Analyzing junior high school students' mathematical reasoning in problem-solving: A focus on the Treffinger-oriented learning approach

Defi Fatikhatul Hidayah, Slamet Hw

Abstract


Mathematical reasoning is a fundamental ability that helps students solve various problems. This study aims to analyze students' mathematical reasoning in solving word problems using the Treffinger approach. This qualitative research with a phenomenological design involves researchers as the main instrument and uses mathematical reasoning tests and interview guides. The results showed that students tend to reread problems and annotate them before presenting mathematical ideas, indicating the positive influence of the Treffinger approach. Students use scratch sheets to justify answers and check the validity of their problem-solving steps, although some students still make mistakes in previous stages. The results show that the Treffinger approach encourages students' reasoning abilities in solving problems, from presenting the problem to checking the validity of the answer. However, students' understanding of mathematical concepts is also essential in problem-solving. This research implies an alternative solution for teachers to improve students' mathematical reasoning abilities through classroom learning.

Keywords


mathematical reasoning, mathematical story problems, problem-solving, Treffinger

Full Text:

PDF

References


A. R. Simangunsong and E. M. Panggabean, “Konektivitas belajar himpunan matematika dengan aljabar abstrak,” J. Penelitian, Pendidik. dan Pengajaran JPPP, vol. 4, no. 2, pp. 85–90, 2023, doi: 10.30596/jppp.v4i2.14892.

S. Sachdeva and P.-O. Eggen, “Students’ Critical thinking about learning mathematics,” Int. Electron. J. Math. Educ., vol. 16, no. 3, pp. 1–18, 2021, doi: 10.29333/iejme/11003.

L. Fajriyah, Y. Nugraha, P. Akbar, and M. Bernard, “Pengaruh kemandirian belajar siswa SMP terhadap kemampuan penalaran matematis,” J. Educ., vol. 01, no. 02, pp. 288–296, 2019.

A. Mulyana and U. Sumarmo, “Meningkatkan kemampuan penalaran matematik dan kemandirian belajar siswa SMP melalui pembelajaran berbasis masalah,” Didaktik, vol. 9, no. 1, pp. 40–51, 2015.

D. R. Arifanti, “Mathematical reasoning in problem-solving in three dimensions,” J. Phys. Conf. Ser., 2020, pp. 1–7, doi: 10.1088/1742-6596/1613/1/012077.

S. I. Hasanah, C. F. Tafrilyanto, and Y. Aini, “Mathematical reasoning: The characteristics of students’ mathematical abilities in problem solving,” in Journal of Physics: Conference Series, 2019, pp. 1-8, doi : 10.1088/17426596/1188/1/012057.

E. A. Akinmola, “Developing mathematical problem solving ability : A panacea for a sustainable development in the 21st century by science and technical education department ,” Int. J. Educ. Researc, vol. 2, no. 2, pp. 1–8, 2014.

D. Setialesmana, A. Sunendar, and L. Katresna, “Analysis of students mathematics reasoning ability in view of mathematical problem solving ability,” J. Phys. Conf. Ser., vol. 1764, 2021, pp. 1–6, doi: 10.1088/1742-6596/1764/1/012123.

R. Reski, N. Hutapea, and S. Saragih, “Peranan model problem based learning (PBL) terhadap kemampuan pemecahan masalah matematis dan kemandirian belajar siswa,” JURING (Journal Res. Math. Learn)., vol. 2, no. 1, p. 049, 2019, doi: 10.24014/juring.v2i1.5360.

S. F. Akuba, D. Purnamasari, and R. Firdaus, “Pengaruh kemampuan penalaran, efikasi diri dan kemampuan memecahkan masalah terhadap penguasaan konsep matematika,” JNPM (Jurnal Nas. Pendidik. Mat., vol. 4, no. 1, p. 44, 2020, doi: 10.33603/jnpm.v4i1.2827.

A. A. Rizqi, “Kemampuan komunikasi matematis siswa melalui blended learning berbasis pemecahan masalah,” Prism. Pros. Semin. Nas. Mat., vol. 1, no. 1, pp. 191–202, 2016.

W. Suana, M. Raviany, and F. Sesunan, “Blended learning berbantuan whatsapp: pengaruhnya terhadap kemampuan berpikir kritis dan kemampuan pemecahan masalah,” Gravity J. Ilm. Penelit. dan Pembelajaran Fis., vol. 5, no. 2, 2019.

A. Astuti, “Peran kemampuan komunikasi matematika terhadap prestasi belajar matematika siswa,” J. Form., vol. 2, no. 2, pp. 102–110, 2012, doi: 10.30998/formatif.v2i2.91.

N. Afiani, “Pengaruh kemampuan komunikasi matematis dan kemandirian belajar terhadap prestasi belajar matematika,” JKPM (Jurnal Kaji. Pendidik. Mat., vol. 2, no. 1, pp. 1–13, 2017.

K. Gafoor and A. Kurukkan, “Why High School Students Feel Mathematics Difficult? An Exploration of Affective Beliefs,” in UGC Spons. Natl. Semin. Pedagog. Teach. Educ. Trends Challenges, Kerala, India, Agust. 18-19, 2015, pp. 1–6.

L. N. Safrida, A. R. As’ari, and S. Sisworo, “Pengembangan perangkat pembelajaran berbasis problem solving polya untuk meningkatkan kemampuan penalaran matematis siswa materi peluang kelas XI SMA,” J. Pendidik. - Teor. Penelitian, dan pengemb., vol. 1, no. 4, pp. 583–591, 2016.

M. Munasiah, “Pengaruh kecemasan belajar dan pemahaman konsep matematika siswa terhadap kemampuan penalaran matematika,” Form. J. Ilm. Pendidik. MIPA, vol. 5, no. 3, pp. 220–232, 2016, doi: 10.30998/formatif.v5i3.649.

S. Ndiung, Sariyasa, E. Jehadus, and R. A. Apsari, “The effect of treffinger creative learning model with the use rme principles on creative thinking skill and mathematics learning outcome,” Int. J. Instr., vol. 14, no. 2, pp. 873–888, 2021, doi: 10.29333/iji.2021.14249a.

J. W. Kusuma, U. Jefri, A. Hidayat, and H. Hamidah, “Application of treffinger learning model to improve creative reasoning and mathematical problem solving skills as well as student learning interests,” JTAM (Jurnal Teor. dan Apl. Mat., vol. 4, no. 2, p. 204, 2020, doi: 10.31764/jtam.v4i2.2840.

C. D. Rosita, “Kemampuan penalaran dan komunikasi matematis : apa, mengapa, dan bagaimana ditingkatkan pada mahasiswa,” Euclid, vol. 1, no. 1, pp. 33–46, 2014, doi: 10.33603/e.v1i1.342.

Eka Rusmianingrum and R. Setyaningsih, “Analysis of students’ mathematical reasoning in solving story problems based on gender at SMPN 4 Kongbeng,” AIP Confrence Proceeding, 2023, pp. 1–10, doi: 10.1063/5.0154697.

R. Febriandi, T. Herman, Z. Abidin, and F. Laely, “Analysis of Mathematical Reasoning Ability and Mathematical Creative Thinking Elementary School Students in Solving Story Problems,” Int. Conf. on Elementary Educ., pp. 660–671, 2022.

R. Sagala, P. Nuangchalerm, A. Saregar, and R. A. Z. El Islami, “Environment-friendly education as a solution to against global warming: A case study at Sekolah Alam Lampung, Indonesia,” J. Educ. Gift. Young Sci., vol. 7, no. 2, pp. 85–97, 2019, doi: 10.17478/jegys.565454.

J. W. Creswell, Educational research - planning, conducting, and evaluating quantitative and qualitative research. Boston : Pearson, 2015.

Hendriana, Heris, E. E. Rohaeti, and U. Sumarmo, The role of problem-based learning to improve students’ mathematical problem-solving ability and self confidence. Bandung: Refika Aditama, 2017.

M. Miles, M. B., & Huberman, Qualitative Data Analysis Second Edition. Thousand Oaks : SAGE Publ., 1994.

M. Coccia, “New perspectives in innovation failure analysis: a taxonomy of general errors and strategic management for reducing risks,” Technol. Soc., vol. 75, no. 1, pp. 1–13, 2023, doi: 10.1016/j.techsoc.2023.102384.

D. Niemi, “Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explanations,” J. Educ. Res., vol. 89, no. 6, pp. 351–363, 1996, doi: 10.1080/00220671.1996.9941339.

D. Saxton, P. Kohli, E. Grefenstette, and F. Hill, “Analysing mathematical reasoning abilities of neural models,” 7th Int. Conf. Learn. Represent. ICLR 2019, 2019, pp. 1–17, doi: 10.48550/arXiv.1904.01557.

R. Handayani, Hajidin, M. Duskri, and E. Maidiyah, “Development of learning tools using treffinger learning model to improve creative thinking,” J. Phys. Conf. 2018, pp. 1–8, doi: 10.1088/1742-6596/1088/1/012090.

Y. Irna, S. 1, S. Budi Waluya, and & Dwijanto, “Creative mathematical thinking ability viewed from the student learning styles in treffinger model article info,” J. Prim. Educ., vol. 9, no. 3, pp. 269–275, 2020.

Barnett-Clarke, W. F. C., R. Marks, and S. Ross, Rational numbers: Developing essential understanding of rational numbers for teaching mathematics in grades 3-5:. Reston VA: NCTM, 2010.

D. J. Treffi, “Creative Problem Solving (CPS): Powerful tools for managing change and developing talent,” Gift. Talent. Int., vol. 22, no. 2, pp. 1–20, 2007, doi: 10.1080/15332276.2007.11673491.

NCTM, Principles and Standards of School Mathematics. Reston, VA, USA, 2000.

M. Afnanda, “Menelaah Kembali teori belajar dan gaya belajar,” Qual. Res. Educ. Psychol., vol. 1, no. 01, pp. 12–22, 2023.

T. Häkkinen and K. Mäkelä, “Environmental adaption of concrete : Environmental impact of concrete and asphalt pavements,” VTT Tied. - Valt. Tek. Tutkimusk., vol. 8, no. 1752, pp. 172–181, 1996, doi: 10.1187/cbe.08.

L. H. Muhaimin, R. A. Sholikhakh, and S. Yulianti, “Unlocking the secrets of students ’ mathematical literacy to solve mathematical problems : A systematic literature review,” Eurasia J. Math. Sci. Technol. Educ., vol. 20, no. 4, pp. 1–15, 2024, doi: 10.29333/ejmste/14404.

I. Cahya and A. Warmi, “Analisis tingkat kemampuan penalaran matematis siswa smp pada materi relasi dan fungsi,” Pros. Semin. Nas. Mat. dan Pendidik. Mat. Sesiomadika, pp. 602–609, 2019.




DOI: http://dx.doi.org/10.24042/ijsme.v7i2.22207

Refbacks

  • There are currently no refbacks.




Copyright (c) 2024 Unit Riset dan Publikasi Ilmiah FTK UIN Raden Intan Lampung

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

Creative Commons License

Indonesian Journal of Science and Mathematics Education is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License