Investigasi Desain Pengajaran untuk Penalaran Matematis
DOI:
https://doi.org/10.24256/jpmipa.v11i1.3428Keywords:
Desain Pengajaran, Systematic Literature Review (SLR), Penalaran Matematika.Abstract
Abstract:
Learning mathematics requires students to have various abilities and skills, including mathematical reasoning ability. This study aims to identify any matters related to teaching design in mathematics education toward students' mathematical reasoning abilities. The method used was Systematic Literature Review (SLR) and the collection of literature used as research subjects were carried out by searching the Scopus database and using inclusion criteria in the form of (1) written in English, (2) published in the last ten years (2013-2022), and (3) indexed by Scopus. There are 24 articles identified that meet the inclusion criteria and were analyzed based on teaching design categorization by van der Akker that has been modified by Lithner. The results found that there are learning designs that affect various mathematical reasoning abilities, namely the Zone of Proximal Development (ZPD), Realistic Mathematics Education (RME), and Theory of Didactical Situation (TDS), where various claims in the form of interventions such as learning models, learning instructions and teaching media or materials, which have been seen to effectively improve students' mathematical reasoning abilities.Â
Abstrak:
Pembelajaran matematika menuntut kemampuan dan keterampilan siswa, salah satunya kemampuan penalaran matematika. Penelitian ini bertujuan mengindentifikasi desain pembelajaran matematika terkait kemampuan penalaran matematis siswa. Metode yang digunakan yaitu Systematic Literature Review (SLR) dengan mengidentifikasi database Scopusdengan kriteria inklusi berupa (1) ditulis dalam Bahasa Inggris, (2) diterbitkan selama sepuluh tahun terakhir (2013-2022), dan (3) terindeks Scopus. Terdapat 24 artikel yang teridentifikasi memenuhi kriteria tersebut yang selanjutnya dianalisis berdasarkan kategorisasi desain pengajaran menurut van der Akker yang dimodifikasi oleh Lithner. Hasil penelitian ini menemukan terdapat desain pengajaran yang mempengaruhi berbagai kemampuan penalaran matematis, yaitu Zone of Proximal Development (ZPD), Realistic Mathematics Education (RME), dan Theory of Didactical Situation (TDS), dengan berbagai klaim diantaranya intervensi model pembelajaran, instruksi pembelajaran, dan media atau bahan ajar, yang secara efektif meningkatkan kemampuan penalaran matematika siswa.
References
Adeniyi, Samuel, and Olaotan Kuku. “Effectiveness of Two Instructional Methods on Reasoning Ability of Children with Hearing Impairment in Nigeria.†Specijalna Edukacija i Rehabilitacija 17, no. 4 (2018): 395–417. https://doi.org/10.5937/specedreh17-18600.
Andalia, Linda, Usman, and M. Subianto. “The Application Of Problem-Based Learning Model To Improve Students’ Mathematical Reasoning Skills.†International Journal of Scientific & Technology Research, March 25, 2020, 3532–36. https://www.semanticscholar.org/paper/The-Application-Of-Problem-Based-Learning-Model-To-Andalia-Usman/b90628f69d6abefcaf0dc415874bb5bc10b23896.
Andrews-Larson, Christine, Estrella Johnson, Valerie Peterson, and Rachel Keller. “Doing Math with Mathematicians to Support Pedagogical Reasoning About Inquiry-Oriented Instruction.†Journal of Mathematics Teacher Education 24, no. 2 (April 1, 2021): 127–54. https://doi.org/10.1007/s10857-019-09450-3.
Apriyani, Dwi Dani, and Erlando Doni Sirait. “Pengaruh Kecerdasan Numerik Dan Minat Belajar Terhadap Kemampuan Penalaran Matematika.†Simposium Nasional Ilmiah & Call for Paper Unindra (Simponi) 1, no. 1 (2019). https://doi.org/10.30998/simponi.v0i0.246.
Arıcı, Sevil, and Fatma Aslan-Tutak. “The Effect of Origami-Based Instruction on Spatial Visualization, Geometry Achievement, and Geometric Reasoning.†International Journal of Science and Mathematics Education 13, no. 1 (February 1, 2015): 179–200. https://doi.org/10.1007/s10763-013-9487-8.
Baroody, Arthur J., David J. Purpura, Michael D. Eiland, and Erin E. Reid. “The Impact of Highly and Minimally Guided Discovery Instruction on Promoting the Learning of Reasoning Strategies for Basic Add-1 and Doubles Combinations.†Early Childhood Research Quarterly 30 (January 1, 2015): 93–105. https://doi.org/10.1016/j.ecresq.2014.09.003.
Battista, Michael T. “Shape Makers.†Computers in the Schools 17, no. 1–2 (May 31, 2001): 105–20. https://doi.org/10.1300/J025v17n01_09.
Beatty, Chloé, and Suzanne M. Egan. “The Role of Screen Time and Screen Activity in the Nonverbal Reasoning of 5-Year-Olds: Cross-Sectional Findings from a Large Birth Cohort Study.†Cyberpsychology, Behavior and Social Networking 23, no. 6 (June 2020): 406–11. https://doi.org/10.1089/cyber.2019.0420.
Brousseau, Guy. Theory of Didactical Situations in Mathematics: Didactique Des Mathématiques, 1970–1990. Springer Science & Business Media, 2006.
Chen, Chengyuan, Wheijen Chang, and Shihyin Lin. “Spiral Teaching Sequence and Concept Maps for Facilitating Conceptual Reasoning of Acceleration,†August 2019, 1–17. https://www.proquest.com/docview/2336304821?pq-origsite=primo.
Dhlamini, Zwelithini Bongani, Kabelo Chuene, Kwena Masha, and Israel Kibirige. “Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment.†Eurasia Journal of Mathematics, Science and Technology Education 15, no. 11 (May 23, 2019): em1772. https://doi.org/10.29333/ejmste/105481.
Fowler, Samuel, Chelsea Cutting, JohnPaul Kennedy, Simon N. Leonard, Florence Gabriel, and Wayne Jaeschke. “Technology Enhanced Learning Environments and the Potential for Enhancing Spatial Reasoning: A Mixed Methods Study.†Mathematics Education Research Journal 34, no. 4 (December 1, 2022): 887–910. https://doi.org/10.1007/s13394-021-00368-9.
Hershkowitz, Rina, Raymond Duval, Maria G. Bartolini Bussi, Paolo Boero, Richard Lehrer, Thomas Romberg, R. Berthelot, M. H. Salin, and Keith Jones. “Reasoning in Geometry.†In Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study, edited by Carmelo Mammana and Vinicio Villani, 29–83. New ICMI Study Series. Dordrecht: Springer Netherlands, 1998. https://doi.org/10.1007/978-94-011-5226-6_3.
Hilton, Annette, and Geoff Hilton. “Primary School Teachers Implementing Structured Mathematics Interventions to Promote Their Mathematics Knowledge for Teaching Proportional Reasoning.†Journal of Mathematics Teacher Education 22, no. 6 (December 1, 2019): 545–74. https://doi.org/10.1007/s10857-018-9405-7.
Hino, Keiko, and Hisae Kato. “Teaching Whole-Number Multiplication to Promote Children’s Proportional Reasoning: A Practice-Based Perspective from Japan.†ZDM 51, no. 1 (April 1, 2019): 125–37. https://doi.org/10.1007/s11858-018-0993-6.
Hjelte, Alexandra, Maike Schindler, and Per Nilsson. “Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review.†Education Sciences 10, no. 10 (October 2020): 289. https://doi.org/10.3390/educsci10100289.
Hohensee, Charles. “Preparing Elementary Prospective Teachers to Teach Early Algebra.†Journal of Mathematics Teacher Education 20, no. 3 (June 1, 2017): 231–57. https://doi.org/10.1007/s10857-015-9324-9.
Iskandar, Ananda Putri, and Leonard Leonard. “Modifikasi Model Pembelajaran Tipe Numbered Heads Together (NHT) Dengan Strategi Pembelajaran Tugas Dan Paksa Terhadap Kemampuan Penalaran Matematika Siswa.†Jurnal Mercumatika: Jurnal Penelitian Matematika Dan Pendidikan Matematika 4, no. 1 (2019): 1–13.
Jitendra, Asha K., Michael R. Harwell, and Soo-hyun Im. “Sustainability of a Teacher Professional Development Program on Students’ Proportional Reasoning Skills.†The Journal of Experimental Education 0, no. 0 (July 15, 2022): 1–20. https://doi.org/10.1080/00220973.2022.2092832.
Jitendra, Asha K., Michael R. Harwell, Stacy R. Karl, Soo-hyun Im, and Susan C. Slater. “Investigating the Generalizability of Schema-Based Instruction Focused on Proportional Reasoning: A Multi-State Study.†The Journal of Experimental Education 89, no. 4 (October 2, 2021): 587–604. https://doi.org/10.1080/00220973.2020.1751580.
Jitendra, Asha K., Jon R. Star, Danielle N. Dupuis, and Michael C. Rodriguez. “Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment.†Journal of Research on Educational Effectiveness 6, no. 2 (April 1, 2013): 114–36. https://doi.org/10.1080/19345747.2012.725804.
Johansson, Helena. “Mathematical Reasoning Requirements in Swedish National Physics Tests.†International Journal of Science and Mathematics Education 14, no. 6 (August 1, 2016): 1133–52. https://doi.org/10.1007/s10763-015-9636-3.
Kaur, Berinderjeet, and Tin Lam Toh. Reasoning, Communication and Connections in Mathematics: Yearbook 2012, Association of Mathematics Educators. World Scientific, 2012. https://doi.org/10.1142/8466.
Kertil, Mahmut, Ayhan Kursat Erbas, and Bulent Cetinkaya. “Developing Prospective Teachers’ Covariational Reasoning Through a Model Development Sequence.†Mathematical Thinking and Learning 21, no. 3 (July 3, 2019): 207–33. https://doi.org/10.1080/10986065.2019.1576001.
Khaeroh, Amanatul, Nurul Anriani, and Anwar Mutaqin. “Pengaruh Model Pembelajaran Problem Based Learning terhadap Kemampuan Penalaran Matematis.†TIRTAMATH: Jurnal Penelitian dan Pengajaran Matematika 2, no. 1 (July 18, 2020): 73–85. https://doi.org/10.48181/tirtamath.v2i1.8570.
Khotimah, Rita, Christina Sari, and Masduki Masduki. “The Effect of Concept Map Learning Model on Student’s Reasoning.†Universal Journal of Educational Research 8 (November 30, 2020): 6139–45. https://doi.org/10.13189/ujer.2020.082250.
Larkin, Kevin, Christina Lommatsch, Ilyse Resnick, and Thomas Lowrie. “The Design and Use of a Digital Tool to Support the Development of Preschool Children’s Logical Reasoning.†Journal of Research on Technology in Education 0, no. 0 (August 2, 2022): 1–14. https://doi.org/10.1080/15391523.2022.2107590.
Lee, Chun-Yi, and Ming-Jang Chen. “Effects of Polya Questioning Instruction for Geometry Reasoning in Junior High School.†Eurasia Journal of Mathematics, Science and Technology Education 11, no. 6 (September 29, 2015): 1547–61. https://doi.org/10.12973/eurasia.2015.1419a.
Lerman, Stephen, ed. Encyclopedia of Mathematics Education. Cham: Springer International Publishing, 2020. https://doi.org/10.1007/978-3-030-15789-0.
Lester, Frank K. Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics. IAP, 2007.
Lithner, Johan. “Principles for Designing Mathematical Tasks That Enhance Imitative and Creative Reasoning.†ZDM 49, no. 6 (November 1, 2017): 937–49. https://doi.org/10.1007/s11858-017-0867-3.
Maclinton, David, and Dedek Andrian. “Pengembangan Media Pembelajaran Prisma Berbasis Macromedia Flash Dengan Desain Pembelajaran Assure.†INOMATIKA 4, no. 1 (January 30, 2022): 83–97. https://doi.org/10.35438/inomatika.v4i1.323.
Moher, David, Alessandro Liberati, Jennifer Tetzlaff, Douglas G. Altman, Doug Altman, Gerd Antes, David Atkins, Virginia Barbour, Nick Barrowman, and Jesse A. Berlin. “Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The Prisma Statement (Chinese Edition).†Journal of Chinese Integrative Medicine 7, no. 9 (2009): 889–96. https://doi.org/10.3736/jcim20090918.
Moss, Joan, Zachary Hawes, Sarah Naqvi, and Beverly Caswell. “Adapting Japanese Lesson Study to Enhance the Teaching and Learning of Geometry and Spatial Reasoning in Early Years Classrooms: A Case Study.†ZDM 47, no. 3 (June 1, 2015): 377–90. https://doi.org/10.1007/s11858-015-0679-2.
Muir, Tracey, Kim Beswick, Rosemary Callingham, and Katara Jade. “Experiencing Teaching and Learning Quantitative Reasoning in a Project-Based Context.†Mathematics Education Research Journal 28, no. 4 (December 1, 2016): 479–501. https://doi.org/10.1007/s13394-016-0176-0.
Mukono, S. “Grade 11 Mathematics Learner’s Concept Images and Mathematical Reasoning on Transformations of Functions,†2015. https://www.semanticscholar.org/paper/Grade-11-mathematics-learner%27s-concept-images-and-Mukono/e132e3613d43c91e6f2e15406032296c542fdbb4.
Mumu, Jeinne, and Benidiktus Tanujaya. “Measure Reasoning Skill of Mathematics Students.†International Journal of Higher Education 8 (September 27, 2019): 85. https://doi.org/10.5430/ijhe.v8n6p85.
Munasiah, Munasiah. “Pengaruh Kecemasan Belajar dan Pemahaman Konsep Matematika Siswa terhadap Kemampuan Penalaran Matematika.†Formatif: Jurnal Ilmiah Pendidikan MIPA 5, no. 3 (February 29, 2016). https://doi.org/10.30998/formatif.v5i3.649.
Nurhayati, Afrizawati, and Yandra Rivaldo. “Pembelajaran Matematika Dengan Pendekatan Investigatif Untuk Meningkatkan Kemampuan Penalaran Dan Representasi Matematis Siswa Sekolah Dasar.†Al-Mafahim: Jurnal Pendidikan Guru Madrasah Ibtidaiyah 4, no. 1 (February 25, 2021): 8–15. http://ejournal.stit-alkifayahriau.ac.id/index.php/almafahim/article/view/34.
Otten, Mara, Marja van den Heuvel-Panhuizen, Michiel Veldhuis, Jan Boom, and Aiso Heinze. “Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of Two Learning Environments for Linear Equations.†Education Sciences 10, no. 6 (June 2020): 163. https://doi.org/10.3390/educsci10060163.
Pahrudin, Agus, Nur Ahid, Syamsul Huda, Nita Ardianti, Fredi Ganda Putra, Bambang Sri Anggoro, and Watcharin Joemsittiprasert. “The Effects of the ECIRR Learning Model on Mathematical Reasoning Ability in the Curriculum Perspective 2013: Integration on Student Learning Motivation.†The Effects of the ECIRR Learning Model on Mathematical Reasoning Ability in the Curriculum Perspective 2013: Integration on Student Learning Motivation 9, no. 2 (March 30, 2020): 675–84. https://eu-jer.com/the-effects-of-the-ecirr-learning-model-on-mathematical-reasoning-ability-in-the-curriculum-perspective-2013-integration-on-student-learning-motivation.html.
Putra, Aan, Hendra Syarifuddin, and Zulfah Zulfah. “Validitas Lembar Kerja Peserta Didik Berbasis Penemuan Terbimbing Dalam Upaya Meningkatkan Pemahaman Konsep Dan Kemampuan Penalaran Matematis.†Edumatika : Jurnal Riset Pendidikan Matematika 1, no. 2 (December 14, 2018): 56–62. https://doi.org/10.32939/ejrpm.v1i2.302.
Shabani, Karim, Khatib Mohammad, and Saman Ebadi. “Vygotsky’s Zone of Proximal Development: Instructional Implications and Teachers’ Professional Development.†English Language Teaching 3 (November 16, 2010). https://doi.org/10.5539/elt.v3n4p237.
Sidenvall, Johan. “Literature Review of Mathematics Teaching Design for Problem Solving and Reasoning.†Nordisk Matematikkdidaktikk, NOMAD:[Nordic Studies in Mathematics Education] 24, no. 1 (2019): 51–74.
Siregar, Nur, Roslinda Rosli, and Siti Maat. “The Effects of a Discovery Learning Module on Geometry for Improving Students’ Mathematical Reasoning Skills, Communication and Self-Confidence.†International Journal of Learning, Teaching and Educational Research 19 (March 30, 2020): 214–28. https://doi.org/10.26803/ijlter.19.3.12.
Siwawetkul, Weeracha, and Prakob Koraneekij. “Effect of 5e Instructional Model on Mobile Technology to Enhance Reasoning Ability of Lower Primary School Students.†Kasetsart Journal of Social Sciences 41, no. 1 (2020): 40–45. https://so04.tci-thaijo.org/index.php/kjss/article/view/229138.
Smit, Robbert, Patricia Bachmann, Verena Blum, Thomas Birri, and Kurt Hess. “Effects of a Rubric for Mathematical Reasoning on Teaching and Learning in Primary School.†Instructional Science 45, no. 5 (October 1, 2017): 603–22. https://doi.org/10.1007/s11251-017-9416-2.
Swidan, Osama, Sara Bagossi, Silvia Beltramino, and Ferdinando Arzarello. “Adaptive Instruction Strategies to Foster Covariational Reasoning in a Digitally Rich Environment.†The Journal of Mathematical Behavior 66 (June 1, 2022): 100961. https://doi.org/10.1016/j.jmathb.2022.100961.
Uyen, Bui, Lu Ngan, Nguyen Thao, and Duong Tong. “Impulsing the Development of Students’ Competency Related to Mathematical Thinking and Reasoning through Teaching Straight-Line Equations.†International Journal of Learning, Teaching and Educational Research 20 (June 30, 2021): 38–65. https://doi.org/10.26803/ijlter.20.6.3.
Xin, Yan Ping, Joo Young Park, Ron Tzur, and Luo Si. “The Impact of a Conceptual Model-Based Mathematics Computer Tutor on Multiplicative Reasoning and Problem-Solving of Students with Learning Disabilities.†The Journal of Mathematical Behavior 58 (June 1, 2020): 100762. https://doi.org/10.1016/j.jmathb.2020.100762.
Zahari, C. L., Y. Kusumah, and Darhim. “Enhanced Visuospatial Reasoning of Students with Hybrid Learning Model.†International Journal of Scientific & Technology Research 9, no. 3 (March 2020): 3955–57. https://www.semanticscholar.org/paper/ENHANCED-VISUOSPATIAL-REASONING-OF-STUDENTS-WITH-Zahari-Kusumah/93fe6768548701f7532ff93cafd9cc94b48d6559.
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