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All Journal Journal of Research and Advances in Mathematics Education Mandalika Mathematics and Educations Journal Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education
Pratama Wahyu Purnama
Department Of Mathematics Education, Yogyakarta State University,
Education Mathematics Social Sciences Other

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The effectiveness of goal-free problems for studying triangle similarity in collaborative groups Purnama, Pratama Wahyu; Retnowati, Endah
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 6 Issue 1 January 2021
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v6i1.11198

Abstract

Similarity is a topic in Geometry which investigates similar elements of a plane. This topic has a high complexity that generates cognitive load in working memory. A deep understanding of the concept is needed to solve similarity problems. Based on cognitive load theory, learning by goal-free problems is suggested since it can minimize cognitive load. This research examined the effectiveness of presenting similarity inquiries using goal-free problems for learning by collaboration. Using a factorial design: 2 presentation techniques (goal-free vs. goal-given problems) x 2 groupings (collaborative vs. individual) in authentic classrooms, the experiment consisted of four consecutive phases: introductory, learning phase, retention test, and transfer test. One-hundred eleven eighth-graders from four classrooms in a junior high school in Yogyakarta, Indonesia, served as research participants. The findings showed that students who were learning using goal-free problems possessed significantly higher scores of retention and transfer tests, as well as experience lower cognitive load during both tests. On the contrary, it was found that studying individually yielded a significantly higher transfer score than studying collaboratively. Since there was no interaction effect, it may be concluded that goal-free problems can be effective for either collaborative or individual learning.
Eksplorasi Motif Geblek Renteng: Aplikasi Grup Kristalografi dengan Graphical User Interface (GUI) Putranto, Sumbaji; Ratnasari, Gamarina Isti; Purnama, Pratama Wahyu
Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education Vol. 3 No. 02 (2023): October 2023
Publisher : Pusat Studi Pengembangan Pembelajaran Matematika Sekolah UIN Sunan Kalijaga Yogyakarta Jl. Marsda Adisucipto, Yogyakarta 55281

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14421/quadratic.2023.032-02

Abstract

Geblek is one of Kulon Progo's specialty foods made from cassava flour with a shape resembling a figure eight. Geblek is the main pattern used in the batik typical of Kulon Progo. The batik motif uses repetitive and symmetrical patterns. The application of mathematics, especially cryptography, can be used to find repetitive patterns that can inspire batik motifs. This research aims to describe how a basic geblek pattern from Kulon Progo can be transformed into various other patterns using the concept of plane crystallography. The geblek pattern is applied to 17 crystallographic groups, resulting in 17 batik motifs. The use of Graphical User Interface (GUI) in MATLAB will make it easier to form batik motifs. Based on the exploration results, 17 patterns were derived from the basic pattern of Kuln Progo geblek. Uniquely, from these 17 patterns, there are the same and similar patterns. In other words, the patterns found from the basic geblek pattern do not reach 17 patterns. The development pattern of Kulon Progo geblek is further described in this article.
Optimalisasi working memory siswa melalui desain worked example berbasis cognitive load theory pada materi SPLDV Purnama, Pratama Wahyu; Hidayati, Indah Nikmatul
Mandalika Mathematics and Educations Journal Vol 7 No 4 (2025): Desember
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i4.11029

Abstract

Systems of Linear Equations with Two Variables (SPLDV) contain numerous symbols and present high complexity in their solution processes, which can create substantial cognitive demands for middle school students. Instructional design that minimizes irrelevant cognitive load while optimizing schema formation is essential to accommodate the limited capacity of working memory. Cognitive Load Theory (CLT) offers effective strategic alternatives for managing cognitive load during learning, particularly in reducing extraneous cognitive load. One recommended approach is the implementation of worked example strategies. This article focuses on developing a worked example design for SPLDV material based on CLT principles. The research comprises three phases: examining the cognitive load of SPLDV content, reviewing fundamental CLT principles, and constructing instructional design using worked example strategies. The research produces a worked example design featuring structured solution steps that eliminate split attention and redundancy effects, successfully reducing extraneous cognitive load and enhancing working memory effectiveness in learning SPLDV. These findings can serve as a foundation for further design development or empirical validation in broader educational contexts.
Co-Authors Endah Retnowati Hidayati, Indah Nikmatul Putranto, Sumbaji Ratnasari, Gamarina Isti