Rosi Widia Asiani Rosi, Susi Marisa Susi, Indah Nurul Hazairin Indah, Sherli Permata Sherli, Cut Multahadah Cut, Yuliana Safitri Fitri

Improving Mathematical Problem-Solving Ability through Project-Based Learning in Elementary Linear Algebra: A Study of Mathematics Education Students

Introduction

Improving mathematical problem-solving ability through project-based learning in elementary linear algebra: a study of mathematics education students. This study shows Project-Based Learning (PjBL) with Hill Cipher projects moderately improves mathematical problem-solving in Elementary Linear Algebra for math education students.

Abstract

Elementary Linear Algebra covers the study of matrices and vectors. One practical application of matrix concepts in daily life and technology is the Hill Cipher cryptosystem. Cryptography is the science of securing confidential messages, while the Hill Cipher is a cryptographic method that uses matrices in the encryption process. The Hill Cipher can be applied as a project in Project-Based Learning (PjBL) for the Elementary Linear Algebra course, particularly in the topic of matrices, with the aim of improving students’ problem-solving abilities. This approach serves as an alternative to the conventional learning methods commonly used. Through the implementation of PjBL, it is expected that the course learning outcomes can be achieved and that students will become more creative and innovative in solving problems. This study is a quantitative research with quasi experimental design conducted on third-semester students of the 2023/2024 academic year in the Mathematics Education (Tadris Matematika) program, Faculty of Tarbiyah and Teacher Training, UIN Sulthan Thaha Saifuddin Jambi. Observation sheets were used to examine the implementation of the PjBL model, including the alignment between the learning process and the syntax and principles of PjBL, as well as the effectiveness of the projects used. Tests were administered to measure students’ mathematical problem-solving ability after the implementation of the PjBL model, in the form of essay questions referring to indicators of mathematical problem-solving ability. The effect of the effectiveness of the PjBL implementation to improve students problem-solving ability was analyzed using the N-gain test on the results of the mathematical problem-solving ability test. The obtained N-gain score was 0.5786, which falls into the moderate category, indicating that the PjBL model is moderately effective to improve problem solving ability.

Review

The paper "Improving Mathematical Problem-Solving Ability through Project-Based Learning in Elementary Linear Algebra" presents a compelling case for integrating Project-Based Learning (PjBL) into higher education mathematics curricula. The authors identify a pertinent challenge—enhancing problem-solving skills—and propose an innovative solution by using the Hill Cipher cryptosystem as a practical project within an Elementary Linear Algebra course. This approach is theoretically sound, aiming to move beyond conventional teaching methods to foster creativity and innovation, which are crucial competencies for mathematics education students. The choice of the Hill Cipher is particularly commendable as it effectively bridges abstract mathematical concepts like matrices and vectors with a tangible, real-world application, thereby increasing student engagement and relevance. Methodologically, the study employs a quantitative quasi-experimental design, which is an appropriate framework for evaluating the effectiveness of a pedagogical intervention. The target population of third-semester Mathematics Education students is clearly defined. However, the abstract's description of the problem-solving ability measurement could benefit from further clarification. It states that tests were administered "after the implementation of the PjBL model," implying a post-test only design for problem-solving ability. While an N-gain test was used for analysis, which typically requires pre- and post-test data, the explicit mention of only a post-test for problem-solving ability raises questions about the baseline measurement. For a quasi-experimental design aiming to show improvement, the absence of a clearly stated pre-test or a comparison group might limit the causal attribution of the observed effects solely to the PjBL intervention. Greater detail on the specific "indicators of mathematical problem-solving ability" and how they were operationalized in the essay questions would also enhance the study's transparency and rigor. The study's finding that the PjBL model achieved a moderate effectiveness, indicated by an N-gain score of 0.5786, is a promising result. This suggests that incorporating real-world projects such as the Hill Cipher can indeed make a positive contribution to students' mathematical problem-solving abilities in linear algebra. The implication for educators is to consider adopting such applied, project-based methodologies to enrich the learning experience and achieve deeper understanding. For future research, it would be beneficial to conduct a more robust quasi-experimental design, possibly including a control group or explicitly detailing pre-test measurements for problem-solving ability. Additionally, exploring the long-term impact of PjBL or incorporating qualitative methods to understand the student experience and the specific mechanisms through which PjBL enhances problem-solving could provide richer insights and further refine best practices.

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