Thinking Process of Secondary Level Students in Constructing Proof by Mathematical Induction in Terms of Their Attitude toward Mathematics
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Keywords

Mathematical Induction
Proof
Thinking Process
Attitude toward Mathematics

How to Cite

Laili, N., & Siswono, T. (2021). Thinking Process of Secondary Level Students in Constructing Proof by Mathematical Induction in Terms of Their Attitude toward Mathematics. Jurnal Tadris Matematika, 4(1), 121-138. https://doi.org/10.21274/jtm.2021.4.1.121-138

Abstract

This research aims to describe secondary-level students' thinking processes in terms of their attitude toward mathematics in constructing proof by mathematical induction. This qualitative research involved two students who were selected from 30 students of  second grade of senior high school that categorized into two groups, namely the students who have a positive and negative attitude toward mathematics by using Attitude Toward Mathematics Inventory (ATMI) questionnaire. One student from each category was selected to be given a proving test and interviewed. Students’ process of proving test and interview recording were collected and analyzed to identify their thinking process. This research points out that both students who have positive and negative attitudes towards mathematics can recall the information in their memory regarding the characteristics and steps to prove using mathematical induction. However, the student who has negative attitudes towards mathematics tends to experience some difficulties in processing information, especially in the induction step, caused by panic, depression, and insecurity. The student who has a positive attitude towards mathematics also experiences some difficulties in the proving process, namely understanding what to prove and compiling the induction steps. However, she keeps trying and believes that she would be able to solve it. Hence, she can solve the proof completely.

https://doi.org/10.21274/jtm.2021.4.1.121-138
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References

Adinata, Y. C., Budiyono, B., & Indriati, D. (2020). Misconceptions in mathematical induction for eleventh-grade students – HOTS categorized items Misconceptions in mathematical induction for eleventh-grade students – HOTS categorized items. J. Phys.: Conf. Ser. 1469 012153. https://doi.org/10.1088/1742-6596/1469/1/012153

Ahmadi, Y., Kusumah, Y. S., & Jupri, A. (2019). Analysis of high school students’ errors in mathematical proving : the case of mathematical induction. J. Phys.: Conf. Ser. 1211 012068, 1–7. https://doi.org/10.1088/1742-6596/1211/1/012068

Akin, A., & Kurbanoglu, I. N. (2011). The Relationship between math anxiety, math attitudes, and self-efficacy: A structural equation model. Studia Psychologica, 53(3), 263–273. https://arts.units.it/handle/11368/2942931

Ashkenazi, Y., & Itzkovitch, E. (2014). Proof by mathematical induction. International Journal of Innovation and Research in Educational Sciences, 1(3), 186–190. http://www.ijires.org/administrator/components/com_jresearch/files/publications/IJIRES_86_Final.pdf

Çiftçi, K., & Yildiz, P. (2019). The effect of self-confidence on mathematics achievement: The meta-analysis of Trends in International Mathematics and Science Study (TIMSS). International Journal of Instruction, 12(2), 683–694. https://doi.org/10.29333/iji.2019.12243a

Cooper, A. A. (2019). Understanding mathematical induction by writing analogies. Prompt: A Journal of Academic Writing Assignment, 3(2), 14–24. http://thepromptjournal.com/index.php/prompt/article/view/38

Cyr, S. (2011). Development of beginning skills in proving and proof writing by elementary school students. Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education, 1–10. http://lettredelapreuve.org/pdf/CERME7/Cerme7_WG1_Cyr.pdf

Doruk, M. (2019). Preservice mathematics teachers’ determination skills of proof techniques: The case of integers. International Journal of Education in Mathematics Science and Technology, 7(4), 335–348. https://www.ijemst.net/index.php/ijemst/article/view/729

Fauziyah, N. (2020). Proses kognisi siswa Autism Spectrum Disorder (ASD) tingkat SMA dalam menyelesaikan masalah matematika berdasarkan perbedaan tingkat inteligensi. Universitas Negeri Surabaya.

Furinghetti, F., & Morselli, F. (2009). Every unsuccessful problem solver is unsuccessful in his or her own way : affective and cognitive factors in proving. Educ Stud Math, 70, 71–90. https://doi.org/10.1007/s10649-008-9134-4

Güler, G. (2016). The difficulties experienced in teaching proof to prospective mathematics teachers: Academician views. Higher Education Studies, 6(1), 145–158. https://doi.org/10.5539/hes.v6n1p145

Hannula, M. S. (2002). Attitude towards mathematics: Emotions, expectations and values. Educational Studies in Mathematics, 49(1), 25–46. https://link.springer.com/article/10.1023/A:1016048823497

Hasan, B. (2016). Proses berpikir mahasiswa dalam mengkonstruksi bukti menggunakan induksi matematika berdasarkan teori pemerosesan informasi. APOTEMA : Jurnal Program Studi Pendidikan Matematika, 2(1), 33–40. https://doi.org/10.31597/ja.v2i1.126

Hemmi, K., & Löfwall, C. (2010). Why do we need proof. CERME 6, Congress of the European Society for Research in Mathematics Education, 201–210. http://www.divaportal.org/smash/record.jsf?pid=diva2:400484

Isroil, A., Budayasa, I. K., & Masriyah, M. (2017). Profil berpikir siswa SMP dalam menyelesaikan masalah matematika ditinjau dari kemampuan matematika. Jurnal Review Pembelajaran Matematika, 2(2), 93–105. https://doi.org/10.15642/jrpm.2017.2.2.93-105

Jones, V. O. (2007). Cognitive processes during problem solving of middle school students with different levels of mathematics anxiety and self-esteem: Case studies. Dissertation Abstracts International Section A: Humanities and Social Sciences Vol, 67(8-A), 2915.

Lim, S. Y., & Chapman, E. (2013). Development of a short form of the attitudes toward mathematics inventory. Educ Stud Math, 82, 145–164. https://doi.org/10.1007/s10649-012-9414-x

Marchis, I. (2015). Factors that influence secondary school students ’ attitude to mathematics. Procedia - Social and Behavioral Sciences, 29(October), 786–793. https://doi.org/10.1016/j.sbspro.2011.11.306

Marchiş, I. (2013). Relation between students’ attitude towards mathematics and their problem solving skills. PedActa, 3(2), 59–66.

Martino, P. Di, & Zan, R. (1992). Attitude toward mathematics: Some theoretical issues. Dipartimento Di Matematica Università Di Pisa, ITALY, 1–8. https://erepo.uef.fi/handle/123456789/7398

Mazana, M. Y., Montero, C. S., & Casmir, R. O. (2019). Investigating students ’ attitude towards learning mathematics. International Electronic Journal of Mathematics Education, 14(1), 207–231.

Mudhiah, I. D., & Amin, S. M. (2020). Profil berpikir siswa dalam menyelesaikan soal matematika ditinjau dari kecerdasan emosional. MATHEdunesa: Jurnal Ilmiah Pendidikan Matematika, 9(1), 136–144.

Ngilawajan, D. A. (2013). Proses berpikir siswa SMA dalam field independent dan field dependent. Pedagogia, 2(1), 71–83. http://ojs.umsida.ac.id/index.php/pedagogia/article/view/48

Pantaleon, K. V., Juniati, D., Lukito, A., & Mandur, K. (2018). The written mathematical communication profile of prospective math teacher in mathematical proving The written mathematical communication profile of prospective math teacher in mathematical proving. Journal of Physics: Conference Series, 947(1), 012070. https://doi.org/10.1088/1742-6596/947/1/012070

Relaford-doyle, J. (2020). Characterizing students’ conceptual difficulties with mathematical induction using visual proofs. International Journal of Research in Undergraduate Mathematics Education, 1–20.

Tapia, M. (1996). The attitudes toward mathematics instrument introduction. Annual Meeting of the Mid -South Educational Research Association, 1–21. https://eric.ed.gov/?id=ED404165

Tella, A. (2007). The impact of motivation on student’s academic achievement and learning outcomes in mathematics among secondary school students in Nigeria. Eurasia Journal of Mathematics, Science and Technology Education, 3(2), 149–156. https://doi.org/10.12973/ejmste/75390

Warli, Cintamulya, I., & Rahayu, P. (2020). Scaffolding process based on students diagnostic difficulties in proving group problems by using mathematics mapping Scaffolding process based on students diagnostic difficulties in proving group problems by using mathematics mapping. Journal of Physics: Conference Series, 1422(1), 012012. https://doi.org/10.1088/1742-6596/1422/1/012012

Widyastuti, R. (2015). Proses berfikir siswa dalam menyelesaikan masalah matematika berdasarkan teori Polya ditinjau dari adversity quotient tipe climber. Al-Jabar : Jurnal Pendidikan Matematika, 6(2), 183–194. http://ejournal.radenintan.ac.id/index.php/al-jabar/article/view/48/0

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