Designing a Hypothetical Learning Trajectory Based on Investigative Learning

Charina Ulfa; Ariyadi Wijaya; Habibullah Habibullah

doi:10.24235/eduma.v10i1.8024

Designing a Hypothetical Learning Trajectory Based on Investigative Learning

Charina Ulfa⁽¹⁾, Ariyadi Wijaya⁽²⁾, Habibullah Habibullah^(3*),

(1) Universitas Negeri Yogyakarta
(2) Universitas Negeri Yogyakarta
(3) Universitas Negeri Yogyakarta
(*) Corresponding Author

Abstract

This research is a design research that aims to design a hypothetical learning trajectory based on investigative learning. This studyâ€™s subjects were students of class VII in a junior high school in Aceh Barat Daya, consisting of 32 students for the pilot experiment and 31 students for the teaching experiment. The selection of research subjects for these two classes used a random sampling technique. The data collection technique were carried out by observation, interview, and documentation. The research data were analyzed using qualitative analysis. This design research model consists of three stages: preparing for the experiment, experimental design, and retrospective analysis. The results showed that the hypothetical learning trajectory based on group investigative learning that has been designed can help students achieve learning goals. The learning trajectories produced in this study are (1) students can find the size of the object on the two sketchs by measuring and making comparisons of the two sketchs object values (the same amount); (2) students can find the form of the ratio from the size of the two sketchs and students can draw the conclusion that from the ratio value can be obtained the scale value; (3) students can determine the ratio of two different quantities of the investigative activity carried out and can write a form of direct proportion; and (4) students can distinguish the form of direct proportion and inverse proportion problemsÂ

Keywords

Hypothetical Learning; Trajectory; Investigative Learning

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References

Al-Tabany, T. I. B. (2014). Mendesain Model Pembelajaran Inovatif, Progresif, dan Kontekstual: Konsep, landasan, dan implementasinya pada kurikulum 2013 (kurikulum tematik integratif/KTI). (T. T. T. Trianto, Ed.). Jakarta: Kencana.

Andrews-larson, C., Wawro, M., & Zandieh, M. (2017). A hypothetical learning trajectory for conceptualizing matrices as linear transformations. International Journal of Mtahematical Educationin Science and Technology, 48(6), 809â€“829. https://doi.org/10.1080/0020739X.2016.1276225

Benson, S., Addington, S., Arshavsky, N., Cuoco, A., Goldenberg, E. P., & Karnowski, E. (2006). Ways to Think About Mathematics: Activities and Investigations for Grade 6-12 Teachers. California: Corwin Press.

Clements, D. H., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6(2), 81â€“89. https://doi.org/10.1207/s15327833mtl0602

Clements, D. H., & Sarama, J. (2014). Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed.). New York: Routledge.

Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: a framework for connecting standards with curriculum. ZDM Mathematics Education, 46(5), 719â€“733. https://doi.org/10.1007/s11858-014-0598-7

Elizondo-rami, B. R., & Hemandez-solis, A. (2016). Hypothetical learning trajectories that use digital technology to tackle an optimization problem. International Journal of Technology in Mathematics Education, 24(2), 51â€“57. https://doi.org/10.1564/tme

Fuadiah, N. F. (2015). Hypothetical learning trajectory dan peranannya dalam perencanaan pembelajaran matematika. In Seminar Nasional Matematika dan Pembelajarannya, 382â€“387.

Kuncara, A. W., Sujadi, I., & Riyadi. (2016). Analisis proses pembelajaran matematika berdasarkan kurikulum 2013 pada materi pokok peluang kelas X SMA Negeri 1 Surakarta. Jurnal Elektronik Pembelajaran Matematika, 4(3), 352â€“365.

Plomp, T. (2013). Educational Design Research: An Introduction. (T. Plomp & N. Nieveen, Eds.). Netherlands: Netherlands Institute for Curriculum Development (SLO).

Risdiyanti, I., & Prahmana, R. C. I. (2020). Etnomathematics Teori dan Implementasinya : Suatu Pengantar. Yogyakarta: UAD Press.

Sharan, S., Sharan, Y., & Tan, I. G.-C. (2013). The group investigation approach to cooperative learning. In C. E. Hmelo-silver, C. A. Chinn, C. K. K. Chan, & A. M. O. Donnell (Eds.), The international handbook of collaborative learning to cooperative learning (pp. 351â€“369). Routledge. https://doi.org/10.4324/9780203837290.ch20

Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91â€“104. https://doi.org/10.1207/s15327833mtl0602_2

Steffe, L. P. (2009). On the construction of learning trajectories of children: the case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129â€“162. https://doi.org/10.1207/s15327833mtl0602

Suherman, E., et al. (2003). Strategi Pembelajaran Matematika Kotemporer. Bandung: UPI.

Uno, H. B., & Mohamad, N. (2013). Belajar dengan Pendekatan PAILKEM: Pembelajaran Aktif, Inovatif, Lingkungan, kreatif, Efektif, Menarik (4th ed.). Jakarta: PT Bumi Aksara.

Wijaya, A. (2008). Design Research in Mathematics Education : Utrecht Universiteit.

Wijaya, A., Doorman, L. M., & Keijze, R. (2011). Emergent modelling: from traditional Indonesian games to a standard unit of measurement. Journal of Science and Mathematics Education in Southeast Asia, 34(2), 149â€“173.

Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: supporting teachersâ€™ understandings of studentsâ€™ mathematical thinking. Journal of Mathematical Behavior, 32(2), 103â€“121. https://doi.org/10.1016/j.jmathb.2012.12.003

DOI: 10.24235/eduma.v10i1.8024

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