Kemampuan representasi matematis siswa dalam materi teorema pythagoras

Authors

  • Mardiani Mardiani Universitas Tanjungpura
  • Sugiatno Sugiatno Universitas Tanjungpura
  • Dona Fitriawan Universitas Tanjungpura
  • Halini Halini Universitas Tanjungpura
  • Ahmad Yani T Universitas Tanjungpura

DOI:

https://doi.org/10.22460/jpmi.v7i5.23524

Keywords:

Mathematical Representation Ability, Pythagorean Theorem

Abstract

This study aims to analyze the mathematical representation ability of SMA Negeri 1 Sungai Kakap students on Pythagorean theory material using visual, symbolic, and verbal strategies. The method used was quantitative descriptive with the research subjects of 36 students in class X. The collection method included questionnaires, reports, and documentation. The instruments used for data collection in this study are mathematical representation test questions and interviews. Data analysis techniques are carried out with quantitative data analysis techniques and descriptive analysis techniques. Based on the test results, it shows that students' mathematical representation skills need to be improved, with an achievement rate of 43% with a medium category. Students' visual representation ability was only 36%, while verbal and symbolic representation was much higher, at 42% and 50%, respectively. In general, students can answer the questions correctly, but there are errors in interpreting and translating the representation between visual, symbolic, and verbal. These findings point to the need for improved understanding and translation between different forms of mathematical representation to improve understanding of the concept of the Pythagorean theorem.

References

-Duodu, S. B., Ennin, F. C., Borbye, S., & Amoaddai, S. (2019). Pre-Service primary school teachers’ mathematical knowledge for teaching fractions through problem solving. International Journal of Advances in Scientific Research and Engineering, 5(3), 08–17. https://doi.org/10.31695/ijasre.2019.33085

Adu-Gyamfi, K., Bossé, M. J., & Lynch-Davis, K. (2019). Three types of mathematical representational translations: Comparing empirical and theoretical results. School Science and Mathematics, 119(7), 396–404. https://doi.org/10.1111/ssm.12360

Al - Sarry, M. J. S. (2020). The Effect of multiple representations in teaching mathematical concepts in mathematics literacy among intermediate level students. PalArch’s Journal of Archaeology of Egypt …, 17(10), 734–749. https://www.archives.palarch.nl/index.php/jae/article/download/4574/4525

Alamian, V., Barati, A., & Habibi, M. (2020). The Effects of visual representations and manipulatives on reduction of algebraic misconceptions of ninth-grade students. Arch Pharma Pract, 11, 49–58.

Altınbaş, A. A., Ertekin, E., & Solak, S. (2024). A study on multiple representation and self-efficacy perception in systems of linear equations. International Journal of Mathematical Education in Science and Technology, 55(4), 976–996. https://doi.org/10.1080/0020739X.2022.2156933

Alzubi, K. (2021). The Effect of using multiple mathematical representations of rational number concepts in basic grades students in Jordan. International Journal of Educational Research Review, 6(3), 226–234. https://doi.org/10.24331/ijere.838677

Ari Suningsih, A. I. (2021). Analisis kemampuan representasi matematis siswa. Mosharafa: Jurnal Pendidikan Matematika, 10(2), 225–234. https://doi.org/10.36526/tr.v6i2.2225

Arikunto, S., & Jabar, C. S. A. (2018). Evaluasi program pendidikan. In Bumi Aksara.

Baumann, J. M. (2024). Think about it, talk about it: exploring the intersection of knowledge and discourse during text-based discussions. Michigan State University.

Cartwright, K. (2020). Analyzing students’ communication and representation of mathematical fluency during group tasks. The Journal of Mathematical Behavior, 60, 100821. https://doi.org/https://doi.org/10.1016/j.jmathb.2020.100821

Cartwright, K. (2023). Interpreting young children’s multiplicative strategies through their drawn representations. In Mathematics Education Research Journal (Issue 0123456789). Springer Netherlands. https://doi.org/10.1007/s13394-023-00450-4

Çilingir Altiner, E., & Önal, H. (2023). Verbal problem-solving representations of primary. 12(3), 228–244.

Clark, J., & Paivio, A. (1991). Dual coding theory and education. Educational Psychology Review, 3, 149–210. https://doi.org/10.1007/BF01320076

Coetzer, T., Livingston, C., & Barnard, E. (2023). Using visual representations to enhance isiXhosa home language learners’ mathematical understanding. South African Journal of Childhood Education, 13(1), 1–8. https://doi.org/10.4102/sajce.v13i1.1297

Cordero-Siy, E., & Ghousseini, H. (2022). Supporting Understanding Using Representations. Mathematics Teacher: Learning and Teaching PK-12, 115(6), 394–403.

Grundén, H. (2023). Representations of Mathematics Education in Swedish Newspapers—Part of the Structural Influence on Mathematics Teaching. Canadian Journal of Science, Mathematics and Technology Education. https://doi.org/10.1007/s42330-023-00277-y

Hatisaru, V. (2022). The use of representations in solving mathematical problems. Australian Mathematics Education Journal, 4(2), 9–14. https://search.informit.org/doi/10.3316/informit.589932835442188

Heller, B. P. (2023). Students’ Concept Images of Triangle Attributes [Illinois State University]. https://www.proquest.com/dissertations-theses/students-concept-images-triangle-attributes/docview/2913405053/se-2

Just, A., & Cribbs, J. D. (2020). Focusing on visual representations in mathematics. Mathematics Teacher: Learning and Teaching PK-12, 113(12), e100–e106. https://doi.org/10.5951/MTLT.2019.0139

Khatin-Zadeh, O., Farsani, D., & Yazdani-Fazlabadi, B. (2022a). Transforming dis-embodied mathematical representations into embodied representations, and vice versa: a two-way mechanism for understanding mathematics. Cogent Education, 9(1). https://doi.org/10.1080/2331186X.2022.2154041

Khatin-Zadeh, O., Farsani, D., & Yazdani-Fazlabadi, B. (2022b). Transforming dis-embodied mathematical representations into embodied representations, and vice versa: a two-way mechanism for understanding mathematics. Cogent Education, 9(1), 2154041. https://doi.org/10.1080/2331186X.2022.2154041

Kosko, K., Weston, T., & Amador, J. (2021). 360 Video as an Immersive representation of practice: Interactions between reported benefits and teacher noticing. Mathematics Teacher Education and Development, 23(4), 162–181.

Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Problems of representations in the teaching and learning of mathematics.

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

Morales-Carballo, A., Díaz Cárdenas, M., & Damián Mojica, A. (2024). Formation and development of mathematical concepts: Elements for research and teaching. International Electronic Journal of Mathematics Education, 19(1), 1–19. https://doi.org/10.29333/iejme/14023

NCTM. (2000). Principles, N. C. T. M. (2000). standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics. In National Council of Teachers of Mathematics (Vol. 7, Issue 2).

Ningrum, M. P., & Hw, S. (2022). Analisis kemampuan representatif matematis peserta didik dalam menyelesaikan soal teorema pythagoras. AKSIOMA, 11(3), 2151–2159.

Nizaruddin, N., Waluyo, S. B., Rochmad, R., & Isnarto, I. (2020). Profile of Student’s Mathematical Representation Translation on the Verbal Problem. Universal Journal of Educational Research, 8(12B), 8178–8185. https://doi.org/10.13189/ujer.2020.082621

Nurrahmawati, Sa’dijah, C., Sudirman, & Muksar, M. (2021). Assessing students’ errors in mathematical translation: From symbolic to verbal and graphic representations. International Journal of Evaluation and Research in Education, 10(1), 115–125. https://doi.org/10.11591/ijere.v10i1.20819

Pagiling, S. L. (2019). Exploration of students’ representation in solving pythagorean theorem problems based on cognitive style. Journal of Physics: Conference Series, 1321(3). https://doi.org/10.1088/1742-6596/1321/3/032004

Post, M., & Prediger, S. (2024a). Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information. In Mathematics Education Research Journal (Vol. 36, Issue 1). Springer Netherlands. https://doi.org/10.1007/s13394-022-00431-z

Post, M., & Prediger, S. (2024b). Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information. Mathematics Education Research Journal, 36(1), 97–129. https://doi.org/10.1007/s13394-022-00431-z

Rahmawati, D., & Anwar, R. B. (2020). Translation of mathematical representation: characteristics of verbal representation unpacking. Journal of Education and Learning (EduLearn), 14(2), 162–167. https://doi.org/10.11591/edulearn.v14i2.9538

Ridho, M. H. (2023). Analysis of Students ’ Mathematical Representation Ability on Phythagoras Theorem in Junior High School. 11–23.

Soneira, C. (2022). The Use of representations when solving algebra word problems and the sources of solution errors. International Journal of Science and Mathematics Education, 20(5), 1037–1056. https://doi.org/10.1007/s10763-021-10181-2

Unaenah, E., Anggraini, I. A., Aprianti, I., Aini, W. N., Utami, D. C., Khoiriah, S., Refando, A., & Tangerang, U. M. (2020). Teori Van Hiele Dalam Pembelajaran Bangun Datar. Jurnal Pendidikan Dan Ilmu Sosial, 2(2), 365–374. https://ejournal.stitpn.ac.id/index.php/nusantara

Utomo, D. P., & Syarifah, D. L. (2021). Examining mathematical representation to solve problems in trends in mathematics and science study: Voices from Indonesian secondary school students. International Journal of Education in Mathematics, Science and Technology, 9(3), 540–556. https://doi.org/10.46328/IJEMST.1685

Yakar, E. A., & Yilmaz, S. (2022). Mathematical thinking processes for the pythagorean theorem of the secondary school students 1. 3(2), 87–99.

Yaniawati, P., Maat, S. M., Supianti, I. I., & Fisher, D. (2022). The Role of visual representations in geometry learning. European Journal of Educational Research, 11(1), 69–81. https://pdf.eu-jer.com/EU-JER_9_1_395.pdf

Zhao, F. F., Chau, L., & Schuchardt, A. (2021). Blended and more: instructors organize sensemaking opportunities for mathematical equations in different ways when teaching the same scientific phenomenon. International Journal of STEM Education, 8(1), 26. https://doi.org/10.1186/s40594-021-00280-5.

Downloads

Published

2024-09-20

Issue

Section

Articles