Primitive Ideals of Toeplitz Algebra of Ordered Groups

The topology on primitive ideal space of Toeplitz algebras of totally ordered abelian groups can be identified through the upwards-looking topology if and only if the chain of order ideals is well-ordered. We describe the topology on primitive ideal space of Toeplitz algebra of totally ordered abelian groups when the chain of order ideals is not well ordered.DOI : http://dx.doi.org/10.22342/jims.14.2.55.111-11

An Investigation of Master Student Understanding on Mathematical Literacy Problems

Indonesian government has been promoting the National Literacy Movement since 2016 to response disappointing results of the Program for International Student Assessment on literacy and mathematical literacy skills of students. This movement involves many parties, including educational universities, to prepare mathematics education students of master level, as prospective teachers or lecturers, to understand mathematical literacy. To investigate this condition, this study aims to analyze master student understanding on mathematical literacy problems. To do so, we conducted an online survey via Google Form involving 32 master students from several universities in Bandung. In this survey, each master student was called for sending two mathematics problems and solutions that considered to be literacy problems. The results revealed that 17 (53%) involved master students understand mathematical literacy problems. The most frequent category of literacy problems to appear was Change and Relationship followed by categories of Space and Shape, Uncertainty and Data, and Quantity, respectively. Another result showed that word problems seemed to be regarded as the same as mathematical literacy problems by some students. We conclude that master student understanding of mathematical literacy needs to be improved for facing future educational careers

Students’ Obstacles in Learning Sequence and Series Using Onto-Semiotic Approach

Sequences and series is one of the mathematical topics that are related to everyday life. The topic is also taught at several levels of education in Indonesia. However, many students still experrienced difficulties in learning this topic. This study uses an interpretive paradigm that is part of the Didactical Design Research (DDR). This research aims to analyze students’ learning obstacles on the topic of sequence and series using the onto-semiotic approach. To do so, written test consists of five questions related to the conceptual understanding of an arithmetic sequences and series was administered to 23 students from one of the senior high schools in Kota Tangerang Selatan followed by interviews with 4 students. The results show that learning obstacles are classified into epistemological, ontogenic, and didactical obstacles. Based on the onto-semiotics approach, the students had difficulties in defining a mathematical idea on sequences and series topics. They could convert a problem into mathematical model but were confused to use a proper procedure. It can be concluded that students still experience obstacles in learning sequences and series topic. The results of this study can be used by teachers as considerations in designing learning situation on the topic of sequence and series

Advancing Computational Thinking in Mathematics Education: a Systematic Review of Indonesian Research Landscape

Computational Thinking (CT) has emerged as a crucial and foundational skill in the 21st century, capturing the attention of researchers across various domains, including mathematics education in Indonesia. This research identifies and analyzes trends, themes, focuses, and research findings on CT through mathematics learning in Indonesia. This Systematic Literature Review (SLR) adheres to the PRISMA guidelines, encompassing three stages: search, selection, and data analysis. The search process on the Scopus database, utilizing queries aligned with the research objectives, yielded 31 articles related to CT and mathematics education authored by Indonesian researchers. Subsequent selection involved criteria such as research focus, study type, document availability, and intervention differences, resulting in 14 articles. Data analysis employed Bibliometrix and NVivo 14 Plus software. The findings reveal a significant increase in research on CT in mathematics education from Indonesian researchers over the past two years, with an annual growth rate of 5.74%. This publication landscape involves contributions from 39 authors affiliated with 16 higher education institutions in Indonesia. Researchers have delved into diverse themes, including the analysis of CT skill achievement, the development of CT-oriented instructional models and media, and the creation of assessment tools to measure CT skills. These findings underscore the broad relevance of CT in the realm of mathematics education. As a burgeoning field of study, numerous aspects of CT remain open for further research, development, and exploration, especially those related to mathematics. To enhance the impact and implementation of Computational Thinking (CT) within the context of Indonesian education, future research may consider investigating innovative pedagogical approaches, assessing the long-term impact of CT interventions, and exploring the potential integration of CT across various educational levels

USING GRAPHIC CALCULATOR IN TRIGONOMETRIC LEARNING: A DIDACTICAL DESIGN FOR TEACHER

This study explored the activitiesusing a graphing calculator of 10th-grade high school students on the trigonometry topic. A total of 65 students were divided into two classes, the first class consisted of 32 students, and the second class consisted of 33 students. The main objective of this study is to present classroom activities enriched with graphing calculators and observe responses about teaching with this approach. This study is research on developing learning designs within the Didactical Design Research (DDR) framework presented in an exploratory narrative. Data were collected by using two trigonometry worksheets and lesson observations. The worksheets were constructed based on the following focus areas: behaviour of graphs, constructing related-angle formula, and overall performance of the learner. The result of this research is a learning design that has been tested on 65 high school students. The research results on how to analyze the results of the implementation of structured learning designs provide information that educators can use, including the use of graphing calculators to help and make it easier for students to identify graphs more quickly and make students accustomed to using trigonometric function symbols. Another finding from structured instructional designs is that working in groups allows students to share experiences more effectively

Mathematical Justification Research in Mathematics Education Across Grades: A Systematic Literature Review

Justification is a set of responses or responses that a person gives when asked to provide mathematical reasons for the results he makes. Justification can be used as a social process in which mathematical knowledge is explained, and systematically verified based on ideas, definitions, and properties that apply in mathematics such as representations used to display concepts. Research on justification in mathematics education has been carried out for a long time. This study aims to evaluate mathematics justification studies from articles published after 2016 and before April 2022 from ERIC and Google Scholar Databases. The key questions in this study are how these articles are distributed based on year publication, country, participant, mathematics subject, method, and how to support mathematical justification. This study used a Systematic Literature Review (SLR) by Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines including inclusion and exclusion criteria and then the data were extracted, resulting in 30 studies to be reviewed. The result shows that by year of publication the articles fluctuation distributed, based on country no data from Africa and Australia was found in the databases, the participant is mostly preservice mathematics teachers, whereas only one publication studied in high school students, geometry is the most mathematics subject used in research since every grade contain this material, the method is frequently given by qualitative research with various approach, how to supporting mathematical justification is also discussed

IDENTIFYING STUDENTS’ DIFFICULTIES IN UNDERSTANDING AND APPLYING PYTHAGOREAN THEOREM WITH AN ONTO-SEMIOTIC APPROACH

Abstract:This research is conducted to obtain a description of students’ difficulties in understanding and applying Pythagorean theorem based on the onto-semiotic approach. This research applies a qualitative approach with phenomenology interpretation design. Research data were collected using test and interview methods. The research result was deducted from students' answer sheets and interviews. Participants involved in this study were as many as 25 students of UPI Lab School Junior High School Bandung, who had learned Pythagorean theorem, 4 of which also participated in the interview. It showed that students found it complicated to comprehend definition, describe symbols or notations of mathematical objects, and interpret mathematical objects. Meanwhile, in solving problems related to the application of the Pythagorean theorem, students could describe procedure, algorithm, and technique in solving questions well.Abstrak:Penelitian ini bertujuan untuk mendapatkan gambaran kesulitan siswa dalam memahami dan menerapkan Teorema Pythagoras menggunakan pendekatan onto-semiotika. Penelitian ini menggunakan pendekatan kualitatif dengan desain interpretasi fenomenologi. Metode pengumpulan data, yaitu tes dan wawancara. Partisipan penelitian yang dilibatkan dalam uji kemampuan siswa adalah 25 orang siswa SMP Lab School UPI Bandung yang pernah belajar materi teorema Pythagoras, 4 orang dari 25 orang siswa tersebut dilibatkan dalam wawancara. Hasil penelitian menunjukkan bahwa siswa mengalami kesulitan dalam memahami definisi, mendeskripsikan simbol atau notasi dari objek matematika, serta kesulitan dalam memaknai objek matematika, sedangkan dalam menyelesaikan permasalahan penerapan teorema Pythagoras, siswa mampu mendeskripsikan prosedur, algoritma, dan teknik penyelesaikan masalah dengan baik

Students' mathematical argumentation ability when proving mathematical statements based on self-efficacy

Argumentation as an aspect of problem-solving has been studied in mathematics education. However, mathematical proof still needs to be resolved further. This study investigates students' mathematical argumentation skills when proving mathematical statements based on their self-efficacy. The research subjects were 43 mathematics education students at a university in Aceh Province who had taken a number theory course. The study used a qualitative approach with a case study design: students’ mathematical proving self-efficacy. Data was obtained using self-efficacy questionnaires and mathematical proof test instruments that experts have validated, while the data triangulation used was an in-depth interview. The results of this study reveal that students' mathematical argumentation skills in proving mathematical statements have differences based on their self-efficacy. The mathematical argumentation ability of students with high self-efficacy involves all aspects of argumentation well so that the construction of the proof is scientifically correct. Meanwhile, the argumentation ability of students with moderate or low self-efficacy still does not involve essential aspects of argumentation. So, the proof results are not scientifically correct because they have not arrived at the proper conclusion