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All Journal AKSIOMA: Jurnal Program Studi Pendidikan Matematika Didaktik : Jurnal Ilmiah PGSD STKIP Subang
Lia Ardiansari
Universitas Panca Marga
Education Mathematics

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BRIDGING OF ARITHMETIC AND ALGEBRA: A RELATIONAL LOCAL INSTRUCTIONAL THEORY Lia Ardiansari; Faridahtul Jannah; M. Sahrul Rozi
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol. 15 No. 2 (2026)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v15i2.14895

Abstract

Bridging arithmetic and algebra remains a persistent challenge in mathematics education, largely due to students’ operational interpretations of the equal sign and fragmented coordination of representations. Existing instructional approaches often emphasize procedural fluency without systematically supporting the relational understanding required to connect these domains. This study aims to develop and examine a relational instructional trajectory that functions as a conceptual bridge between arithmetic and early algebra. Using a Didactical Design Research (DDR) approach, the study involved 29 fifth-grade students from an elementary school in East Java, including five students in a pilot experiment and twenty-four students in a teaching experiment. The “Jembatan Aritmatika (Arithmetic Bridge)” e-module was designed based on an initial analysis of students’ learning obstacles, particularly in understanding equality and symbolic representations. Data were collected through pre- and post-tests, questionnaires, classroom observations, and semi-structured interviews. Data analysis combined qualitative analysis of students’ reasoning patterns with quantitative comparisons of pre- and post-intervention performance. The findings indicate a shift from procedural and counting-based strategies toward relational reasoning. Students increasingly interpreted the equal sign as expressing equivalence and demonstrated improved coordination of symbolic and contextual representations in solving early algebraic tasks. This study contributes a relational Local Instructional Theory (LIT) that specifies a progressive learning trajectory—from contextual and visual representations to symbolic reasoning—and explicit didactical anticipations for bridging arithmetic and algebra, grounded in empirically identified learning obstacles.
BRIDGING ARITHMETIC TO ALGEBRA: IMPLEMENTING AN E-MODUL THROUGH DIDACTICAL DESIGN RESEARCH Lia Ardiansari; Dyah Ariyanti; Mohammad Sahrul Rozi; Muhammad Fajar Assiddiqi
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol. 14 No. 4 (2025)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v14i4.13880

Abstract

Students' difficulties in understanding algebraic concepts often stem from a procedural approach to arithmetic without deep conceptual grounding. This study aims to develop and implement an interactive e-module titled “Jembatan Aritmatika”, designed to help students build a conceptual transition from arithmetic to algebra by deepening their understanding of the equal sign (=) as a relational symbol. The study adopts a Didactical Design Research (DDR) approach, consisting of three main phases: preliminary design, experimental teaching, and retrospective analysis. The participants were upper-grade elementary school students who engaged with the e-module across several learning sessions. Instruments included pre-test and post-test questions, observation sheets, and student response questionnaires. The results showed that the e-module effectively enhanced students' understanding of the relational meaning of the equal sign and introduced them to the fundamental structure of algebraic equations in a gradual and meaningful way. Strategies such as visualization, contextual problem-solving, and the progressive use of symbolic representation proved helpful in supporting students’ reasoning about quantitative relationships. The study concludes that the “Jembatan Aritmatika” e-module holds promise as an effective learning medium for facilitating students' conceptual transition from arithmetic to algebra.
PENERAPAN MODEL PEMBELAJARAN PROBLEM BASED LEARNING (PBL) BERBANTUAN MEDIA PAPAN NILAI TEMPAT UNTUK MENINGKATKAN HASIL BELAJAR MATEMATIKA PADA MATERI NILAI TEMPAT SISWA KELAS II SDN BULANG 1 Rahmaudina Rizkiyah; Ribut Prastiwi Sriwijayanti; Lia Ardiansari
Didaktik : Jurnal Ilmiah PGSD STKIP Subang Vol. 12 No. 03 (2026): Volume 12 No. 03, September 2026 Published
Publisher : STKIP Subang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36989/didaktik.v12i03.17394

Abstract

ABSTRACT This study was conducted to improve the mathematics learning outcomes of second-grade students on the topic of place value through the implementation of the Problem-Based Learning (PBL) model assisted by place value board media at SDN Bulang 1. The research was motivated by the low student achievement caused by teacher-centered instructional practices and the limited use of interactive learning media, resulting in many students failing to meet the minimum mastery criteria. This research employed Classroom Action Research (CAR) consisting of two cycles, with each cycle comprising planning, implementation, observation, and reflection stages. The participants were 16 second-grade students. Data were collected through observation and learning outcome tests and analyzed descriptively to evaluate improvements across the cycles. The findings demonstrated that the application of the Problem-Based Learning model supported by place value board media effectively enhanced students’ mathematics learning outcomes. In the pre-test, only 5 students (31.25%) achieved mastery, while 11 students (68.75%) did not. After the implementation of Cycle I, the number of students achieving mastery increased to 10 (62.5%). Further improvement was observed in Cycle II, where 15 students (93.75%) met the mastery criteria and only 1 student (6.25%) remained below the expected standard. These results indicate that integrating the Problem-Based Learning model with place value board media creates a more active and meaningful learning environment and significantly improves students’ understanding and achievement in learning place value concepts. Keywords: Problem Based Learning, Scoreboard, Learning Outcomes
Co-Authors Dyah Ariyanti Faridahtul Jannah M. Sahrul Rozi Mohammad Sahrul Rozi Muhammad Fajar Assiddiqi Rahmaudina Rizkiyah Ribut Prastiwi Sriwijayanti