Hypothetical learning trajectory (HLT) for proof logic topics on algebra course: What’re the experts think about?

https://doi.org/10.24042/ajpm.v11i1.6204

Riza Agustiani, Rahmat Nursalim

Abstract


Proof has a role in the formation and development of mathematics in the history of mathematics. The ability to construct proof is one indicator of mathematical reasoning which is an important component of mathematics learning outcomes, especially in Algebra. This qualitative research aims to describe the design process of the Hypothetical Learning Trajectory for Proof Logic Topics. This research is based on design research. This research consists of three stages: preparing for the experiment, the design experiment, and the retrospective analysis. Data collection techniques in this research are walkthrough and interview. The walkthrough and interview were conducted in the first stage of design research (preparing the experiment) with two activities: expert review and reader proof to collect materials to revise the HLT. Four experts participated in the expert review. The experts are chosen based on the experience, both research experience, and teaching experience. The result of this research is the design of HLT for proof logic topics consist of four activities: reading proof, completing proof, examining proof, and Constructing proof. The four activities were well-done on the design experiment stage.

 


Keywords


Algebra; Hypothetical Learning Trajectory; Proof Logic.

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References


Adams, N. E. (2015). Bloom’s taxonomy of cognitive learning objectives. Journal of the Medical Library Association: JMLA, 103(3), 152.

Agustiani, R. (2015). Profil pengetahuan pedagogik konten mahasiswa calon guru matematika dalam melaksanakan pembelajaran dengan pendekatan PMRI. Jurnal Pendidikan Matematika RAFA, 1(2), 288–305.

Andrews-Larson, C., Wawro, M., & Zandieh, M. (2017). A hypothetical learning trajectory for conceptualizing matrices as linear transformations. International Journal of Mathematical Education in Science and Technology, 48(6), 809–829.

Andriani, P. (2015). Penalaran Aljabar dalam Pembelajaran Matematika. Beta: Jurnal Tadris Matematika, 8(1), 1–13.

Armstrong, P. (2016). Bloom’s taxonomy. Vanderbilt University Center for Teaching.

Arnawa, I. M. (2010). Mengembangkan Kemampuan Mahasiswa dalam Memvalidasi Bukti pada Aljabar Abstrak melalui Pembelajaran Berdasarkan Teori APOS. Jurnal Matematika Dan Sains, 14(2), 62–68.

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS theory. A Framework for Research and Curriculum Development in Mathematics Education, 5–15.

García-Martínez, I., & Parraguez, M. (2017). The basis step in the construction of the principle of mathematical induction based on APOS theory. The Journal of Mathematical Behavior, 46, 128–143.

Gravemeijer, K. (2016). Design-research-based curriculum innovation. Quadrante, 25(2), 7–23.

Güler, G. (2016). The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views. Higher Education Studies, 6(1), 145–158.

Hanna, G., & Villiers, M. de. (2012). Proof and Proving in Mathematics Education: The 19th ICMI Study. Springer Science & Business Media.

Hasan, B. (2016). Proses Berpikir Mahasiswa dalam Mengkonstruksi Bukti Menggunakan Induksi Matematika Berdasarkanteori Pemerosesan Informasi. APOTEMA: Jurnal Program Studi Pendidikan Matematika, 2(1), 33–40.

Merta Dhewa, K., Rosidin, U., Abdurrahman, A., & Suyatna, A. (2017). The development of Higher Order Thinking Skill (Hots) instrument assessment in physics study. IOSR Journal of Research & Method in Education (IOSR-JRME), 7(1), 26–32.

Ozdemir, A. S., Goktepe, S., & Kepceoglu, I. (2012). Using mathematics history to strengthen geometric proof skills. Procedia-Social and Behavioral Sciences, 46, 1177–1181.

Prahmana, R. C. I. (2017). Design research (Teori dan implementasinya: Suatu pengantar). Rajawali Pers.

Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM, 47(6), 877–891.

Sidharta, B. A., & Gunarsa, A. (2016). Pengantar logika: Sebuah langkah pertama pengenalan medan telaah. Refika Aditama.

Sopamena, P. (2017). Karakteristik Proses Berpikir Mahasiswa dalam Mengonstruksi Bukti Keterbagian. Matematika Dan Pembelajaran, 5(2), 169–192.

Suandito, B. (2017). Bukti Informal dalam Pembelajaran Matematika. Al-Jabar: Jurnal Pendidikan Matematika, 8(1), 13–24.

Wright, V. (2014). Towards a hypothetical learning trajectory for rational number. Mathematics Education Research Journal, 26(3), 635–657.

Yudhanegara, M. R., & Lestari, K. E. (2017). How to Develop Students’ Experience on Mathematical Proof in Group Theory Course by Conditioning-Reinforcement-Scaffolding. 5th SEA-DR (South East Asia Development Research) International Conference 2017 (SEADRIC 2017).




DOI: https://doi.org/10.24042/ajpm.v11i1.6204

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Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.