Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners’ understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners’ transition from whole numbers to rational numbers enabled them to deal with the more complex concept of fractions. A qualitative case study approach was followed. A test was administered to 40 learners. Based on their written responses, eight learners were purposefully selected for an interview. The findings revealed that learners’ definitions of fraction were neither complete nor precise. Particularly pertinent were challenges related to the concept of equivalent fractions that include fraction elements, namely the numerator and denominator in the phase of rational number. These gaps in understanding may have originated in the early stages of schooling when learners first conceptualised fractions during the late concrete learning phase. For this reason, we suggest a developmental intervention using physical manipulatives to promote understanding of fractions before inductively guiding learners to construct algorithms and transition to the more abstract applications of fractions required in Grade 9.

Bimbingan Belajar di Rumah Menggunakan Alat Peraga Blok Pecahan pada Masa Pandemi Covid 19

The impact of the COVID-19 pandemic is not only on the safety aspect of people's lives but also on the education aspect. One of the problems faced is that students have problems understanding each material given by the teacher because what has experienced so far is that students only get assignments online (What's App, E-Learning), then students do the assignments and send them back. At that moment, there is no direct explanation from the teacher, and each student's answer only relies on the internet (google), even though students need an understanding of the concepts in the material provided, especially mathematics for fractions. One of the activities that help students develop themselves in improving their learning abilities is the tutor. Solution offered to students who live in RT 003, Paupire Village, in this service activity is to provide Student learning assistance and guidance by using fractional block teaching aids during the Covid 19 Pandemic to increase understanding of concepts and learning outcomes. Tutoring can increase students' motivation and academic value, increase understanding of fraction concepts and learning outcomes.

Design, Development, and Initial Testing of Asset-Based Intervention Grounded in Trajectories of Student Fraction Learning

One of the most relentless areas of difficulty in mathematics for children with learning disabilities (LDs) and difficulties is fractions. We report the development and initial testing of an intervention designed to increase access to and advancement in conceptual understanding. Our asset-based theory of change—a tested and confirmed learning trajectory of fraction concepts of students with LDs grounded in student-centered instruction—served as the basis for our multistage scientific design process. We report on foundational (i.e., a theory of change, establishment and refinement of learning trajectories, and core instructional components) and evaluative (pilot data on student outcomes) components of the intervention. The results of the study reveal positive effects of the program’s fidelity and potential to improve student outcomes in school settings. The positive outcomes support continued exploration and expansion of a new framework for supplemental intervention grounded in trajectories of student learning.

Conhecimentos de Licenciandos em Matemática para o Ensino de Frações

Este texto tem como propósito oportunizar uma discussão sobre conhecimentos relacionados ao conteúdo frações e ao seu ensino. A discussão sobre o ensino das frações está apoiada nas ideias de Magina e Campos e de Morales, dentre outros; e de Shulman no que se refere aos conhecimentos necessários para o ensino. Os dados foram coletados por meio da aplicação de dois questionários com cinco situações problema envolvendo os diferentes conceitos de fração, um para estudantes do Ensino Fundamental e outro para estagiários do Curso de Matemática – Licenciatura. Os resultados sinalizam que apesar dos licenciandos evidenciarem saber responder corretamente situações envolvendo os diferentes significados de fração, as estratégias de ensino propostas por eles deixam claro que no momento de pensar em uma forma de explicar esse conteúdo costumam recorrer ao significado de fração como parte-todo, demonstrando, assim, conhecimento pedagógico do conteúdo insuficiente para lecionar frações. E que acreditam que o uso de recursos materiais auxiliares pode contribuir no aprendizado desse conhecimento. Palavras-chave: Estratégias de Ensino. Frações. Formação de Professores. Abstract The goal of this paper is to present a discussion on knowledge related to fractions and how to teach them. The discussion on teaching fractions is based on the ideas of Magina and Campos and on Morales, among others; and on Shulman regarding the knowledge necessary for teaching. The data were collected from two questionnaires with five situations involving the different fraction concepts, one applied to students in Basic Education and the other applied to interns in the Mathematics Teaching Degree Program. The results indicate that while the student-teachers know how to correctly respond to situations involving the different meanings of fractions, the teaching strategies they proposed make it clear that when they have to think about how to explain the subject, they usually appeal to the part-whole meaning of fractions, thus demonstrating insufficient pedagogical knowledge for teaching fractions. Moreover, they believe that using auxiliary material resources can contribute to learning this knowledge. Keywords: Teaching Strategies. Fractions. Teacher Training.

Representasi Visual Dalam Menyelesaikan Masalah Pecahan

<p class="Abstrak"><strong>Abstract:</strong> This study aims to describe the visual representation of grade 5 students in elementary schools in solving fraction problems. The research method used is descriptive qualitative. Data is collected through interviews, recording and student work. The research subjects were 3 students namely those who had high, medium and low mathematical abilities based on the results of the last report card. The results showed that there was no relationship between students 'mathematical abilities and students' visual representation. Students with high mathematical abilities can accurately represent the concept of fractions in the form of a picture but cannot represent the concept of fraction multiplication and compare two fraction numbers into the exact image. Students with moderate and low mathematical abilities cannot represent fraction concepts and multiplication concepts and compare two fraction numbers into image shapes correctly. Based on the results of this study it is expected that the teachers will provide a deeper understanding of the use of visual representation in fraction learning.</p><strong>Abstrak:</strong> Penelitian ini bertujuan untuk mendeskripsikan representasi visual siswa kelas V sekolah dasar dalam menyelesaikan masalah pecahan. Metode penelitian yang digunakan adalah kualitatif deskriptif. Data dikumpukan melalui wawancara, perekaman dan pekerjaan siswa. Subjek penelitian berjumlah tiga siswa, yaitu siswa yang memiliki kemampuan matematika tinggi, sedang, dan rendah berdasarkan hasil rapor terakhir. Hasil penelitian menunjukkan bahwa tidak ada hubungan antara kemampuan matematika siswa dengan representasi visual siswa. Siswa berkemampuan matematika tinggi dapat merepresentasikan konsep pecahan ke dalam bentuk gambar dengan tepat, tetapi tidak dapat merepresentasikan konsep perkalian pecahan dan membandingkan dua bilangan pecahan ke dalam bentuk gambar dengan tepat. Siswa berkemampuan matematika sedang dan rendah tidak dapat merepresentasikan konsep pecahan, dan konsep perkalian serta membandingkan dua bilangan pecahan ke dalam bentuk gambar dengan tepat. Berdasarkan hasil penelitian ini diharapkan bagi para guru untuk memberikan pemahaman yang lebih dalam tentang penggunaan representasi visual dalam pembelajaran pecahan.

Pembelajaran Ramah Anak bagi Orang Tua dan Guru Taman Kanak-Kanak di Kecamatan Bontotiro

his paper is the result of the Community Partnership Program (PKM) activity by presenting the use ofAcrylic Manipulative Aids (APMA) for learning fraction concepts for math teachers. The purpose of the activity isto maximize active learning activities in the classroom and use teaching aids in mathematics learning activities. Thetarget is for junior high school teachers in Bulukumba District where 21 people are involved in the activity. Theform of activities is training, while implementation information is fulfilled by providing worksheets andquestionnaires as response sheets for activities. The results of the training activities carried out received a positiveresponse. Not only is APMA considered feasible as a medium of learning or teaching aids, but it can also be used tohelp students overcome difficulties in learning the concept of fractions, fraction operations consisting of addition,subtraction, multiplication, and division. In addition, by convincing the teacher to respond that APMA can completethe explanations contained in mathematics textbooks. In other words, in addition to learning by using learningresources derived from books, APMA is also useful to supplement the provision of understanding to students in theclassroom.

Complexity of (Re)Learning the Meaning of Multiplication of Fractions in the Context of a Mathematics Content Course

The context in which preservice teachers (PSTs) learn the mathematical knowledge required for teaching in an elementary classroom is still less obvious. This chapter addresses the complexity of PSTs (re)learning the mathematical knowledge for teaching multiplication of fractions in a mathematics content course. The existing literature on PSTs' learning in a mathematics content course has focused on models for designing the course and efforts for designing innovative pedagogies. In addition, more recent studies have explored the design and implementation of mathematical tasks in a content course. However, studies that have provided insights into the affordances and complexity involved in developing fraction concepts using the basic principles of critical thinking are limited. The aim of this chapter is to explore the extent to which PSTs can develop a conceptual understanding of multiplication of fractions in the context of a mathematics content course designed using the basic principles of critical thinking. The complexities, challenges and tensions confronted by PSTs and the instructor as they (re) learn the meaning of multiplication in more nuanced ways will be discussed.