Enhancing Mathematical Representation Skills through the MID Model: Does Cognitive Style Matter?

Authors

  • Santi Widyawati Universitas Nahdathul Ulama (UNU) Lampung
  • Siti Qomariyah Universitas Nahdathul Ulama (UNU) Lampung
  • Fredi Ganda Putra (Scopus ID: 57208306223) Universitas Islam Negeri Raden Intan Lampung
  • Khoirunnisa Imama UIN Raden Intan Lampung
  • Cahniyo Wijaya Kuswanto UIN Raden Intan Lampung

DOI:

https://doi.org/10.58524/smartsociety.v5i1.657

Keywords:

Cognitive style, Mathematical reasoning ability, Mathematical representation ability, Meaningful Instructional Design (MID).

Abstract

The ability to represent mathematical ideas is a fundamental component of mathematical understanding and communication. However, many students still struggle to express mathematical concepts in varied forms such as visual, symbolic, or verbal representations. This study aims to examine the effectiveness of the Meaningful Instructional Design (MID) learning model in improving students’ mathematical representation skills, while also considering the role of students’ cognitive styles. A quasi-experimental research design was implemented involving two groups: an experimental group taught using the MID model and a control group taught using conventional expository methods. The participants were selected using a cluster random sampling technique from a population of junior high school students. Data were collected through a validated mathematical representation test and a cognitive style questionnaire. The collected data were then analyzed using two-way ANOVA with a 5 percent level of significance, following prerequisite tests for normality and homogeneity using SPSS version 25 and Microsoft Excel. The results showed that students who learned through the MID model exhibited significantly higher mathematical representation skills than those taught using the expository model. Furthermore, students’ cognitive styles also had a significant main effect on their representation abilities. Despite these main effects, the interaction between the learning model and cognitive style was not statistically significant. These findings indicate that the MID model is a robust instructional approach that can enhance students’ mathematical representation skills across different cognitive style profiles. The study highlights the importance of adopting meaningful learning frameworks that prioritize concept-building and student engagement, regardless of learners’ individual differences. 

Author Biography

References

Alabdulaziz, M. S., Hassan, H. F., & Soliman, M. W. (2022). The effect of the interaction between crowdsourced style and cognitive style on developing research and scientific thinking skills. Eurasia Journal of Mathematics, Science and Technology Education, 18(10). Scopus. https://doi.org/10.29333/ejmste/12428

Ana, S. N., Istihana, I., & Andriani, S. (2022). Pengaruh MID (meaningful instructional design) dan Self efficacy terhadap peningkatan kemampuan pemecahan masalah. PHI: Jurnal Pendidikan Matematika, 6(1), Article 1. https://doi.org/10.33087/phi.v6i1.193

Apriani, A., Prihatiningtyas, N. C., & Husna, N. (2023). Pengaruh Model Pembelajaran Meaningful Instructional Design (MID) Terhadap Kemampuan Pemecahan Masalah Matematis Siswa Pada Materi Sistem Persamaan Linear Tiga Variabel. Innovative: Journal Of Social Science Research, 3(2), 12131–12144.

Assingkily, M. J. (2024). Utilizing Meaningful Instructional Design to Enhance Elementary School Students’ Learning Capabilities. Cendekiawan: Jurnal Pendidikan Dan Studi Keislaman, 3(1), 385–390.

Blazar, D., & Pollard, C. (2023). Challenges and Tradeoffs of “Good” Teaching: The Pursuit of Multiple Educational Outcomes. Journal of Teacher Education, 74(3), 229–244. https://doi.org/10.1177/00224871231155830

Carter, J. (2012). The Role of Representations in Mathematical Reasoning1. Philosophia Scientae, 16–1. https://doi.org/10.4000/philosophiascientiae.716

Daulay, I. S., Hasibuan, S. B., & Nasution, S. (2023). The Use of Meaningful Instruction Design (Mid) Learning Model to Improve Student Learning Outcomes in Force and Motion Science Subject Materials. Al-Aulad: Journal of Islamic Primary Education, 6(2), 108–117.

Evendi, E., Al Kusaeri, A. K., Pardi, M. H. H., Sucipto, L., Bayani, F., & Prayogi, S. (2022). Assessing students’ critical thinking skills viewed from cognitive style: Study on implementation of problem-based e-learning model in mathematics courses. Eurasia Journal of Mathematics, Science and Technology Education, 18(7). Scopus. https://doi.org/10.29333/ejmste/12161

Glean, G. R., Sidabutar, R., & Simarmata, G. (2023). The Effect of Meaningful Instructional Design (MID) Learning Model on Students’ Mathematical Reasoning Ability on the Material of Arithmetic Rows and Rows in Class VIII SMP Negeri 2 Tebing Tinggi. EduMatika: Jurnal MIPA, 3(4), 83–93.

Ho, S., & Kozhevnikov, M. (2023). Cognitive style and creativity: The role of education in shaping cognitive style profiles and creativity of adolescents. British Journal of Educational Psychology, 93(4), 978–996. https://doi.org/10.1111/bjep.12615

Indriani, I. S. (2024). Pengaruh model pembelajaran meaningful instructional design (MID) terhadap kemampuan penalaran matematis ditinjau dari self efficacy siswa Mts [Skripsi, Universitas Islam Negeri Sultan Syarif Kasim Riau]. https://repository.uin-suska.ac.id/84352/

Irma, N. (2023). Pengaruh model pembelajaran meaningful instructional design (MID) terhadap kemampuan analisis matematis dan penalaran adaptif matematis [Diploma, UIN RADEN INTAN LAMPUNG]. https://repository.radenintan.ac.id/30549/

Kurniawan, A., Rahmiati, D., Marhento, G., Suryani, Y., Jalal, Maulidia, N., Daniarti, Y., Kasmawati, Wigati, E., Harun, A., Nugroho, Agun, H., Supadmi, Syamiyah, Niana, E., Yunarti, T., Utami, S., HudiaH, A., & Artiani, E. L. (2022). Metode Pembelajaran Dalam Student Centered Learning (SCL). Pendidikan, 2.

Kusumawati, I., Firdaus, F. M., & Oktari, V. (2024). Implementation of Meaningful Instruction Design Model Assisted by Comic on Students Understanding of Multiplication. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(1), Article 1. https://doi.org/10.15294/smb0aq35

Laamena, C. M., & Laurens, T. (2021). Mathematical literacy ability and metacognitive characteristics of mathematics pre-service teacher. Infinity Journal, 10(2), 259–270.

Lefrida, R., Siswono, T. Y. E., & Lukito, A. (2023). Exploring The Field-Independent Student’s in Understanding Derivative Concepts: A Case of Commognitive Perspective. Acta Scientiae, 25(3), 180–207. Scopus. https://doi.org/10.17648/acta.scientiae.7097

Lubna, Suhirman, & Prayogi, S. (2023). Evaluation of STEM students’ critical thinking in terms of cognitive style through problem-based distance learning. Journal of Education and E-Learning Research, 10(3), 557–568. Scopus. https://doi.org/10.20448/jeelr.v10i3.4972

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21.

Manfreda Kolar, V., & Hodnik, T. (2021). Mathematical literacy from the perspective of solving contextual problems. European Journal of Educational Research, 10(1), 467–483.

Pedersen, M. K., Bach, C. C., Gregersen, R. M., Højsted, I. H., & Jankvist, U. T. (2021). Mathematical representation competency in relation to use of digital technology and task design—A literature review. Mathematics, 9(4), 444.

Pitriani, K., & Suardipa, I. P. (2023). Peningkatan pemahaman konsep matematika pada materi trigonometri siswa melalui penerapan model pembelajaran meaningful intructional design berbantuan media pembelajaran interaktif animasi. Widyaguna: Jurnal Ilmiah Pendidikan Guru Sekolah Dasar, 1(1), Article 1.

Rosidah, I. I., Rahayu, B., & Nurhayati, D. F. (2018). Penerapan Metode Meaningful Instructional Design (MID) Dalam Bimbingan Klasikal Untuk Meningkatkan Kemampuan Crirical Thinking Siswa. Seminar Nasional Dan Workshop Bimbingan Dan Konseling 2018, Mid.

Salam, M. (2023). Cognitive Conflict Strategy: Mathematical Representation Based on Cognitive Style. Mosharafa: Jurnal Pendidikan Matematika, 12(2), 339–350.

Saputri, V., & Kamsurya, R. (2020). Mathematical Representation Ability and Mathematics Self Efficacy in CORE Learning Models with Open-Ended Approach. ANARGYA: Jurnal Ilmiah Pendidikan Matematika, 3(2). https://doi.org/10.24176/anargya.v3i2.5353

Sassetti, S., Cavaliere, V., & Lombardi, S. (2022). The rhythm of effective entrepreneurs’ decision-making process. The pathways of alertness scanning and search and cognitive style. A mediation model. International Entrepreneurship and Management Journal, 18(2), 555–578. https://doi.org/10.1007/s11365-021-00759-1

Sianturi, M., Suliantin, R., & Fitrianti, H. (2022). Relationships Between Cognitive Styles and Indigenous Students’ Mathematics Academic Outcomes. Journal of Learning for Development, 9(3), 528–544. Scopus. https://doi.org/10.56059/jl4d.v9i3.684

Sirota, M., Dewberry, C., Juanchich, M., Valuš, L., & Marshall, A. C. (2021). Measuring cognitive reflection without maths: Development and validation of the verbal cognitive reflection test. Journal of Behavioral Decision Making, 34(3), 322–343. https://doi.org/10.1002/bdm.2213

Situmorang, A., Saryantono, B., & Noviyana, H. (2021). Pengaruh model meaningful instructional design terhadap kemampuan koneksi matematika siswa kelas VIII semester ganjil UPT SMP negeri 7 Bandar Lampung tahun pelajaran 2021/2022. Jurnal Mahasiswa Pendidikan Matematika (JMPM), 3(1), Article 1.

Son, A. L., Darhim, & Fatimah, S. (2020). Students’ mathematical problem-solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222. Scopus. https://doi.org/10.22342/jme.11.2.10744.209-222

Sternberg, R. J. (1987). Intelligence and Cognitive Style. In Aptitude, Learning, and Instruction. Routledge.

Suningsih, A., Budayasa, I. K., & Ismail. (2024). Critical thinking of masculine students with impulsive cognitive style in solving geometry problems. Perspektivy Nauki i Obrazovania, 71(5), 290–304. Scopus. https://doi.org/10.32744/pse.2024.5.17

Syamsulrizal, Khabibah, S., Lukito, A., & Madzkiyah, A. F. (2025). Students’ Critical Thinking Dispositions in View of Cognitive Styles: Exhibiting Confidence in Reasoning and Inquisitive. Perspektivy Nauki i Obrazovania, 73(1), 583–594. Scopus. https://doi.org/10.32744/pse.2025.1.37

Via, A. P. (2024). Pengaruh model pembelajaran meaningful instructional design (MID) terhadap kemampuan representasi dan kemampuan koneksi matematis peserta didik [Diploma, UIN Raden Intan Lampung]. https://repository.radenintan.ac.id/34195/

Wirdaningsih, S. (2024). Pengaruh Model Pembelajaran Meaningful Instructional Design terhadap Kemampuan Penalaran Matematis Ditinjau dari Minat Belajar Siswa [Skripsi, Universitas Islam Negeri Sultan Syarif Kasim Riau]. https://repository.uin-suska.ac.id/77651/

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Published

2025-05-08