,

Puri Pramudiani, Zulkardi, Yusuf Hartono, Barbara van Amerom

IndoMs. J.M.E
Vol.2 No.2 July 2011, pp. 215-230

Decimals is important domain in mathematics. Indonesian curriculum, nevertheless, leads most teachers to introduce decimals merely as another notation for fractions or percentages. Teaching and learning of decimal is conducted in a very formal way, in which decimal is directly converted from fraction which has denominator ten or one hundred without using of concrete situations to introduce its concept to students. As consequence, many students assumed that decimal is just the number containing point (comma) without knowing the meaning of it. At the same time, they might think that there were no other numbers between two concecutive whole numbers.
The researcher, therefore, conducted this study aiming at developing an instructional program that enables students to discover decimals and get insight about their magnitude through measurement activity as a meaningful way. RME underlies the design of context and activities used in this study.  
This research was done under design research methodology, conducted in six lessons at grade 5 SDN 21 Palembang by involving 26 students and a teacher as research subject. The learning activities in this study were generally designed to help students explore the notation and the meaning of decimals. There are four activities design by researcher in this study; those are:
Activity 1
Playing come closer game with an expectation that students are able to determine the numbers between the other numbers. Through this activity, it could be known that whether students have already perceived an idea about decimals based on their daily experiences or they have no idea at all about any number between two concecutive whole numbers.
Activity 2
Measuring the weight of the things (duku and body) using weight scale and digital weight scale. Through those activities, students were encouraged to do the precise and accurate measurement so they eventually could find decimals in weighing body activity, for instance, by observing the scales that when the needle pointed to the position between two consecutive numbers there should be comma numbers (decimals) in it, e.g between 35,6 appeared on the digital weight between 35 and 36.   
Activity 3
Measuring the weight of rice helped students to invent the meaning of one-digit decimals by finding that there were ten partitions containing one digit decimals between two concecutive whole numbers which eventually lead to the idea that decimals refer to the number of base ten, i.e: 0,2 is at the second stripe from ten stripe overall (two over ten).
Activity 4
Measuring the volume of beverages aimed at developing students’ acquisition for the idea of two-digit decimals. By using model of measuring cup, the students could perceive the idea that there are decimals between two concecutive whole numbers, and between two concecutive one-digit decimals there are other decimals, namely two-digit decimals.  Furthermore, they also found the idea that decimals refer to the partitioning base tenth of tenth by noticing the stripes provided by measuring cup.
To conclude, context and activities designed (weight and volume measurement) can become the concrete situation for learning decimals. It could provoke students’ thinking about decimal idea developing from informal level to pre-formal level containing insightful mathematical ideas. Or the other word, decimals can be taught in a meaningful way by applying RME approach, however it was known as abstract for most students.

  • Digg
  • Del.icio.us
  • StumbleUpon
  • Reddit
  • RSS
Read User's Comments(0)
posted by harpenidewantara

Abbreviating Strategies of Addition and Subtraction up to 20 through Structures (Meiliasari, 2008)

posted by harpenidewantara | Label: ,



The research written by Meiliasari was done under design research methodology, conducted at  SDN Percontohan Kompleks IKIP Jakarta, during the period of May to August 2008. In this study, researcher concerned about addition and subtraction up to 20, particularly for those in the low grade of primary school by applying Realistic Mathematics Education. Noticing to the evidences found, most of children very likely rely on using fingers to keep track of their counting when doing addition or subtraction at the beginning. They count all objects one by one that surely will spend a lot of time, for instance the sum of 3 + 4 = 1, 2, 3, 4, 5, 6, 7. This is assumed as the simple way to solve addition and subtraction problems. When encountering the larger numbers, nonetheless, such way is no longer effective.  
The researcher, therefore, conducted this study aiming at developing an instructional program that helped students to abbreviate strategies of addition and subtraction up to 20 through structures. Structures of numbers, either line or group and combination model as well, were used as a visualization to enhance students’ thinking process in constructing meaningful and flexible structures such as using ‘doubles’,’ splitting’, and ‘friends of 10’ which eventually will make students easier to solve the addition and subtraction problems.  
The research was divided into two parts; part 1 was conducted between May to June, whilst part 2 was running in July. Over those periods, five students who represented the high, middle, and low achiever groups were picked in the 1st part. Then, hypothetical learning trajectory will be tested in the learning experiment in the 2nd part. Lastly, the collected data through interview and video recording during teaching learning experiment were analyzed in the retrospective analysis phase.
The learning activities in this study were generally designed to help students count effectively. To begin with, the researcher gave students the candy packaging activity to develop their structure awareness. In this activity, they were asked to make several arrangements of candy packing –in fives, tens, or other group structures- with an expectation that they would be able to realize that structuring helps them do a faster counting.  In addition, working with concrete object (candy) as the characteristic of RME would make students construct the concept of material easily.
The next activity was providing the double song and completing the worksheet concerning about double structure. Then, the 3rd  activity was opened with flash card games forcing students to count quickly how many objects in the card. To do so, they should recognize the structure well instead of counting objects one by one. For example, when having the 8 card, some students might see 8 as 10 – 2, whilst other students use doubling structure 4 + 4 = 8. Through this activity, students could realize the importance of structure in shortening the counting process.
The following week, the activity was followed by developing students’ understanding of the ‘friends of 10’. For example, if there are only 7 candies in the box, to make it 10 how many more need to be put in? The result showed that friends of 10 strategy has allowed students to work faster and easier. Morerever, a trick so called ‘number pair’ in Indonesian language, pairing the numbers whose same first letter such as satu-sembilan, dua-delapan, and so on, worked well on students’ memorizing.
To conclude, a challenging and interesting instructional program will make students more motivated and get involved in the activity actively. It is important to make activity goes along naturally with the real context in students’ surrounding. As children mostly do in doing addition or subtraction, counting concrete objects using finger is simple and always works. When working in larger number, however, students should be encouraged to use flexible and meaningful strategies such as splitting, doubling, and friend of 10 to make their counting process easier and more effective.

  • Digg
  • Del.icio.us
  • StumbleUpon
  • Reddit
  • RSS
Read User's Comments(0)
posted by harpenidewantara
Langganan: Postingan (Atom)