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Learning obstacle instrument analysis of proportion concept with praxiology framework Maudy, Septiani Yugni; Ruli, Redo Martila
Journal of Didactic Mathematics Vol 5, No 3 (2024): December
Publisher : Mahesa Research Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34007/jdm.v5i3.2435

This study explores the development and application of a praxiology-based instrument designed to identify and address learning obstacles in the teaching of the concept of proportion in early algebra. Proportion plays a crucial role in connecting concrete numerical concepts with abstract algebraic thinking; however, many students face significant challenges when transitioning from numerical to algebraic representations. The study utilizes a praxiology framework, which emphasizes the relationship between the type of mathematical task, the techniques employed by students, and the underlying theoretical principles that shape students' understanding. This framework provides a deeper understanding of how task design can influence students' mathematical practices, making it particularly effective for diagnosing learning obstacles in proportion-related tasks. The instrument, which was applied to seventh-grade students in Bandung, Indonesia, consists of five types of tasks aimed at developing students’ skills in arithmetic-algebraic representations and solving linear equations in both abstract and contextual forms. By predicting students' potential solutions and analyzing their problem-solving strategies, the study highlights how the praxiological approach facilitates the identification of key difficulties in students' understanding of proportion. The findings demonstrate that this approach not only helps to diagnose learning obstacles more effectively but also supports the creation of targeted instructional strategies that improve students’ grasp of proportional reasoning. This research contributes valuable insights into the use of praxiology in mathematics education, offering a robust framework for analyzing and overcoming learning obstacles in early algebra instruction.

Didactical design of the proportionality concept based on anthropological theory of the didactic Yugni Maudy, Septiani; Ruli, Redo Martila
Beta: Jurnal Tadris Matematika Vol. 18 No. 1 (2025): Beta May
Publisher : Universitas Islam Negeri (UIN) Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20414/betajtm.v18i1.690

[English]: This study aims to develop a didactic design grounded in the Anthropological Theory of the Didactic (ATD), with a focus on mathematical praxeology, to enhance students’ understanding of proportionality. The study uses the Didactical Design Research (DDR) methodology, which consists of three primary stages: retrospective analysis, metadidactical analysis, and prospective didactical situation analysis. Classroom observations, teacher and student interviews, and the examination of diagnostic tasks completed by thirty seventh-grade students at a junior high school in West Java, Indonesia, were used to gather data. The findings, which are interpreted using the Brousseau's framework, classify learning obstacles into three categories: (1) Ontogenic obstacles, which are associated with students' developmental readiness and prior knowledge; (2) Epistemological obstacles, which include misusing additive reasoning in multiplicative contexts and misinterpreting unit rates; and (3) Didactic obstacles, which are caused by unfamiliar task structures, implicit information, and insufficient instructional representations. The study has developed five learning tasks based on the praxeological framework, which included task, technique, technology, and theory. Despite not yet being used in classrooms, the didactic design's development is supported by both theoretical and empirical evidence. This study offers a different strategy for teachers dealing with proportionality learning obstacles and helps create more meaningful and contextually relevant math instruction. It also creates opportunities for further study to examine how the suggested design is implemented and how it affects students' mathematical thinking. [Bahasa]: Penelitian ini bertujuan untuk mengembangkan desain didaktik berbasis Teori Antropologi Didaktik (ATD) dengan fokus pada praksiologi matematika untuk membantu siswa agar lebih memahami konsep proporsionalitas. Metode yang digunakan adalah Didactical Design Research (DDR), yang terdiri dari tiga tahap utama: analisis retrospektif, analisis metadidaktik, dan analisis situasi didaktik prospektif. Data dikumpulkan melalui observasi di kelas, wawancara dengan guru dan siswa, serta analisis tugas diagnostik yang dikerjakan oleh 30 siswa kelas VII di sebuah SMP di Jawa Barat. Menggunakan kerangka Brousseau hasil penelitian ini menunjukkan bahwa hambatan belajar siswa terbagi menjadi tiga jenis: (1) hambatan ontogenik, yaitu terkait kesiapan dan pengetahuan awal siswa; (2) hambatan epistemologis, seperti penggunaan penalaran aditif yang salah dalam konteks yang seharusnya menggunakan penalaran multiplikatif, serta kesalahan dalam memahami laju satuan; dan (3) hambatan didaktik, yang muncul karena struktur tugas yang asing, informasi yang tidak jelas, serta kurangnya representasi yang memadai dalam pembelajaran. Berdasarkan temuan tersebut, dirancang lima tugas pembelajaran melalui pendekatan praksiologi. Studi ini memberikan alternatif strategi bagi guru untuk mengatasi kesulitan belajar proporsionalitas dan mendukung terciptanya pembelajaran matematika yang lebih bermakna dan relevan dengan konteks siswa. Selain itu, penelitian ini juga membuka peluang untuk penelitian lebih lanjut terkait penerapan desain ini dan dampaknya terhadap cara berpikir matematika siswa.

Many paths, one unknown: Uncovering the diverse minds behind algebraic thinking Maudy, Septiani Yugni
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 2 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i2.19502

This qualitative study examines the diversity in algebraic thinking among high school students (Grades VII-IX) by considering algebraic activity models, reasoning types, and generalization layers. We used clinical interviews along with task-based assessments so that we could investigate students' problem-solving processes with just a hermeneutic phenomenological approach. Participants solved contextualized algebra problems using several solution strategies. These strategies included visual representations, arithmetic generalizations, proportional reasoning, and symbolic parameterization. The findings reveal three key conclusions: (1) students think algebraically and develop along a continuum from concrete representations to abstract symbolic reasoning; (2) cultural and instructional contexts influence their ability to transition between factual, contextual, and symbolic generalization layers quite greatly; and (3) multimodal approaches understand algebra better via accommodating diverse cognitive styles. This study contributes in two primary ways for mathematics education research: First, it analyzes semiotic progression within non-Western educational contexts through such culturally-situated framework, which then addresses a gap for current algebra research. Second, it offers design principles validated empirically for creating inclusive algebraic tasks. These tasks do support multiple entry points as well as solution pathways. The results do show that it is important for us to teach in an adaptive manner by both recognizing and then nurturing diverse mathematical styles of thinking in algebra education.

From Arithmetic to Algebra: Students’ Epistemological Obstacles Ruli, Redo Martila; Juandi, Dadang; Dahlan, Jarnawi Afgani; Maudy, Septiani Yugni
SJME (Supremum Journal of Mathematics Education) Vol 9 No 2 (2025): Supremum Journal of Mahematics Education
Publisher : Fakultas Keguruan dan Ilmu Pendidikan Universitas Singaperbangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35706/sjme.v9i2.205

The initial algebraic concept typically introduced to students is the linear equation in one variable. One of the earliest difficulties students encounter with this concept is comprehending the significance of a variable. This study aims to investigate the epistemological obstacles faced by students in acquiring proficiency in linear equations in one variable. A qualitative phenomenological methodology was employed in this research. The participants consisted of 35 eighth-grade students enrolled in a junior high school who had previously studied linear equations in one variable. In the initial phase of the study, the researcher formulated two word problems. The utilization of word problems was intended to elucidate students’ thought processes in articulating their ideas or reasoning in written form. Subsequently, interviews were conducted with four selected students to corroborate the researcher’s interpretation of their written responses. The findings and discussion reveal that the conceptual deficiencies acquired during instruction contributed to the emergence of epistemological learning obstacles among students. This learning obstacle was identified through the solutions proposed by students, which were predominantly arithmetic rather than algebraic. Although the students acknowledged that the problem they were dealing with was related to the concept of linear equations in one variable, the majority still encountered difficulties in providing solutions in the form of a linear equation in one variable., particularly in the forms and .

Educators’ Knowledge Transposition: the Algebra Devolution of Thinking Maudy, Septiani Yugni; Ruli, Redo Martila
Jurnal Riset Pendidikan Matematika Vol. 12 No. 2 (2025): November 2025
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/jrpm.v12i2.84986

In mathematics learning, knowledge is in the form of meaning, and it is part of the transposition process so that it is situational and in the form of abstraction from the context of its use. The process begins with repersonalization (the process of mathematizing a mathematical concept as done by mathematicians) and recontextualization (provide a new mathematical context) so that it becomes knowledge that is a posteriori. The role of educators is so fundamental because it is related to the stages. This study is based on the hermeneutic phenomenology. Data collection is carried out in the form of documentation studies, observations, and reflective argumentative dialogue. The image of knowledge is collectively constructed, and the knowledge is emerged from conjoining understandings between educator and researcher. The educators’ experiences were traced from a reflective-argumentative dialogue to investigate what educators have done and what will be done in mathematics teaching practice. The researcher also examined the educators’ knowledge transposition in thinking algebraically. These were projected in three knowledge conceptions of educators' thinking process. There are at least five main issues revealed concerning knowledge for practice, knowledge in practice, and knowledge of practice. The transposition of educator knowledge becomes devolution of algebraic thinking from educators to students.

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