The purpose of this study was to describe mathematical hands-on activities that can support stude... more The purpose of this study was to describe mathematical hands-on activities that can support students to gain better understanding of dividing fractions. This preliminary research phase was started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT), then in the pilot experimental phase the revised HLT was implemented, and ended with the teaching experimental phase by developing a learning trajectory for 12-year old students in understanding division of fractions. In developing the trajectory, a design research methodology was employed by using four contextual-based learning series (sharing biscuit, sharing remaining chocolate bar, arranging bedroom mats, and running around school yard), including providing some concrete materials or pictorial models as manipulative tools. Seven mathematics experts and twenty five 12-year old students were involved during the research. The four designed learning goals were determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions. Students succeeded in demonstrating their understanding and stated that 16:1/2 = 32; 25/36:5 = 5/36; 24/64:1/2 = 6/8; and 15/2:3/4 = 10 respectively at the end of each designed activity. The interesting results of this study are not a proof, so that a much larger study is needed to determine if the results are due to this approach or due to the teachers’ enthusiasm or what is known as the Hawthorne Effect.
The purpose of this study is to describe the mathematical-hands-on-activities that can support st... more The purpose of this study is to describe the mathematical-hands-on-activities that can support students to gain their better understanding in dividing fractions. This study is started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT) (preliminary research phase), implementing the revised HLT (pilot experiment phase), and ended by developing a learning trajectory of 12-year-olds students in understanding division on fraction (teaching experiment phase). In developing the trajectory, a design research is employed by using four contextual-based learning series (biscuit sharing, sharing the remaining chocolate bar, arranging bedroom mats, and run surrounding ceremony flag field), including providing some concrete materials or pictorial models as its manipulative tools. Seven mathematics experts and twenty-five 12-year-olds students are involved during the research. Among four designed learning goals, they are determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions, students succeed to demonstrate their understanding and stated that "16 : 1/2 = 32", "25/36 : 5 = 5/36", "24/64 : 1/2 = 6/8", and "15/2 : 3/4 = 10" respectively in the end of each designed activity.
This study is a Classroom Action Research with 25 of 7 th grade students of SMP Nasional KPS Bali... more This study is a Classroom Action Research with 25 of 7 th grade students of SMP Nasional KPS Balikpapan as the subjects. It was held in year academic 2007/2008. The aim is to find out the influence of the use of blog as media in learning mathematics, towards the increase of students’ Grade Point Average (GPA) and motivation in learning mathematics. The result showerd that learning mathematics with the aid of blog could increase students GPA and motivation. Besides, the higher intensity of the blog use, the more increase of students’ GPA and motivation in learning mathematics.
The study aims to improve the quality of students’ logical thinking on the concept of linear equa... more The study aims to improve the quality of students’ logical thinking on the concept of linear equation in one variable using Pohon Matematika (Mathematics Tree). The Method was collaboration between problem posingandopen-ended learning approach.The study was a Classroom Action Research with two cycles. Twenty one students were participated.Students were observed during these cycles and given formative test at the end of the cycles. The observation results suggest that students can create their own new mathematical problems or solve the given problems by using various ideas. The results of formative test showed that the score of 76% of the students were above the minimal passing grade. This suggests that mathematics learning process using Pohon Matematika is effective.
Not many people realize the contribution of mathematics on students’ life. Surely there are some ... more Not many people realize the contribution of mathematics on students’ life. Surely there are some concepts that help students on solving daily problem like the concepts of number and measuring. But then, when we talk about algebra, it is certain that students will find difficulty on classifying daily problems that can be solved by algebra concept. The key of all those matters are the pattern to shape the communication habit that is orderly fit with their thinking map. This article is trying to show various mathematic problem that help building the students’ logic thinking communication, followed by related research that were succeed on grouping the students’ logic thinking and communication in five level. This research showed students’ competency on communication, based on the rubric assessment that is held by the researcher.
The purpose of this study was to describe mathematical hands-on activities that can support stude... more The purpose of this study was to describe mathematical hands-on activities that can support students to gain better understanding of dividing fractions. This preliminary research phase was started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT), then in the pilot experimental phase the revised HLT was implemented, and ended with the teaching experimental phase by developing a learning trajectory for 12-year old students in understanding division of fractions. In developing the trajectory, a design research methodology was employed by using four contextual-based learning series (sharing biscuit, sharing remaining chocolate bar, arranging bedroom mats, and running around school yard), including providing some concrete materials or pictorial models as manipulative tools. Seven mathematics experts and twenty five 12-year old students were involved during the research. The four designed learning goals were determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions. Students succeeded in demonstrating their understanding and stated that 16:1/2 = 32; 25/36:5 = 5/36; 24/64:1/2 = 6/8; and 15/2:3/4 = 10 respectively at the end of each designed activity. The interesting results of this study are not a proof, so that a much larger study is needed to determine if the results are due to this approach or due to the teachers’ enthusiasm or what is known as the Hawthorne Effect.
The purpose of this study is to describe the mathematical-hands-on-activities that can support st... more The purpose of this study is to describe the mathematical-hands-on-activities that can support students to gain their better understanding in dividing fractions. This study is started by testing, analyzing, and refining the initial hypothetical learning trajectory (HLT) (preliminary research phase), implementing the revised HLT (pilot experiment phase), and ended by developing a learning trajectory of 12-year-olds students in understanding division on fraction (teaching experiment phase). In developing the trajectory, a design research is employed by using four contextual-based learning series (biscuit sharing, sharing the remaining chocolate bar, arranging bedroom mats, and run surrounding ceremony flag field), including providing some concrete materials or pictorial models as its manipulative tools. Seven mathematics experts and twenty-five 12-year-olds students are involved during the research. Among four designed learning goals, they are determining the quotient of division of integer by proper fraction, proper fraction by integer, two proper fractions, and two fractions, students succeed to demonstrate their understanding and stated that "16 : 1/2 = 32", "25/36 : 5 = 5/36", "24/64 : 1/2 = 6/8", and "15/2 : 3/4 = 10" respectively in the end of each designed activity.
This study is a Classroom Action Research with 25 of 7 th grade students of SMP Nasional KPS Bali... more This study is a Classroom Action Research with 25 of 7 th grade students of SMP Nasional KPS Balikpapan as the subjects. It was held in year academic 2007/2008. The aim is to find out the influence of the use of blog as media in learning mathematics, towards the increase of students’ Grade Point Average (GPA) and motivation in learning mathematics. The result showerd that learning mathematics with the aid of blog could increase students GPA and motivation. Besides, the higher intensity of the blog use, the more increase of students’ GPA and motivation in learning mathematics.
The study aims to improve the quality of students’ logical thinking on the concept of linear equa... more The study aims to improve the quality of students’ logical thinking on the concept of linear equation in one variable using Pohon Matematika (Mathematics Tree). The Method was collaboration between problem posingandopen-ended learning approach.The study was a Classroom Action Research with two cycles. Twenty one students were participated.Students were observed during these cycles and given formative test at the end of the cycles. The observation results suggest that students can create their own new mathematical problems or solve the given problems by using various ideas. The results of formative test showed that the score of 76% of the students were above the minimal passing grade. This suggests that mathematics learning process using Pohon Matematika is effective.
Not many people realize the contribution of mathematics on students’ life. Surely there are some ... more Not many people realize the contribution of mathematics on students’ life. Surely there are some concepts that help students on solving daily problem like the concepts of number and measuring. But then, when we talk about algebra, it is certain that students will find difficulty on classifying daily problems that can be solved by algebra concept. The key of all those matters are the pattern to shape the communication habit that is orderly fit with their thinking map. This article is trying to show various mathematic problem that help building the students’ logic thinking communication, followed by related research that were succeed on grouping the students’ logic thinking and communication in five level. This research showed students’ competency on communication, based on the rubric assessment that is held by the researcher.
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