Analisis Kemampuan Berpikir Matematis Siswa pada Pembelajaran Aritmatika Sosial Ditinjau dari Model Pembelajaran dan Self Efficacy Siswa

Nandang Arif Saefuloh; Wahyudin Wahyudin; Sufyani Prabawanto; Usep Kosasih; Samnur Saputra; Deti Ahmatika; Iden Rainal Ihsan

doi:10.26877/aks.v14i2.15950

Analisis Kemampuan Berpikir Matematis Siswa pada Pembelajaran Aritmatika Sosial Ditinjau dari Model Pembelajaran dan Self Efficacy Siswa

Nandang Arif Saefuloh, Wahyudin Wahyudin, Sufyani Prabawanto, Usep Kosasih, Samnur Saputra, Deti Ahmatika, Iden Rainal Ihsan

Abstract

The main problem in this study is students' ability to think mathematically in solving mathematical problems in learning social arithmetic in their class through minimum guidance-based learning (PBL and DL). This research uses a mixed method to look at the description of students' mathematical thinking abilities and the tendency of these abilities based on students' self-efficacy levels. The results showed that the increase in students' mathematical thinking skills at each level of low self-efficacy based on n-gain calculations. In addition, there is no significant difference in the scores for improving students' mathematical thinking skills based on the learning model and the level of self-efficacy. There is no significant interaction between the Learning Model and the Level of Self-efficacy in determining the increase in the average score of students' mathematical thinking abilities. Other findings show that students with low self-efficacy tend to have limitations in the ability to think mathematically in the process of conjecture and convincing. On the other hand, students with moderate and high self-efficacy have more complete mathematical thinking abilities, including specialization, generalization, conjecture, and convincing. However, in the process of conjecture and convincing, two sub-processes are found, namely knowledge modification using factual knowledge, contextual tools, or substantive thinking, as well as the process of selecting relevant information in solving problems. Therefore, the two groups are divided into four groups based on the way students use conjecture and convincing mathematical thinking abilities, namely: (1) students use specialization mathematical thinking skills based on the knowledge learned from the teacher, (2) students use specialization mathematical thinking abilities based on knowledge acquired in everyday life, (3) students use convincing mathematical thinking abilities by examining the formula used or based on knowledge learned from the teacher, and (4) students use convincing mathematical thinking abilities based on the knowledge obtained in everyday life (factual knowledge).

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References

Anderson, L., W., et al. (2001). A taxonomy for learning, teaching, and assessing : a revision of Bloom's taxonomy of educational objectives. USA: Addison Wesley Longman, Inc.

Andra, M., H., Koeswanti, H., D., Radia, E.,H. (2019). Meningkatkan Hasil Belajar Matematika Menggunakan Model Discovery Learning pada Siswa Kelas IV Sekolah Dasar. Jurnal Pendidikan Dasar. Vol 7. No 1.

Argyle, S., F. (2012). Mathematical Thinking: from Cacophony to Consensus. Dissertation. Kent State University College and Graduate School of Education, Health, and Human Services.

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.

Bandura, A., & Schunk, D. H. (1981). Cultivating competence, self-efficacy, and intrinsic interest through proximal self-motivation. Journal of Personality and Social Psychology. 41. P. 586-598.

Boole, M., E. (2005). Philosophy & Fun of Algebra. London: C.W. Daniel, LTD.

Depaepe, F., De Corte, E., & Verschaffel, L. (2015). Students’ nonrealistic mathematical modeling as a drawback of teachers’ beliefs about and approaches to word problem solving. From beliefs to dynamic affect systems in mathematics education. Exploring a mosaic of relationships and interactions. In B. Pepin & B. Roesken-Winter (Eds.). pp. 137–159. Cham: Springer.

Dwirahayu, G., Kustiawati, D., Bidari, I. (2018). Pengaruh Habits of Mind terhadap Kemampuan Generalisasi Matematis. Jurnal Penelitian dan Pembelajaran Matematika. Vol. 11 No. 2. 91-104.

Fatade, A.,O., Mogari, D., Arigbabu, A., A. (2013). Effect Of Problem-Based Learning On Senior Secondary School Students’ Achievements In Further Mathematics. Acta Didactica Napocensia. Volume 6 Number 3. p.27-44.

Fraenkel, J.R, Wallen, N., Hyun, H. (2012). How to Design and Evaluate Research in Education. New York: McGraw-Hill.

Fyhn, A.B. (2008). A Climbing Class’ Reinvention of Angles. Educational Studies in Mathematics. Vol. 67. No. 1. pp. 19-35. Springer.

Gros, H., Thibaut, J.P., & Sander, E. (2020). Semantic Congruence in Arithmetic: A New Conceptual Model for Word Problem Solving. Educational Psychologist. 55. 1-19.

Henderson, P.B., et al. (2002). Materials Development in support of Mathematical Thinking. Proceeding ITiCSE-WGR '02 Working group reports from ITiCSE on Innovation and technology in computer science education. Pages 185-190.

Hendriana, H., Rohaeti, E. E., dan Sumarmo, U. (2017). Hard Skills dan Soft Skills Matematik Siswa. Bandung: PT. Refika Aditama.

Hillocks, G., J., Shulman. (1999). Ways of Thinking, Ways of Teaching. London: Teacher College Press.

Kementerian Pendidikan dan Kebudayaan Badan Penelitian dan Pengembangan Pusat Kurikulum dan Perbukuan. (2013). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 58 Tahun 2014 tentang Kurikulum 2013 Sekolah Menengah Pertama/Madrasah Tsanawiyah. hal 607.

Kirschner, P., A., Sweller, J., & Clark, R., E. (2006) Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist. 41:2, 75-86.

Lane, C.P. and Harkness, S.S. (2012). Game show mathematics: Specializing, conjecturing, generalizing, and Convincing. Journal of Mathematical Behavior 31 (2012) 163– 173.

Mason, J., Burton, L., Stacey, K. (2010). Thinking Mathematically. Pearson Education Limited.

Mustafa, S., Sari, V., & Baharullah. (2019). The Implementation of Mathematical Problem-Based Learning Model as an Effort to Understand the High School Students’ Mathematical Thinking Ability. International Education Studies. Vol. 12. No. 2. p. 117-123.

Nepal, B. (2016). Relationship between Mathematical Thinking and Mathematics Achievement. IOSR Journal of Research & Method in Education (IOSR-JRME). Volume 6, Issue 6 Ver. IV.

Pardimin. (2018). Self-Efficacy Matematika dan Self-Efficacy Mengajar Matematika Guru Matematika. Jurnal Ilmu Pendidikan. Jilid 24, Nomor 1, hlm. 29-37.

Parker, P. D., et. al. (2014). Juxtaposing math self-efficacy and self-concept as predictors of long-term achievement outcomes. Educational Psychology, 34:1, 29-48, DOI: 10.1080/01443410.2013.797339

Pinter, H., H., et.al. (2017). The Importance of Structure, Clarity, Representation, and Language in Elementary Mathematics Instruction. Investigation in Mathematic Learning. Vol 10.

Polya, G. (1957). How to Solve It, A New Aspect of Mathematical Method 2nd. New Jersey: Princeton University Press.

Pongsakdi, N., et al. (2019). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. ZDM Mathematics Education. 52. 33–44.

Saefuloh, N. A., Kartasasmita, B. G., & Kosasih, U. (2020a). Meningkatkan Kemampuan Pemecahan Masalah Matematis Siswa SMP melalui Strategi Konflik Kognitif Pendekatan Problem-Based Learning (PBL) dengan Sikap Siswa Sebagai Variabel Intervening. UJMES (Uninus Journal of Mathematics Education and Science), 5(1), 022-032.

Saefuloh, N. A., Wahyudin, W., Prabawanto, S., & Kosasih, U. (2020b). Kemampuan Berpikir Siswa pada Materi Aljabar. Teorema: Teori dan Riset Matematika. 5(2), 203-210.

Salado, A., Chowdhury, A., H., Norton, A. (2019). Systems thinking and mathematical problem solving. School Science and Mathematics. 119. 49-58.

Spindler, R. (2020). Aligning Modeling Projects with Bloom's Taxonomy. PRIMUS. 30:5. 601-616. DOI: 10.1080/10511970.2019.1619208.

Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behavior. Elsevier Inc.

Stacey, K. (2006). What Is Mathematical Thinking And Why Is It Important? in Progress report of the APEC project: “Colaborative Studies on Innovations for Teaching and Learning Mathematics in Diferent Cultures (II) – Lesson Study focusing on Mathematical Thinking–”, Tokyo: CRICED, University of Tsukuba.

Sunaryo, Y. (2017). Pengukuran Self-Efficacy Siswa dalam Pembelajaran Matematika di Mts Negeri 2 Ciamis. Jurnal Teori dan Riset Matematika (TEOREMA). Vol. 1 No. 2.

Sweller, J. (2009). What Human Cognitive Architecture Tells Us About Constructivism. Constructivist Instruction: Success or Failure?. P. 127-143. New York: Routledge. 270 Madison Ave.

Tall, D. (2002). Advanced Mathematical Thinking. USA: Kluwer Academic Publishers.

Uyangör, S., M. (2019) Investigation of the Mathematical Thinking Processes of Students in Mathematics Education Supported with Graph Theory. Universal Journal of Educational Research 7(1).

Verschaffel, L., Depaepe, F., & Van Dooren, W. (2015). Individual differences in word problem solving. Oxford handbook of numerical cognition. In R. C. Kadosh & A. Dowker (Eds.). pp. 953–974. Oxford: Oxford University Press.

Verschaffel, L., Schukajlow, S., Star, J., & Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM Mathematics Education. 52. 1-16.

Wintarti A., dkk. (2008). Contextual Teaching and Learning Matematika: Sekolah Menengah Pertama/Madrasah Tsanawiyah Kelas VII Edisi 4. Pusat Perbukuan, Departemen Pendidikan Nasional.

Yıldız, P., Özdemir, İ., E., Y. (2019). Mathematics self-efficacy beliefs and sources of self-efficacy: A Descriptive Study with two Elementary School Students. International Journal of Progressive Education. Volume 15 Number 3. p. 194-206.

Zhou, D., et.al. (2019): Teacher-student relationship and mathematical problem-solving ability: mediating roles of self-efficacy and mathematical anxiety. Educational Psychology. DOI: 10.1080/01443410.2019.1696947.

Zysberg, L & Schwabsky, N. (2020). School climate, academic selfefficacy and student achievement. Educational Psychology. DOI: 10.1080/01443410.2020. 1813690.

DOI: https://doi.org/10.26877/aks.v14i2.15950