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Jaap den Hertog
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Education Mathematics

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 1 
Helping Students Acquainted with Multiplication in Rectangular Model Tasman, Fridgo; Hertog, Jaap den; Zulkardi, Zulkardi; Hartono, Yusuf
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.747.185-198

Abstract

Usually, multiplication is introduced to students to represent quantities that come in group. However there is also rectangular array model which is also related to multiplication. Barmby et al (2009) has shown that the rectangular model such as array representations encourage students to develop their thinking about multiplication as a binary operation with row and column representing two inputs. Considering that finding, this study focusses on a design research that was conducted in Indonesia in which I investigate second grade students’ (between 7 and 8 years old) in Madrasah Ibtidaiyah Negeri (MIN) 2 Palembang, Indonesia, ability to structuring the situation and their ability to represent rectangular model into multiplication sentence. The results shows us that students activity to structuring the situation, looking the number of objects in row or in column, lead them to repeated addition and transform it into multiplication sentence.Keywords: Rectangular pattern, Multiplication DOI: http://dx.doi.org/10.22342/jme.2.2.747.185-198
Structured Arrangement Supporting The Development of Splitting Level in Doing Multiplication By Number Up To 20 Meryansumayeka, Meryansumayeka; Darmawijoyo, Darmawijoyo; Ilma, Ratu; Hertog, Jaap den
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.748.199-214

Abstract

In guiding students to construct a mathematical concept themselves, learning process should be started by a context which is suit with the concept. In this research, we focused on structured arrangement which was believed to be able to support students ages 8 – 9 years old developing splitting strategy in doing multiplication. This study was a design research underlined by tenets of Realistic Mathematics Education (RME). The result show that giving structured objects, recognizing number relation in multiplication, and maintaining flexible calculation have important roles in supporting the development of mental calculation achieving splitting level.Key words: design research, mental calculation, splitting level, structured arrangement DOI: http://dx.doi.org/10.22342/jme.2.2.748.199-214
Supporting First Grade Students Learning Number Facts Up To 10 Using A Parrot Game Putra, Zetra Hainul; Darmawijoyo, Darmawijoyo; Ilma, Ratu; Hertog, Jaap den
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.776.163-172

Abstract

Knowing number facts up to 10 become crucial if we want students to solve addition and subtraction problems  using more abbreviated strategies. Otherwise, students will keep counting one-by-one until they get an answer. One of important number facts is number pairs that make ten because it is an important ‘benchmark’ that students will refer to constantly. Considering the important of number facts up to 10, we designed a parrot game activity to supports students learning process. We designed an instructional activity based on Realistic Mathematics Education (RME) approach. We tried this instructional activity with twenty seven first grade students in SDN 179 Palembang. As a result, we found that many first grade students were able to know number facts up to 10, but they still need models to support their thinking.Keywords: number facts up to 10, number pairs that make 10, and parrot game. DOI: http://dx.doi.org/10.22342/jme.2.2.776.163-172
Helping Students Acquainted with Multiplication in Rectangular Model Fridgo Tasman; Jaap den Hertog; Zulkardi Zulkardi; Yusuf Hartono
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.747.185-198

Abstract

Usually, multiplication is introduced to students to represent quantities that come in group. However there is also rectangular array model which is also related to multiplication. Barmby et al (2009) has shown that the rectangular model such as array representations encourage students to develop their thinking about multiplication as a binary operation with row and column representing two inputs. Considering that finding, this study focusses on a design research that was conducted in Indonesia in which I investigate second grade students’ (between 7 and 8 years old) in Madrasah Ibtidaiyah Negeri (MIN) 2 Palembang, Indonesia, ability to structuring the situation and their ability to represent rectangular model into multiplication sentence. The results shows us that students activity to structuring the situation, looking the number of objects in row or in column, lead them to repeated addition and transform it into multiplication sentence.Keywords: Rectangular pattern, Multiplication DOI: http://dx.doi.org/10.22342/jme.2.2.747.185-198
Supporting First Grade Students Learning Number Facts Up To 10 Using A Parrot Game Zetra Hainul Putra; Darmawijoyo Darmawijoyo; Ratu Ilma; Jaap den Hertog
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.776.163-172

Abstract

Knowing number facts up to 10 become crucial if we want students to solve addition and subtraction problems  using more abbreviated strategies. Otherwise, students will keep counting one-by-one until they get an answer. One of important number facts is number pairs that make ten because it is an important ‘benchmark’ that students will refer to constantly. Considering the important of number facts up to 10, we designed a parrot game activity to supports students learning process. We designed an instructional activity based on Realistic Mathematics Education (RME) approach. We tried this instructional activity with twenty seven first grade students in SDN 179 Palembang. As a result, we found that many first grade students were able to know number facts up to 10, but they still need models to support their thinking.Keywords: number facts up to 10, number pairs that make 10, and parrot game. DOI: http://dx.doi.org/10.22342/jme.2.2.776.163-172
Structured Arrangement Supporting The Development of Splitting Level in Doing Multiplication By Number Up To 20 Meryansumayeka Meryansumayeka; Darmawijoyo Darmawijoyo; Ratu Ilma; Jaap den Hertog
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.2.2.748.199-214

Abstract

In guiding students to construct a mathematical concept themselves, learning process should be started by a context which is suit with the concept. In this research, we focused on structured arrangement which was believed to be able to support students ages 8 – 9 years old developing splitting strategy in doing multiplication. This study was a design research underlined by tenets of Realistic Mathematics Education (RME). The result show that giving structured objects, recognizing number relation in multiplication, and maintaining flexible calculation have important roles in supporting the development of mental calculation achieving splitting level.Key words: design research, mental calculation, splitting level, structured arrangement DOI: http://dx.doi.org/10.22342/jme.2.2.748.199-214
Co-Authors Darmawijoyo, Darmawijoyo Fridgo Tasman Meryansumayeka Meryansumayeka Ratu Ilma Ratu Ilma Indra Putri Yusuf Hartono Zetra Hainul Putra Zulkardi Zulkardi Zulkardi Zulkardi