Improving elementary students' mathematical reasoning abilities through sociohumanistic-based learning
Year 2020,
, 1457 - 1469, 15.12.2020
Rosidah Hidayat
Wahyudin Wahyudin
Jailani Jailani
Bayu Rahmat Setiadi
Abstract
This study aimed to determine the improvement of students' mathematical reasoning abilities through sociohumanistic-based learning. This research was a quasi-experimental study with a non-equivalent control group design. The population in this study were all class IV in one elementary school in Salatiga. The sample consisted of two classes, namely classes and selected by purposive sampling. The instrument used was a mathematical reasoning ability test. Data analysis used t-test (Independent Sample t-Test) and Mann Whitney. The analysis results show that: (1) based on the results on a limited, medium, and wide-scale try-out, the developed model is easy-practical-effective in its implementation; (2) the improvement in mathematical reasoning skill of the students taught using the model is higher than that of taught using direct instructions; and (3) Sociohumanistic-based learning has several advantages especially can generate endorphins (hormone of happiness) to make the students love math, can foster self-reliance of learners, able to activate the storage capabilities of the human brain into long-term memory. Based on the results of this research and development, it can be concluded that the developed model is easy, practical, and effective to improve the mathematical reasoning skill of elementary school students.
Supporting Institution
Yogyakarta State University
Thanks
We express our deep gratitude to the dissertation promoter, the Yogyakarta State University of post-graduate program, and the management of Universitas Sarjanawiyata Tamansiswa to complete my doctoral studies in the field of Teacher Education and Elementary Education.
References
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- Arbayah. (2013). Humanistik Learning Model. Jurnal Dinamika Ilmu, 13(2).
- Ärlebäck, J. B., & Doerr, H. M. (2017). Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence. ZDM-Mathematics Education, 50(1–2), 187–200. https://doi.org/10.1007/s11858-017-0881-5
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- Ball, D. L., Lewis, J., & Thames, M. H. (2008). Making Mathematics Work in School. Journal for Research in Mathematics Education, 14(2008), 13–44.
- Bandura, A. (1997). Self-efficacy: The exercise of control (pp. 3-604). New York: WH Freeman.
- Barmby, P., Bilsbourough, L., Harries, T., & Higgins, S. (2009). Primary Mathematics: Teaching for Understanding. McGraw-Hill Education. https://doi.org/10.2307/3615672.
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de Groot-Reuvekamp, M., Ros, A., van Boxtel, C. (2018). A successful professional development program in history: What matters? Teaching and Teacher Education, 75, 290-
301. https://doi.org/10.1016/j.tate.2018.07.005.
- Douek. (2005). Communication in the mathematics classroom: argumentation and development of mathematical knowledge. In: Chronaki A, Christiansen IM (eds) Challenging perspectives on mathematics classroom communication. Information Age Publishing, Greenwich, CT, pp 145–172.
- Flegas, K., & Charalampos, L. (2013). Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students. Canadian Journal of Science, Mathematics and Technology Education, 13(1), 70–89. https://doi.org/10.1080/14926156.2013.758326
- Freire, P. (2011). Education of the Oppressed. Jakarta: LP3ES.
- Grant, B. C. (1992). Integrating sport into the physical education curriculum in New Zealand Secondary School. Quest, 4(4), 304 – 316.
- Hadi, W. (2016). Improving the reasoning abilities of junior high school students through discovery learning with a scientific approach (Quasi-experimental study at a junior high school in West Jakarta). Kalamatika, I(1), 93–108.
- Haglund, R. (2004). Using Humanistic Content and Teaching Methods to Motivate Students and Counteract Negative Perceptions of Mathematics. Humanistic Mathematics Network Journal, 27(4). http://scholarship.claremont.edu/hmnj/vol1/iss27/4
- Hake, R. R. (1999). Analyzing change/gain scores. Unpublished.[online] URL: http://www. Physics. Indiana. Edu/~ sdi/AnalyzingChange-Gain. pdf.
- Hergenhahn, B.R., Olson, Matthew H. (2008). Theories of Learning, 7th edition. Jakarta: Kencana Prenada Media Group.
- Illeris, K. (2018). An overview of the history of learning theory. European Journal of Education, 53(1), 86–101. doi:10.1111/ejed.12265
- Jedemark, M. (2019). A scientific approach in the assessment of the school-based part of the teacher education programme in Sweden, Journal of Curriculum Studies, 51 (3), 420-436, DOI: 10.1080/00220272.2019.1567820.
- Joseph, S., Murphy, D. & Holford, J. (2020): Positive education: A new look at Freedom to Learn. Oxford Review of Education, 46(5), 549-562. https://doi.org/10.1080/03054985.2020.1726310.
- Kaur, B., & Toh, T. L. (2012). Reasoning, Communication and Connections in a-Level Mathematics. Reasoning, Communication and Connections in Mathematics, 127–147. https://doi.org/10.1142/9789814405430_0007
- Krummheuer, G. (1995). 'The ethnography of argumentation,' in Cobb, P and Bauersfeld, H (eds), The Emergence of Mathematical Meaning Interaction in Classroom Cultures, Hillsdale, NJ, Lawrence Erlbaum, pp 229-269
- Leppink, J. (2019). Statistical Methods for Experimental Research in Education and Psychology. Switzerland AG: Springer.
- Lithner, J. (2000). Mathematical reasoning in school tasks. Educational Studies in Mathematics, 41(2), 165-190.
- Maharani, H. R., & Sukestiyarno. (2017). Learning Analysis based on Humanism Theory and Mathematics Creative Thinking Ability of Students. International Conference on Mathematics: Education, Theory, and Application, 01(2017).
- Morris, C.W. (1994). Norm, Values, and Society. Wien: Kluwer Academic Publisher.
- Mueller, E. T. (2006). Commonsense Reasoning. San Fransisco: Morgan Kaufmann.
- Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. International Association for the Evaluation of Educational Achievement.
- Herengracht 487, Amsterdam, 1017 BT, The Netherlands.
- Nabavi, R. T. (2011). Bandura’s Social Learning Theory & Social Cognitive Learning Theory. Teheran: University of Science and Culture.
- NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
- Obersteiner, A., Reiss, K. & Heinze, A. Psychological Theories in Mathematics Education. J Math Didakt 39, 1–6 (2018). https://doi.org/10.1007/s13138-018-0134-3
- Permana, Y. & Sumarmo, U., (2007). Developing of high school students' mathematical reasoning and connection skills through problem-based learning. Educationist, 1(2), p. 116.
- Reys, R., Lindquist, Marry M., & Lambdin, Diana V., (2009). Helping children Mathematics (9th ed), USA: John Wiley & Sons, Inc.
- Santrock, J. W. (2017). Educational Psychology, 6th Edition. New York: McGraw-Hill Education.
- Selznick, P. (2008). A Humanist Science Values and Ideals in Social Inquiry. California: Stanford University Press.
- Sharp, A. (2012) Humanistic Approaches to Learning. In: Seel N.M. (eds) Encyclopedia of the Sciences of Learning. Boston, MA: Springer, https://doi.org/10.1007/978-1-4419-1428-6_530
- Sunggingwati, D., & Nguyen, H. T. M. (2013). Teachers' questioning in reading lessons: A case study in Indonesia. Electronic Journal of Foreign Language Teaching, 10(1), 80–95.
- Supriyadi, E. (2011). Education with a Humanistic Approach, Cianjur.
- Taormina, R.J. & Gao, J.H. (2013). Maslow and the Motivation Hierarchy: Measuring Satisfaction of the Needs. American Journal of Psychology, 126 (2), 155-177. DOI: 10.5406/amerjpsyc.126.2.0155
- Uno, H.B. (2012). Learning Model to Create a Creative and Effective Teaching and Learning Process. Jakarta: PT. Bumi Aksara.
- Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2017). Mapping Variation in Children's Mathematical Reasoning: The Case of 'What Else Belongs?' International Journal of Science and Mathematics Education, 15(5), 873–894. https://doi.org/10.1007/s10763-016-9725-y
- Van de Walle, J. A., Karp, K, S., & Bay-Williams, J. M. (2010). Elementary School Mathematics: Teaching developmentally (7th ed). Boston: Allyn & Balcon.
- Widodo, S., Rahayu, P., Adjie, N., Widodo, S.A., & Setiadi, B.R. (2018). The Development of Arithmetic Gamification Using Digital Dice. International Journal of Engineering & Technology, 7 (3,2), 751-755.
- Zaini, A., & Marsigit, M. (2014). Comparison of the Effectiveness of Learning Mathematics with Realistic and Conventional Mathematical Approaches in terms of Students' Mathematical Reasoning and Communication Ability. Jurnal Riset Pendidikan Matematika, 1(2), 152. https://doi.org/10.21831/jrpm.v1i2.2672
Year 2020,
, 1457 - 1469, 15.12.2020
Rosidah Hidayat
Wahyudin Wahyudin
Jailani Jailani
Bayu Rahmat Setiadi
References
- Adegoke, B. A. (2013). Modeling the Relationship between Mathematical Reasoning Ability and Mathematics Attainment. Journal of Education and Practice, 4(17), 54–61.
- Arifanti, D.R. (2020). Mathematical reasoning in problem-solving in three dimensions. Ahmad Dahlan International Conference on Mathematics and Mathematics Education. Journal of Physics: Conference Series, 1613 (2020) 012077. doi:10.1088/1742-6596/1613/1/012077.
- Attridge, A & Inglis, M. (2013.) "Advanced Mathematical Study and the Development of Conditional Reasoning Skills." Plos One Journal. 8(7), July 2013, e69399.
- Arbayah. (2013). Humanistik Learning Model. Jurnal Dinamika Ilmu, 13(2).
- Ärlebäck, J. B., & Doerr, H. M. (2017). Students’ interpretations and reasoning about phenomena with negative rates of change throughout a model development sequence. ZDM-Mathematics Education, 50(1–2), 187–200. https://doi.org/10.1007/s11858-017-0881-5
- Ball DL & Bass H. (2003). Making mathematics reasonable in school. In: Kilpatrick J, Martin WG, Schifter DE (eds) A research companion to principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston, VA, pp 27–44.
- Ball, D. L., Lewis, J., & Thames, M. H. (2008). Making Mathematics Work in School. Journal for Research in Mathematics Education, 14(2008), 13–44.
- Bandura, A. (1997). Self-efficacy: The exercise of control (pp. 3-604). New York: WH Freeman.
- Barmby, P., Bilsbourough, L., Harries, T., & Higgins, S. (2009). Primary Mathematics: Teaching for Understanding. McGraw-Hill Education. https://doi.org/10.2307/3615672.
- Battista, M. T. (2016). Reasoning and Sense-Making in the Mathematics Classroom: Grades 3–5, Virginia: National Council of Teachers of Mathematics.
- Bragg, L., & Herbert, E. (2018). What can be learned from teachers assessing mathematical reasoning: a case study. Mathematics Education Research Group of Australasia, 178-185.
- Brodie, K. (2010). Teaching Mathematical Reasoning in Secondary School Classrooms. New York: Springer.
de Groot-Reuvekamp, M., Ros, A., van Boxtel, C. (2018). A successful professional development program in history: What matters? Teaching and Teacher Education, 75, 290-
301. https://doi.org/10.1016/j.tate.2018.07.005.
- Douek. (2005). Communication in the mathematics classroom: argumentation and development of mathematical knowledge. In: Chronaki A, Christiansen IM (eds) Challenging perspectives on mathematics classroom communication. Information Age Publishing, Greenwich, CT, pp 145–172.
- Flegas, K., & Charalampos, L. (2013). Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students. Canadian Journal of Science, Mathematics and Technology Education, 13(1), 70–89. https://doi.org/10.1080/14926156.2013.758326
- Freire, P. (2011). Education of the Oppressed. Jakarta: LP3ES.
- Grant, B. C. (1992). Integrating sport into the physical education curriculum in New Zealand Secondary School. Quest, 4(4), 304 – 316.
- Hadi, W. (2016). Improving the reasoning abilities of junior high school students through discovery learning with a scientific approach (Quasi-experimental study at a junior high school in West Jakarta). Kalamatika, I(1), 93–108.
- Haglund, R. (2004). Using Humanistic Content and Teaching Methods to Motivate Students and Counteract Negative Perceptions of Mathematics. Humanistic Mathematics Network Journal, 27(4). http://scholarship.claremont.edu/hmnj/vol1/iss27/4
- Hake, R. R. (1999). Analyzing change/gain scores. Unpublished.[online] URL: http://www. Physics. Indiana. Edu/~ sdi/AnalyzingChange-Gain. pdf.
- Hergenhahn, B.R., Olson, Matthew H. (2008). Theories of Learning, 7th edition. Jakarta: Kencana Prenada Media Group.
- Illeris, K. (2018). An overview of the history of learning theory. European Journal of Education, 53(1), 86–101. doi:10.1111/ejed.12265
- Jedemark, M. (2019). A scientific approach in the assessment of the school-based part of the teacher education programme in Sweden, Journal of Curriculum Studies, 51 (3), 420-436, DOI: 10.1080/00220272.2019.1567820.
- Joseph, S., Murphy, D. & Holford, J. (2020): Positive education: A new look at Freedom to Learn. Oxford Review of Education, 46(5), 549-562. https://doi.org/10.1080/03054985.2020.1726310.
- Kaur, B., & Toh, T. L. (2012). Reasoning, Communication and Connections in a-Level Mathematics. Reasoning, Communication and Connections in Mathematics, 127–147. https://doi.org/10.1142/9789814405430_0007
- Krummheuer, G. (1995). 'The ethnography of argumentation,' in Cobb, P and Bauersfeld, H (eds), The Emergence of Mathematical Meaning Interaction in Classroom Cultures, Hillsdale, NJ, Lawrence Erlbaum, pp 229-269
- Leppink, J. (2019). Statistical Methods for Experimental Research in Education and Psychology. Switzerland AG: Springer.
- Lithner, J. (2000). Mathematical reasoning in school tasks. Educational Studies in Mathematics, 41(2), 165-190.
- Maharani, H. R., & Sukestiyarno. (2017). Learning Analysis based on Humanism Theory and Mathematics Creative Thinking Ability of Students. International Conference on Mathematics: Education, Theory, and Application, 01(2017).
- Morris, C.W. (1994). Norm, Values, and Society. Wien: Kluwer Academic Publisher.
- Mueller, E. T. (2006). Commonsense Reasoning. San Fransisco: Morgan Kaufmann.
- Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. International Association for the Evaluation of Educational Achievement.
- Herengracht 487, Amsterdam, 1017 BT, The Netherlands.
- Nabavi, R. T. (2011). Bandura’s Social Learning Theory & Social Cognitive Learning Theory. Teheran: University of Science and Culture.
- NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
- Obersteiner, A., Reiss, K. & Heinze, A. Psychological Theories in Mathematics Education. J Math Didakt 39, 1–6 (2018). https://doi.org/10.1007/s13138-018-0134-3
- Permana, Y. & Sumarmo, U., (2007). Developing of high school students' mathematical reasoning and connection skills through problem-based learning. Educationist, 1(2), p. 116.
- Reys, R., Lindquist, Marry M., & Lambdin, Diana V., (2009). Helping children Mathematics (9th ed), USA: John Wiley & Sons, Inc.
- Santrock, J. W. (2017). Educational Psychology, 6th Edition. New York: McGraw-Hill Education.
- Selznick, P. (2008). A Humanist Science Values and Ideals in Social Inquiry. California: Stanford University Press.
- Sharp, A. (2012) Humanistic Approaches to Learning. In: Seel N.M. (eds) Encyclopedia of the Sciences of Learning. Boston, MA: Springer, https://doi.org/10.1007/978-1-4419-1428-6_530
- Sunggingwati, D., & Nguyen, H. T. M. (2013). Teachers' questioning in reading lessons: A case study in Indonesia. Electronic Journal of Foreign Language Teaching, 10(1), 80–95.
- Supriyadi, E. (2011). Education with a Humanistic Approach, Cianjur.
- Taormina, R.J. & Gao, J.H. (2013). Maslow and the Motivation Hierarchy: Measuring Satisfaction of the Needs. American Journal of Psychology, 126 (2), 155-177. DOI: 10.5406/amerjpsyc.126.2.0155
- Uno, H.B. (2012). Learning Model to Create a Creative and Effective Teaching and Learning Process. Jakarta: PT. Bumi Aksara.
- Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2017). Mapping Variation in Children's Mathematical Reasoning: The Case of 'What Else Belongs?' International Journal of Science and Mathematics Education, 15(5), 873–894. https://doi.org/10.1007/s10763-016-9725-y
- Van de Walle, J. A., Karp, K, S., & Bay-Williams, J. M. (2010). Elementary School Mathematics: Teaching developmentally (7th ed). Boston: Allyn & Balcon.
- Widodo, S., Rahayu, P., Adjie, N., Widodo, S.A., & Setiadi, B.R. (2018). The Development of Arithmetic Gamification Using Digital Dice. International Journal of Engineering & Technology, 7 (3,2), 751-755.
- Zaini, A., & Marsigit, M. (2014). Comparison of the Effectiveness of Learning Mathematics with Realistic and Conventional Mathematical Approaches in terms of Students' Mathematical Reasoning and Communication Ability. Jurnal Riset Pendidikan Matematika, 1(2), 152. https://doi.org/10.21831/jrpm.v1i2.2672