Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model (original) (raw)
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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 int...
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https://www.ijrrjournal.com/IJRR\_Vol.9\_Issue.12\_Dec2022/IJRR-Abstract75.html, 2022
In the learning activities of the fourth-grade students at SDN Mangunharjo, they had difficulty understanding learning material, especially fractional material. According to the results of interviews with the fourth-grade teacher, students experienced problems understanding multiplication resulting in learning outcomes under KKM 65. This research aimed to analyze the effectiveness of implementing the PMRI approach to optimizing the results of learning fraction material for class IV students at SDN Mangunharjo. The research method used is a quantitative method with a pre-experimental research design in the form of a one-group-pretest-posttest. Implementation of the PMRI approach with an initial trial of class V at SDN Kemijen 02 with as many as 28 students and a final tryout for class IV at SDN Kemijen 02 as the control class and class IV at SDN Mangunharjo as an experimental class. Techniques and data collection include questionnaires, observations, test questions, and documentation tested for validity, reliability, homogeneity, level of difficulty, and discriminatory power. Based on observations from observers, it showed that the implementation of the PMRI approach in the learning process from the second meeting was 88.75, and the third meeting increased by 91.75 these results were in the very good category. While the results of the posttest class classical completeness test were 82.93 out of 29 students with a percentage of 83%, for the pretest class 42.72 with a percentage of 0% of 29 students, none of the students achieved the minimum completeness criterion score. This data shows that the class with the learning process using the PMRI approach is better than the conventional or lecture learning process. It means that applying the PMRI approach can optimize the learning outcomes of fourth-grade students at SDN Mangunharjo.
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Supporting Fifth Graders in Learning Multiplication of Fraction with Whole Number
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The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local instructional theory to support the students expand their understanding of the meaning of multiplication of fractions with integers. By applying the characteristics of realistic mathematics education (Realistic Mathematics Education), the researchers designed a series of instructional activities related to daily life, such as Indonesia prepares dishes and equitable distribution. Participants of this study were Grade 5 students from an elementary school in Surabaya, along with a mathematics teacher of that class. Some students of the class participated in the first cycle, in order to see how the design of the hypothetical learning trajectory (Hypothetical Learning Trajectory) is running. After going through several revisions, HLT is then implemented in all the other students in grade 5. The results showed that students' prior knowledge affect their learning process. The fractions solve multiplication problems with whole numbers, some students convert the integers to fractions and then use a fraction by a fraction multiplication procedure. The learning process begins with students exploring the contextual situation of fair division, where students extend their understanding that the fraction associated with the division and multiplication. One indicator that the student has broadened his understanding is the more varied representation of the given problem.
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This research aims to obtain a comprehensive picture of the hypothetical learning trajectory (HLT) that should be developed based on students' learning trajectory (LT) in learning fraction division arithmetic operations in grade V elementary school. The HLT was developed based on the analysis of the Learning Implementation Plan document made by the teacher by considering the students' learning trajectory on the material of fraction division arithmetic operation, including the learning carried out by the teacher in the classroom, examining aspects of learning obstacles that occur in the learning process, and examining what didactical situations will be built, predicting student responses that may occur to the situation created, and determining didactical and pedagogical anticipation of these responses. The HLT in this study started with the context of generating the idea of number division, learning the concept of number division such as natural numbers divided by natural numbers, and recalling the concept of fractions and the concept of division of fractions. The learning objective designed in the HLT is that students can solve problems with at least two ways related to division of fractions.
Journal on Mathematics Education, 2017
By taking the role as a mentor and a facilitator, a teacher in the 4 th grade of elementary school needs to look at the condition of the students in the concrete thinking stage. Learning process needs to be adjusted such that the abstract objects in mathematics can be represented through concrete objects as a bridge to enter the knowledge that the students already had, especially for the material of fraction. This research aims to analyze the achievement and the improvement of students' mathematics reasoning ability through the implementation of Indonesian realistic mathematics education (PMRI) approach. The research subject consisted of 51 students in the experiment group and 45 students in the control group which categorized into three levels (low, intermediate, and high). The result suggests that the achievement and the improvement of students' reasoning ability in the mathematics learning using PMRI approach are better than the conventional learning.
Developing a hypothetical learning trajectory of fraction based on RME for junior high school
Journal of Physics: Conference Series, 2020
Preliminary research showed the learning trajectory of fraction in the school that could not facilitate students to reinvent fraction concepts. Therefore, this research aimed to produce a hypothetical learning trajectory (HLT) for teaching fraction using realistic mathematics education (RME). The HLT was developed with a design research that consisted of a cyclic process of preparing for the experiment, conducting classroom experiment, and performing retrospective analysis. This study involved 25 students SMPN 1 Timpeh, Indonesia. Data were collected through student activity sheets, videotaping, field notes, and interviews. The data analysis technique used descriptive analysis techniques. The result showed HLT for teaching fraction using RME that could be help all of levels students. This HLT helped students to reinvent fraction concepts through horizontal and vertical mathematical processes. Finally, the HLT facilitated students to make their own models from informal to formal and ...