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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
PENERAPAN MODEL PEMBELAJARAN PROBLEM BASED LEARNING (PBL) UNTUK MENINGKATKAN KEMAMPUAN BERPIKIR KRITIS SISWA PADA PEMBELAJARAN IPAS KELAS IV DI SDN SUKOHARJO 4 Fitriani Ayu Fadila; Ludfi Arya wardana; Lia Ardiansari
Didaktik : Jurnal Ilmiah PGSD STKIP Subang Vol. 12 No. 03 (2026): Volume 12 No. 3, September 2026 Public
Publisher : STKIP Subang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36989/didaktik.v12i03.18136

Abstract

Based on the initial analysis, it was found that the low critical thinking ability of students was caused by the learning which was still centered on the teacher, with the use of learning limited to textbooks. To overcome this, this study aims to improve students' critical thinking ability in science learning, especially the material of changes in the state of matter through the Problem Based Learning (PBL) Learning Model in fourth grade students at SDN Sukoharjo 4. In this study there are two problem formulations, namely (1) How is the application of the Problem Based Learning learning model in the learning of science on the material of changes in the state of matter in class IV of SDN Sukoharjo 4? (2) How is the improvement of the critical thinking skills of class IV students of SDN Sukoharjo 4 in the learning of science on the material of changes in the state of matter before the application of the Problem Based Learning model?. The purpose of this study (1) To determine the application of the Problem Based Learning learning model in the learning of science on the material of changes in the state of matter in class IV of SDN Sukoharjo 4. (2) To determine the critical thinking skills of class IV students of SDN Sukoharjo 4 in the learning of science on the material of changes in the state of matter before the application of the Problem Based Learning learning model. This study uses the Classroom Action Research (CAR) method which is carried out in 2 cycles, where each cycle consists of 2 meetings. The research subjects are class IV students at SDN Sukoharjo 4, totaling 22 students The results of the study showed that there was a significant increase in learning outcomes. Based on the pretest results, the number of students who completed was 3 students (13.63%) and those who had not completed were 19 students (86.36%). In cycle 1 there was an increase with the number of students who achieved completion as many as 10 students (45.45%) while 12 other students (54.54%) who had not completed. Learning if 80% of students get complete learning outcomes. Therefore, learning outcomes at this stage have not met the expected classical completeness standards. Then in cycle II there was a significant increase with the number of students who achieved completeness as many as 19 students (86.36%) while 3 other students (13.63%) who had not completed so that classical completeness was achieved. The results show that the existence of the Problem Based Learning learning model can improve students' critical thinking skills.
Co-Authors Dyah Ariyanti Faridahtul Jannah Fitriani Ayu Fadila Ludfi Arya Wardana M. Sahrul Rozi Mohammad Sahrul Rozi Muhammad Fajar Assiddiqi Rahmaudina Rizkiyah Ribut Prastiwi Sriwijayanti