Guided Discovery Learning to Improve Students' Mathematics Representation and Collaboration at Senior High School 6 Yogyakarta

Retno Hertanti, Kamilah Rohadatul Azizah, Putu Purnama Sari, Margaretha Madha Melissa


Classroom Action Research aimed to assess the mathematical representation ability and collaboration in understanding circle material by implementing the guided discovery learning model. The data collection took place in April 2023 at SHS 6 Yogyakarta, involving 35 students from XI science. The research comprised two cycles, with a diagnostic test conducted in the first cycle focusing on the equation of a circle, particularly the position of points and lines related to the circle. In the second cycle, the diagnostic test concentrated on tangents to the circle. Data were gathered through tests, interviews, and questionnaires. The findings indicated that guided discovery learning effectively enhances both mathematical representation ability and collaboration. The average scores for the pre-cycle test were 78.87, for cycle I were 79.17, and for cycle II were 85. Moreover, the percentage of students achieving a score of 75 or higher increased from 60% in the pre-cycle to 71% in cycle I and further rose to 77% in cycle II. Regarding collaboration skills, in cycle I, 23 students were categorized as having medium-level skills, and 12 were classified as having high-level skills. In cycle II, the distribution changed with 16 students falling into the very high category, 12 in the high category, and seven in the medium category.

Full Text:



Alfieri, L. Brooks, P.J., Aldrich, N.J., & Tenenbaum, H.R. (2011). Does Discovery-Based Instruction Enhance Learning?. Journal of Educational Psychology; American Psychological Association, 103(1), 1–18.

Annajmi, A., & Afri, L.E. (2019). The Effect of Using Student Activity Sheets Based on the Guided Discovery Method on Increasing Students' Mathematical Representation Ability. Mosharafa: Journal of Mathematics Education, 8(1), 95-106.

Asri & Noer. ( 2015 ) . Guided Discovery Learning in Mathematics Learning. UNY 2015 National Seminar on Mathematics and Mathematics Education. ISBN. 978-602-73403-0-5

English, L.D., Gainsburg, J. (2016). Problem-solving in a 21st-century mathematics curriculum. In L.D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed.) (pp. 313–335). Routledge.

Firyal, AS, & Tina, SS (2022). Students' Mathematical Representation Ability between those who received Contextual Teaching and Learning and Discovery Learning. Plusminus: Journal of Mathematics Education, 2 (2), 265-274.

Lutfiadi & Zawawi. ( 2021 ) . Improving 21st Century 4C's Skills Through the Guided Discovery Learning Model. DIDACTICS , Vol 28 No 1 September 2

Kartini. ( 2009 ) . The Role of Representation in Mathematics Learning. Proceedings of the National Seminar on Mathematics and Mathematics Education. ISBN: 978-979-16353-3-2

Kurniasih, I. and Sani, B. ( 2014 ) . Successfully Implementing the 2013 Curriculum. Yogyakarta: Pena Says.

Maulyda MA. ( 2020 ) . NCTM-Based Mathematics Learning Paradigm. Purwokerto: CV. IRDH.

Masruroh, L., & Arif, S. (2021). Effectiveness of the Problem-Based Learning Model Using the Science Education for Sustainability Approach in Improving Collaboration Capabilities. Indonesian Science Tadris Journal, 1 (2), 179-188.

Mulyaningsih, S., Marlina, R., & Effendi, KNS (2020). Analysis of Junior High School Students' Mathematical Representation Ability in Solving Mathematics Problems. JKPM (journal of mathematics education studies). 6(1).

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA

Sabirin, M. (2014). Representation in Mathematics Learning. Journal of Mathematics Education at UIN Antasari Banjarmasin . 1(2).

Sinaga, GM (2016). Students' Mathematical Representation Ability Judging from Learning Style in Quadratic Function Material in High School. Journal of equatorial education and learning. 5(6).

NCTM. (2000). Principles and standards for school mathematics.

Pardede, E. (2015). Effect of Collaboration-Based Guided Discovery Learning Model with Flash Media on Science Process Skills and High-Level Physics Cognitive Learning Outcomes for High School Students (Doctoral dissertation, UNIMED).

Putri, Noer, & Gunowibowo. ( 2017 ) . The Influence of the Guided Discovery Learning Model on Mathematical Representation Ability and Self Confidence. FKIP Unila Mathematics Education Study Program.

Ramziah, S. (2016). Improving the Mathematical Representation Ability of Class X2 Students at SMAN 1 Meneng Building Using Matrix Teaching Materials Based on a Scientific Approach. Mosharafa: Journal of Mathematics Education, 5(2), 138-147.

Saeful, KSA (2022). Increasing Collaboration and Communication Abilities of Class VII Students through the Jigsaw Technique Cooperative Learning Model. Teacher Expert Journal, 2 (2), 189-195.

Shieh, C. J., & Yu, L. A. (2016). Study on Information Technology Integrated Guided Discovery Instruction toward Students Learning Achievement and Learning Retention. Eurasian Journal of Mathematics, Science & Technology Education, 12(4), 833-842.

Simamora, RR, Saragih , S , and Hasratuddin . (2019). Improving Students' Mathematical Problem Solving Ability and Self-Efficacy through Guided Discovery Learning in Local Culture Context. International Electronic Journal Of Mathematics Education. 14(1)

Simangunsong, D. (2022). Literature Study Analysis of Students' Mathematical Representation Ability Using the Discovery Learning Learning Model. Fibonacci Journal: Journal of Mathematics Education, 3 (2), 8-15.

Villegas, J. L., Castro, E., & Gutierrez, J. (2009). Representation in Problem Solving: a case study with optimization problems. Electronic Journal of Research in Educational Psychology, 7(1), 279–308.

Yang, E.F.Y., Liao, C.C.Y., Ching, E., Chang, T., & Chan, T.W. (2010). The Effectiveness of Inductive Discovery Learning in 1:1 Mathematics Classroom. Proceedings of the 18th International Conference on Computers in Education. Putrajaya, Malaysia: Asia-Pacific Society for Computers in Education, 743– 747.

Yenni & Sukmawati, R. (2020). Analysis of Students' Mathematical Representation Ability Based on Learning Motivation. Mosharafa: journal of mathematics education. 9(2).

Yerizon, Putra, AA, & Subhan, M. (2018). Mathematics Learning Instructional Development based on Discovery Learning for Students with Intrapersonal and Interpersonal Intelligence (Preliminary Research Stage). International Electronic Journal of Mathematics Education, 13(3), 97- 101.



  • There are currently no refbacks.

Copyright (c) 2023 Retno Hertanti, Kamilah Rohadatul Azizah, Putu Purnama Sari, Margaretha Madha Melissa

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons - Attribution-NonCommercial-ShareAlike 4.0 International License.

Jurnal Kontinu diterbitkan oleh Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidkan (FKIP), Universitas Islam Sultan Agung (Unissula).

Contact us: GKB Lantai 2, FKIP Unissula Jl. Raya Kaligawe Km.4 Terboyo Kulon, Genuk, Semarang 50112. Email: