Supporting Student’s Thinking In Addition Of Fraction From Informal To More Formal Using Measuring Context

One of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. In addition, students have been trained for the skills and should have mastered such procedures even they do not ‘understand’. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. For this reason, a set of measuring context was designed to provide concrete experiences in supporting students’ reasoning in addition of fractions, because the concept of fractional number was derived from measuring. In the present study we used design research as a reference research to investigate students’ mathematical progress in addition of fractions. In particular, using retrospective analysis to analyze data of fourth graders’ performance on addition of fractions, we implemented some instructional activities by using measuring activities and contexts to provide opportunities students use students’ own strategies and models. The emergent modeling (i.e. a bar model) played an important role in the shift of students reasoning from concrete experiences (informal) in the situational level towards more formal mathematical concept of addition of fractions. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research. Key word: measuring context, addition of fractions, design research, emergent modelin

SUPPORTING STUDENTS’ REASONING THROUGH INTRODUCING FRACTIONS AS PART-WHOLE AND MEASURE MEANING

One of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. Primary school curricula in Indonesia introduce fractions in class III and by class V, students are expected to learn many operastions on fractions. In fact, many students in class V have some misconceptions or misunderstandings about the concepts. For instance, they would say that ¼ is more than 1/3 and ½ + 2/3 = 3/5. In addition, most textbooks used by students contain basically many procedures, they learn fractions mechanically without any conceptual grasp. Moreover the textbooks use only part-whole interpretation as a way to introduce a fractions, it is not enough in facilitating students’ reasoning in the context of task of comparing, finding equivalent fractions and operating fractions. In this paper, we describe data/informations colected during facilitating student in learning fractions using methode combining the part-whole and measure interpretation of fractions. We also will show examples of students’ reasoning indicating teaching fractions using the combination migh prove to be better methode in supporting students’ reasoning about fractions. Key words: reasoning, fractions, part-whole, measur

Fostering Indonesian Prospective Mathematics Teachers' Geometry Proof Competence

It is widely accepted that comprehending and constructing mathematical proof is an essential topic at any level of mathematics education, including higher education. Prospective mathematics teachers (PMTs) learn mathematical proof in university because proof competence could help them understand and explain mathematical concepts to their students when they are a high school teacher. From a small-scale observational study at a university in Malang, Indonesia, I learned that most students faced difficulties understanding and constructing mathematical proof. This situation motivated me to investigate and improve PMTs’ proof competence.For that purpose, I designed a course and investigated how this course supported PMTs in developing proof competence in geometry. My findings indicated that the course supported PMTs in developing their proof competence, particularly in conjecturing, which is a precursor activity of proving, and their understanding and construction of proof. A quasi-experimental study showed that students achieved better results than in the regular course. The designed learning trajectory can inform curriculum designers about effective teaching strategies for geometrical proof, particularly in an early stage at Indonesian universities. I recommend that in the future, PMTs at all Indonesian universities should acquire not only the content knowledge of mathematical proofs (on which this study focused) but also the pedagogical content knowledge. Following this study, proof should be promoted in Indonesian secondary schools, along with guidance for teachers about implementation in their classrooms

Understanding geometric proofs:Scaffolding pre-service mathematics teacher students through dynamic geometry system (dgs) and flow-chart proof

International audienceThe objective of this paper is to discuss the pedagogic potential that is offered by the use of a flow-chart proof with open problems and a Dynamic Geometry System in understanding geometric proofs by pre-service mathematics student teachers at an Indonesian university. Based on a literature review, we discuss aspects and levels of understanding of geometric proof and how to assess students’ understanding of the structure of deductive proofs, and how the use of a Digital Geometry System may support students’ understanding of geometric terms and statements, including definitions, postulates, and theorems. The pedagogic focus consists of exploiting the semiotic potential of a DGS, especially the use of GeoGebra tools that may function as tools of semiotic mediation to understand the geometry statements and the scaffolding potential of flow-chart proof with open problems in identifying the structure of deductive geometry proofs

Understanding geometric proofs:Scaffolding pre-service mathematics teacher students through dynamic geometry system (dgs) and flow-chart proof

International audienceThe objective of this paper is to discuss the pedagogic potential that is offered by the use of a flow-chart proof with open problems and a Dynamic Geometry System in understanding geometric proofs by pre-service mathematics student teachers at an Indonesian university. Based on a literature review, we discuss aspects and levels of understanding of geometric proof and how to assess students’ understanding of the structure of deductive proofs, and how the use of a Digital Geometry System may support students’ understanding of geometric terms and statements, including definitions, postulates, and theorems. The pedagogic focus consists of exploiting the semiotic potential of a DGS, especially the use of GeoGebra tools that may function as tools of semiotic mediation to understand the geometry statements and the scaffolding potential of flow-chart proof with open problems in identifying the structure of deductive geometry proofs

The effect of proof format on reading comprehension of geometry proof:The case of Indonesian prospective mathematics teachers

This study aims to investigate the effects of the use of multiple geometry proof formats on Indonesian students’ reading comprehension of geometry proof (RCGP). Four classes of prospective secondary mathematics teachers (N=125), aged 18 to 19 years, participated in this quasi-experimental study. While the experimental group was instructed in three proof formats (paragraph, two-column and flow-chart proof), the control group was instructed in only the two-column proof format. Similar pre- and post-tests, based on Yang and Lin’s (2008) RCGP test, were administered to both groups. N-Gain scores were used to determine the improvement of both groups. The N-Gain scores showed significantly more improvement of students’ RCGP in the experimental group. More detailed analysis indicated that the use of multiple proof formats supports the students’ understanding of the facets of logical status of statements and the critical ideas in the proof. This study shows the benefits of offering multiple proof formats to support prospective mathematics teachers’ RCGP

Analisis kesulitan matematis mahasiswa berdasarkan teori pemrosesan informasi menggunakan media kahoot!

This approach focuses on students' thinking procedures. This study aims to describe the obstacles of students in innovative learning using Kahoot! in solving mathematics problems according to Robert Gagne's theory. Information processing theory explains how information is received, processed, and stored in memory, where difficulties can arise at each stage, such as limited short-term memory capacity and problems in encoding information into long-term memory. This research method uses a qualitative descriptive approach, with data collection through observation, interviews, and group discussions. The subjects in this study were all OFF G mathematics students in semester 1 at Malang State University in the 2024/2025 academic year, totaling 30 students. The data obtained in this study were written tests in the form of questions on the material of composition functions and inverse functions and interview guidelines. The research results indicate that: (1) students experience obstacles related to understanding each procedure for solving mathematics problems, concepts, procedures, or principles for working on mathematics problems, and (2) the trigger for students' limitations in learning mathematics is the lack of motivation from students to access information that they do not understand

Development of Mathematics E-Modules with Cultural Context to Support Mathematical Literacy

This research aims to develop a culture-based mathematics E-Module to support students' mathematical literacy in a valid, practical, and effective way. The ADDIE development model was used in this research. Data was collected with validation sheets, response questionnaires, and evaluation questions and analyzed descriptively qualitative and quantitative. The validity of the E-Module, with a validation score of 81.5%, fits the valid criteria. Practicality with a response questionnaire score of 90.49% according to practical criteria. Effectiveness was assessed from student evaluation results with an average  percentage of 63.166% according to somewhat effective criteria. The results showed that the E-Module with cultural context is feasible and practical and has a positive impact on improving students' mathematical literacy skills