The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research

Mochamad Guntur; Siti Sahronih; Nur Indah Septia Ningsih; Puja Windari

doi:10.17275/per.23.90.10.6

EN

The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research

Abstract

This study aims to determine the trajectory of students' thinking when solving proportion problems using STEM-based learning media. The participants were 27 fifth-grade students from SD Negeri 2 Pilangsari in Cirebon Regency. The students are divided into four groups using purposive sampling and receive the same treatment. The treatment involved a proportion study that utilized STEM media, and the student’s learning trajectory was monitored based on their problem-solving patterns. Hypothetical Learning Trajectory (HLT) was used to develop the hypotheses. The HLT was used as a guide for the researchers' assumptions. The data were collected through observation by researchers, student work, and documentation. The results of the HLT were used to test the assumptions related to the student's thinking processes and their learning in completing proportion operations using STEM. Based on the results obtained during the practice, some findings exceeded the researcher's expectations and hypotheses, but some did not. These differences become a new finding expected to become a subject for further research, where several groups have different ways of thinking based on mathematical disposition. Through STEM media, the electrical engineering students' high enthusiasm and creativity can be known through the electric graph. In conclusion, proportional relationships are an important mathematical concept with practical applications in various fields. The use of STEM media for teaching materials can help students acquire a better understanding of mathematical concepts and skills.

Keywords

HLT, Learning trajectory, Mathematics, STEM, Proportion material

References

Abramovich, S., Grinshpan, A. Z., & Milligan, D. L. (2019). Teaching mathematics through concept motivation and action learning. Education Research International, 2019, 1–13. https://doi.org/10.1155/2019/3745406
Angraini, L. M. (2021). Didactical design of mathematical reasoning in mathematical basic concepts of courses. JNPM (Jurnal Nasional Pendidikan Matematika), 5(1), 1. https://doi.org/10.33603/jnpm.v5i1.3943
Anwar, L. (2023). Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof. Eurasia Journal of Mathematics, Science and Technology Education, 19(5). https://doi.org/10.29333/ejmste/13160
Ausubel, D. P. (1962). A subsumption theory of meaningful verbal learning and retention. The Journal of General Psychology, 66(2), 213–224. https://doi.org/10.1080/00221309.1962.9711837
Bahamonde, A. D. C., Fortuny Aymemí, J. M., & Gómez I Urgellés, J. V. (2017). Mathematical modelling and the learning trajectory: Tools to support the teaching of linear algebra. International Journal of Mathematical Education in Science and Technology, 48(3), 338–352. https://doi.org/10.1080/0020739X.2016.1241436
Bakker, A., & Van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education (pp. 429–466). Springer Netherlands. https://doi.org/10.1007/978-94-017-9181-6_16
Baroody, A. J. (2022). Lessons learned from 10 experiments that tested the efficacy and assumptions of hypothetical learning trajectories. Education Sciences, 12(3). https://doi.org/10.3390/educsci12030195
Brinberg, D., & McGrath, J. E. (1985). Validity and the research process. In Validity and the Research Process. Sage Publications.
Broietti, F. C. D. (2022). Hypothetical learning trajectory and understanding the content of solutions in the teaching of chemistry. Curriculo Sem Fronteiras, 22. https://doi.org/10.35786/1645-1384.v22.1810
Busch, E. L. (2023). Multi-view manifold learning of human brain-state trajectories. Nature Computational Science, 3(3), 240–253. https://doi.org/10.1038/s43588-023-00419-0

Cazares, S. I. (2019). Design and evaluation of a hypothetical learning trajectory to confidence intervals based on simulation and real data. Bolema - Mathematics Education Bulletin, 33(63), 1–26. https://doi.org/10.1590/1980-4415v33n63a01
Chen, Y. H. (2023). Manipulator trajectory optimization using reinforcement learning on a reduced-order dynamic model with deep neural network compensation. Machines, 11(3). https://doi.org/10.3390/machines11030350
Cuevas-Vallejo, A. (2023). A learning trajectory for university students regarding the concept of vector. Journal of Mathematical Behavior, 70. https://doi.org/10.1016/j.jmathb.2023.101044
Demetriou, A. (2023). A deep learning framework for generation and analysis of driving scenario trajectories. SN Computer Science, 4(3). https://doi.org/10.1007/s42979-023-01714-3
Dhuheir, M. A. (2023). Deep reinforcement learning for trajectory path planning and distributed inference in resource-constrained UAV swarms. IEEE Internet of Things Journal, 10(9), 8185–8201. https://doi.org/10.1109/JIOT.2022.3231341
Feishi, G., Rongjian, H., & Lingyuan, G. (2017). Theory and development of teaching through variation in mathematics in China. In Theory and Development of Teaching through Variation in Mathematics in China (pp. 13–41). BRILL.
Ferreira, P. E. A., & Silva, K. A. P. D. (2019). Modelagem matemática e uma proposta de trajetória hipotética de aprendizagem. Bolema: Boletim de Educação Matemática, 33(65), 1233–1254. https://doi.org/10.1590/1980-4415v33n65a13
George, M., & Apter, A. J. (2004). Gaining insight into patients’ beliefs using qualitative research methodologies. Curr Opin Allergy Clin Immunol, 4(3), 185–189.
Gravemeijer, K. (1994). Developing realistic mathematics education. CD Beta Press.
Guarte, J. M., & Barrios, E. B. (2006). Estimation under purposive sampling. Communications in Statistics - Simulation and Computation, 35(2), 277–284. https://doi.org/10.1080/03610910600591610
Haggarty, L. (Ed.). (2002). Aspects of teaching secondary mathematics: Perspectives on practice. RoutledgeFalmer : Open University Press.
Huh, J. (2023). Deep learning-based autonomous excavation: a bucket-trajectory planning algorithm. IEEE Access, 11, 38047–38060. https://doi.org/10.1109/ACCESS.2023.3267120
Ivars, P. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11). https://doi.org/10.29333/ejmste/93421
Kaitera, S., & Harmoinen, S. (2022). Developing mathematical problem-solving skills in primary school by using visual representations on heuristics. LUMAT: International Journal on Math, Science and Technology Education, 10(2). https://doi.org/10.31129/LUMAT.10.2.1696
Kirk, J., & Miller, M. L. (1988). Reliability and validity in qualitative research. International Journal of Qualitative Studies in Education, 1(1).
Kolaghassi, R. (2023). Deep learning models for stable gait prediction applied to exoskeleton reference trajectories for children with cerebral palsy. IEEE Access, 11, 31962–31976. https://doi.org/10.1109/ACCESS.2023.3252916
Kuncoro, K. S., Zakkia, A., Sulistyowati, F., & Kusumaningrum, B. (2021). Students’ mathematical critical thinking based on self-esteem through problem based learning in geometry. Southeast Asian Mathematics Education Journal, 11(1), 41–52. https://doi.org/10.46517/seamej.v11i1.122
Lestari, T. V. D. (2020). Hypothetical learning trajectory and students’ understanding of the concepts of the arithmetic sequence. Journal of Physics: Conference Series, 1581(1). https://doi.org/10.1088/1742-6596/1581/1/012038
Lidinillah, D. A. M. (2011). Educational design research: A theoretical framework for action. Universitas Pendidikan Indonesia.
Luo, Q. (2023). Deep reinforcement learning based computation offloading and trajectory planning for multi-UAV cooperative target search. IEEE Journal on Selected Areas in Communications, 41(2), 504–520. https://doi.org/10.1109/JSAC.2022.3228558
Mansouri, N. (2023). Machine learning of multi-modal tumor imaging reveals trajectories of response to precision treatment. Cancers, 15(6). https://doi.org/10.3390/cancers15061751
Mattison, R. E. (2023). Longitudinal trajectories of reading and mathematics achievement for students with learning disabilities. Journal of Learning Disabilities, 56(2), 132–144. https://doi.org/10.1177/00222194221085668
Merriam, S. B. (1998). Qualitative research and case study applications in education. Jossey-Bass Publishers.
Mutaqin, E. J., Herman, T., Wahyudin, W., & Muslihah, N. N. (2023). Hypothetical learning trajectory in place value concepts in elementary school. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 125–134. https://doi.org/10.31980/mosharafa.v12i1.1313
Mаhammadovna, S. I. (2023). Features of cluster design in modern paradigms of education. TELEMATIQUE, 22(1), 348–355.
National Council of Teachers of Mathematics (NCTM)). (1989). Curriculum and evaluation standards for school mathematics: A vision of mathematical power and appreciation for all.
Nishimura, M. (2023). Viewbirdiformer: Learning to recover ground-plane crowd trajectories and ego-motion from a single ego-centric view. IEEE Robotics and Automation Letters, 8(1), 368–375. https://doi.org/10.1109/LRA.2022.3221335
Placido, D. (2023). A deep learning algorithm to predict risk of pancreatic cancer from disease trajectories. Nature Medicine, 29(5), 1113–1122. https://doi.org/10.1038/s41591-023-02332-5
Qian, Z. (2023). Reinforcement learning based dual-UAV trajectory optimization for secure communication. Electronics (Switzerland), 12(9). https://doi.org/10.3390/electronics12092008
Risdiyanti, I., & Prahmana, R. C. I. (2021). Designing learning trajectory of set through the indonesian shadow puppets and mahabharata stories. Infinity Journal, 10(2), 331. https://doi.org/10.22460/infinity.v10i2.p331-348
Rokhmawati, L. N., Ratnaningsih, N., & Ni’mah, K. (2023). Aturan penjumlahan dan perkalian dalam kaidah pencacahan: bagaimanakah desain hypothetical learning trajectory berbasis RME? Jurnal Pembelajaran Matematika Inovatif, 6(3), 937–950. https://doi.org/10.22460/jpmi.v6i3.17321
Siemon, D., Barkatsas, T., & Seah, R. (2019). Researching and Using Progressions (Trajectories) in Mathematics Education. BRILL. https://doi.org/10.1163/9789004396449
Silverman, D. (2009). Doing qualitative research (3rd ed.). SAGE Publications Ltd.
Simon, M. A. (2018). Empirically-based hypothetical learning trajectories for fraction concepts: Products of the Learning Through Activity research program. Journal of Mathematical Behavior, 52, 188–200. https://doi.org/10.1016/j.jmathb.2018.03.003
Sukestiyarno, Y. L. (2023). Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability. Eurasia Journal of Mathematics, Science and Technology Education, 19(6). https://doi.org/10.29333/ejmste/13269
Supply, A.-S., Vanluydt, E., Van Dooren, W., & Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educational Studies in Mathematics, 113(3), 371–388. https://doi.org/10.1007/s10649-023-10212-5
Tordesillas, J. (2023). Deep-PANTHER: Learning-based perception-aware trajectory planner in dynamic environments. IEEE Robotics and Automation Letters, 8(3), 1399–1406. https://doi.org/10.1109/LRA.2023.3235678
Tykhonov, A. (2023). A deep learning method for the trajectory reconstruction of cosmic rays with the DAMPE mission. Astroparticle Physics, 146. https://doi.org/10.1016/j.astropartphys.2022.102795
Ulfa, C., & Wijaya, A. (2019). Expanding hypothetical learning trajectory in mathematics instructional. Journal of Physics: Conference Series, 1320(1), 012091. https://doi.org/10.1088/1742-6596/1320/1/012091
Wang, X. (2023). A deep learning model for ship trajectory prediction using automatic identification system (AIS) data. Information (Switzerland), 14(4). https://doi.org/10.3390/info14040212
Wijaya, A., Elmaini, E., & Doorman, M. (2021). A learning trajectory for probability: a case of game-based learning. Journal on Mathematics Education, 12(1), 1–16. https://doi.org/10.22342/jme.12.1.12836.1-16
Yuan, Z. (2023). Hierarchical trajectory planning for narrow-space automated parking with deep reinforcement learning: A federated learning scheme. Sensors, 23(8). https://doi.org/10.3390/s23084087
Yuliardi, R., & Rosjanuardi, R. (2021). Hypothetical learning trajectory in student’s spatial abilities to learn geometric transformation. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 174–190. https://doi.org/10.23917/jramathedu.v6i3.13338
Zhan, T. (2023). VRR-Net: Learning vehicle–road relationships for vehicle trajectory prediction on highways. Mathematics, 11(6). https://doi.org/10.3390/math11061293
Ziyi, Z. (2023). Multi-agent deep-learning based comparative analysis of team sport trajectories. IEEE Access, 11, 43305–43315. https://doi.org/10.1109/ACCESS.2023.3269287
Zou, Y. (2023). A learning trajectory planning for vibration suppression of industrial robot. Industrial Robot. https://doi.org/10.1108/IR-02-2023-0013

Details

Primary Language

English

Subjects

Educational Psychology

Journal Section

Research Article

Authors

Mochamad Guntur ^*
0000-0001-6226-7999
Indonesia

Siti Sahronih
0000-0003-2512-0626
Indonesia

Nur Indah Septia Ningsih
0000-0002-8271-6728
Indonesia

Puja Windari
0009-0003-4957-9957
Indonesia

Early Pub Date

November 2, 2023

Publication Date

November 1, 2023

Submission Date

July 3, 2023

Acceptance Date

September 11, 2023

Published in Issue

Year 2023 Volume: 10 Number: 6

DOI

https://doi.org/10.17275/per.23.90.10.6

IZ

https://izlik.org/JA64MW88UE

APA

Guntur, M., Sahronih, S., Ningsih, N. I. S., & Windari, P. (2023). The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research. Participatory Educational Research, 10(6), 84-103. https://doi.org/10.17275/per.23.90.10.6

AMA

1.Guntur M, Sahronih S, Ningsih NIS, Windari P. The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research. PER. 2023;10(6):84-103. doi:10.17275/per.23.90.10.6

Chicago

Guntur, Mochamad, Siti Sahronih, Nur Indah Septia Ningsih, and Puja Windari. 2023. “The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research”. Participatory Educational Research 10 (6): 84-103. https://doi.org/10.17275/per.23.90.10.6.

EndNote

Guntur M, Sahronih S, Ningsih NIS, Windari P (November 1, 2023) The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research. Participatory Educational Research 10 6 84–103.

IEEE

[1]M. Guntur, S. Sahronih, N. I. S. Ningsih, and P. Windari, “The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research”, PER, vol. 10, no. 6, pp. 84–103, Nov. 2023, doi: 10.17275/per.23.90.10.6.

ISNAD

Guntur, Mochamad - Sahronih, Siti - Ningsih, Nur Indah Septia - Windari, Puja. “The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research”. Participatory Educational Research 10/6 (November 1, 2023): 84-103. https://doi.org/10.17275/per.23.90.10.6.

JAMA

1.Guntur M, Sahronih S, Ningsih NIS, Windari P. The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research. PER. 2023;10:84–103.

MLA

Guntur, Mochamad, et al. “The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research”. Participatory Educational Research, vol. 10, no. 6, Nov. 2023, pp. 84-103, doi:10.17275/per.23.90.10.6.

Vancouver

1.Mochamad Guntur, Siti Sahronih, Nur Indah Septia Ningsih, Puja Windari. The Learning Trajectory Based on STEM of Elementary School Pupils’ in Solving Proportion Material: Didactical Design-Research. PER. 2023 Nov. 1;10(6):84-103. doi:10.17275/per.23.90.10.6