Kemampuan Pemecahan Masalah Matematis melalui Pembelajaran Berbasis Masalah dengan Scaffolding
DOI:
https://doi.org/10.29408/jel.v6i2.2042Keywords:
high schools, early mathematical abilities, problem based learning, scaffolding, mathematical problem solvingAbstract
One of the main goals of school mathematics is the achievement of mathematical problem-solving abilities through problem-based learning. It is expected that these abilities can be achieved well by students. However, the complexity of the problem and minimum confidence become a problem when students experience complex situations created in the problem-based learning process. Scaffolding becomes essential because of the differences in each student's knowledge stored in long term memory. The purpose of the study was to analyze differences in mathematical problem-solving abilities with two different learning and based on initial mathematical abilities. Learning in the experimental class is problem-based learning with scaffolding, and then control class learning is problem-based without scaffolding. The research method used was a quasi-experimental design with a matching-only pretest-posttest control group design. Sample selection using purposive sampling to get samples with the same characteristics, the total number of samples is 60 students with each division 30. The initial mathematics ability has the same role in the mathematical problem-solving ability in the experimental and control classes. That is when students are in the high category then the ability of severe mathematical problem-solving. However, when the two classes are compared, the results are significantly different. Scaffolding becomes a factor that distinguishes the ability to solve mathematical problems.
References
Abdu, R., Schwarz, B., & Mavrikis, M. (2015). Whole-class scaffolding for learning to solve mathematics problems together in a computer-supported environment. ZDM, 47(7), 1163–1178. https://doi.org/10.1007/s11858-015-0719-y.
Abdullah, N. I., Tarmizi, R. A., & Abu, R. (2010). The effects of problem based learning on mathematics performance and affective attributes in learning statistics at form four secondary level. Procedia-Social and Behavioral Sciences, 8, 370–376. https://doi.org/10.1016/j.sbspro.2010.12.052.
Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9(1), 33–52. https://doi.org/10.1007/s10857-006-9005-9.
Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM, 47(7), 1047–1065. https://doi.org/10.1007/s11858-015-0738-8.
Barber, W., King, S., & Buchanan, S. (2015). Problem based learning and authentic assessment in digital pedagogy: Embracing the role of collaborative communities. Electronic Journal of E-Learning, 13(2), 59–67.
Barrows, H. S. (1996). Problem-based learning in medicine and beyond: A brief overview. New Directions for Teaching and Learning, 1996(68), 3–12. https://doi.org/10.1002/tl.37219966804.
Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26. https://doi.org/10.1007/s10857-009-9121-4.
Belland, B. R. (2014). Scaffolding: Definition, current debates, and future directions. In Handbook of research on educational communications and technology (pp. 505–518). Springer. https://doi.org/10.1007/978-1-4614-3185-5.
Belland, B. R., Glazewski, K. D., & Richardson, J. C. (2008). A scaffolding framework to support the construction of evidence-based arguments among middle school students. Educational Technology Research and Development, 56(4), 401–422. https://doi.org/10.1007/s11423-007-9074-1.
Campbell, D. T., & Stanley, J. C. (2015). Experimental and quasi-experimental designs for research. Ravenio Books. http://davidpassmore.net/courses/data/_book/Camp_and_Stanley.pdf
Dolmans, D. H. J. M., Loyens, S. M. M., Marcq, H., & Gijbels, D. (2016). Deep and surface learning in problem-based learning: a review of the literature. Advances in Health Sciences Education, 21(5), 1087–1112. https://doi.org/10.1007/s10459-015-9645-6.
Driver, R., Newton, P., & Osborne, J. (2000). Establishing the norms of scientific argumentation in classrooms. Science Education, 84(3), 287–312. https://doi.org/10.1002/(SICI)1098-237X(200005)84:3<287::AID-SCE1>3.0.CO;2-A.
Ernest, P. (2015). The social outcomes of learning mathematics: Standard, unintended or visionary? International Journal of Education in Mathematics Science and Technology, 3(3), 187–192. https://doi.org/10.18404/ijemst.29471.
Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2011). How to design and evaluate research in education. New York: McGraw-Hill Humanities/Social Sciences/Languages. https://pdfs.semanticscholar.org/60b6/99eda714ac21599455741fb499dd4e68f615.pdf
Frederick, M. L., Courtney, S., & Caniglia, J. (2014). With a little help from my friends: Scaffolding techniques in problem solving. Investigations in Mathematics Learning, 7(2), 21–32. https://doi.org/10.1080/24727466.2014.11790340.
Gazali, R. Y. (2016). Pembelajaran matematika yang bermakna. Math Didactic: Jurnal Pendidikan Matematika, 2(3), 181–190. https://doi.org/10.33654/math.v2i3.47.
Hasan, B. (2015). Penggunaan Scaffolding untuk Mengatasi Kesulitan Menyelesaikan Masalah Matematika. APOTEMA: Jurnal Program Studi Pendidikan Matematika, 1(1), 88–98. https://doi.org/10.31597/ja.v1i1.169.
Herman, T. (2007). Pembelajaran berbasis masalah untuk meningkatkan kemampuan penalaran matematis siswa SMP. Yogyakarta State University. https://eprints.uny.ac.id/4968/1/pembelajaran_berbasis_masalah.pdf.
Holmes, J., & Adams, J. W. (2006). Working memory and children’s mathematical skills: Implications for mathematical development and mathematics curricula. Educational Psychology, 26(3), 339–366. https://doi.org/10.1080/01443410500341056.
Ikhsan, M., & Rizal, S. (2014). Penerapan model pembelajaran berbasis masalah untuk meningkatkan kemampuan berpikir kritis dan disposisi matematis siswa. Jurnal Didaktik Matematika, 1(1). http://www.jurnal.unsyiah.ac.id/DM/article/download/1330/1211.
Jacobsen, A. J., & Børsen, T. (2019). Students’ positioning in transdisciplinary project-based learning. In interdisciplinarity and problem-based learning in higher education (pp. 117–132). Springer. https://doi.org/10.1007/978-3-030-18842-9_10.
Jalani, N. H., & Sern, L. C. (2015). The example-problem-based learning model: applying cognitive load theory. Procedia-Social and Behavioral Sciences, 195, 872–880. https://doi.org/10.1016/j.sbspro.2015.06.366.
Jensen, A. A., Stentoft, D., & Ravn, O. (2019). Interdisciplinarity and problem-based learning in higher education. Innovation and Change in Professional Education. https://doi.org/10.1007/978-3-030-18842-9.
Johnson, A.-A. (2016). The effect of project based learning on the academic achievement of at-risk advanced placement students. https://mdsoar.org/bitstream/handle/11603/2805/Johnson%2C Al-Amin Paper.pdf?sequence=1&isAllowed=y.
Kartikasari, A., & Widjajanti, D. B. (2017). The effectiveness of problem-based learning approach based on multiple intelligences in terms of student’s achievement, mathematical connection ability, and self-esteem. Journal of Physics: Conference Series, 812(1), 12097. https://doi.org/10.1088/1742-6596/812/1/012097.
Kim, J. Y., & Lim, K. Y. (2019). Promoting learning in online, ill-structured problem solving: The effects of scaffolding type and metacognition level. Computers & Education, 138, 116–129. https://doi.org/10.1016/j.compedu.2019.05.001.
Kim, N. J., Belland, B. R., & Axelrod, D. (2018). Scaffolding for optimal challenge in K-12 problem-based learning. The Interdisciplinary Journal of Problem-Based Learning. https://doi.org/10.7771/1541-5015.1712.
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. https://doi.org/10.1207/s15326985ep4102_1.
Könings, K. D., van Zundert, M., & van Merriënboer, J. J. G. (2019). Scaffolding peer-assessment skills: Risk of interference with learning domain-specific skills? Learning and Instruction, 60, 85–94. https://doi.org/10.1016/j.learninstruc.2018.11.007.
Lestari, W. (2017). Pengaruh kemampuan awal matematika dan motivasi belajar terhadap hasil belajar matematika. Jurnal Analisa, 3(1), 76–84. https://doi.org/10.15575/ja.v3i1.1499.
Ley, T., Kump, B., & Gerdenitsch, C. (2010). Scaffolding self-directed learning with personalized learning goal recommendations. International Conference on User Modeling, Adaptation, and Personalization, 75–86. https://doi.org/10.1007/978-3-642-13470-8_9.
Mann, L., Chang, R., Chandrasekaran, S., Coddington, A., Daniel, S., Cook, E., Crossin, E., Cosson, B., Turner, J., Mazzurco, A., & others. (2020). From problem-based learning to practice-based education: a framework for shaping future engineers. European Journal of Engineering Education, 1–21. https://doi.org/10.1080/03043797.2019.1708867.
Mudhiah, S., & Shodikin, A. (2019). Pengaruh model pembelajaran berbasis masalah terhadap kemampuan pemahaman konsep dan penalaran geometris siswa. Jurnal Elemen, 5(1), 43–53. https://doi.org/10.29408/jel.v5i1.974.
Nahdi, D. S., & Jatisunda, M. G. (2020). Conceptual understanding and procedural knowledge: a case study on learning mathematics of fractional material in elementary school. Journal of Physics: Conference Series, 1477, 42037. https://doi.org/10.1088/1742-6596/1477/4/042037.
Octaria, D., & Sari, E. F. P. (2018). Peningkatan self-efficacy mahasiswa melalui Problem Based Learning (PBL) pada mata kuliah program linier. Jurnal Elemen, 4(1), 66–79. https://doi.org/10.29408/jel.v4i1.496.
Park, M.-H., Tiwari, A., & Neumann, J. W. (2019). Emotional scaffolding in early childhood education. Educational Studies, 1–20. https://doi.org/10.1080/03055698.2019.1620692.
Phumeechanya, N., & Wannapiroon, P. (2014). Design of problem-based with scaffolding learning activities in ubiquitous learning environment to develop problem-solving skills. Procedia-Social and Behavioral Sciences, 116, 4803–4808. https://doi.org/10.1016/j.sbspro.2014.01.1028.
Prabawanto, S. (2017). The enhancement of students’ mathematical problem solving ability through teaching with metacognitive scaffolding approach. AIP Conference Proceedings, 1848(1), 40014. https://doi.org/10.1063/1.4983952.
Pucangan, A. A. S. N. A., Handayanto, S. K., & Wisodo, H. (2018). Pengaruh scaffolding konseptual dalam problem based learning terhadap kemampuan pemecahan masalah. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 3(10), 1314–1318.
Purwaningrum, D., & Sumardi, S. (2016). Efek strategi pembelajaran ditinjau dari kemampuan awal matematika terhadap hasil belajar matematika kelas XI IPS. Manajemen Pendidikan, 11(2), 155–167. https://doi.org/10.23917/jmp.v11i2.2862.
Renninger, K. A., Ray, L. S., Luft, I., & Newton, E. L. (2005). Coding online content-informed scaffolding of mathematical thinking. New Ideas in Psychology, 23(3), 152–165. https://doi.org/10.1016/j.newideapsych.2006.05.001.
Rosenshine, B. V, & Meister, C. (1992). The use of scaffolds for teaching less structured cognitive tasks. Educational Leadership, 49(7), 26–33.
Savery, J. R. (2015). Overview of problem-based learning: Definitions and distinctions. Essential Readings in Problem-Based Learning: Exploring and Extending the Legacy of Howard S. Barrows, 9, 5–15. https://doi.org/10.7771/1541-5015.1593.
Schwab, K. (2017). The fourth industrial revolution. World Economic Forum. www.weforum.org.
Sidney, P. G., & Alibali, M. W. (2015). Making connections in math: activating a prior knowledge analogue matters for learning. Journal of Cognition and Development, 16(1), 160–185. https://doi.org/10.1080/15248372.2013.792091.
Simons, K. D., & Ertmer, P. A. (2005). Scaffolding disciplined inquiry in problem-based environments. International Journal of Learning, 12(6), 297–305. https://doi.org/10.18848/1447-9494/CGP/v12i06/47900.
Simons, K. D., & Klein, J. D. (2007). The impact of scaffolding and student achievement levels in a problem-based learning environment. Instructional Science, 35(1), 41–72. https://doi.org/10.1007/s11251-006-9002-5.
Solaz-Portoles, J. J., & Sanjosé-López, V. (2009). Working memory in science problem solving: A review of research. Revista Mexicana de Psicolog{’i}a, 26(1), 79–90.
Star, J. R., Rittle-Johnson, B., Lynch, K., & Perova, N. (2009). The role of prior knowledge in the development of strategy flexibility: The case of computational estimation. ZDM, 41(5), 569–579. https://doi.org/10.1007/s11858-009-0181-9.
Strobel, J., & Van Barneveld, A. (2009). When is PBL more effective? A meta-synthesis of meta-analyses comparing PBL to conventional classrooms. Interdisciplinary Journal of Problem-Based Learning, 3(1), 44–58. https://doi.org/10.7771/1541-5015.1046.
Sumarmo, U. (2016). Pedoman pemberian skor pada beragam tes kemampuan matematik. Kelengkapan Bahan Ajar Mata Kuliah Evaluasi Pembelajaran Matematika Pada Program Magister Pendidikan Matematika STKIP Siliwangi: Tidak Diterbitkan.
Susanto, E., Rusdi, A. S., & others. (2020). Peningkatan kepercayaan diri mahasiswa dalam pembelajaranstatistika dasar melalui Problem Based-Learning. Jurnal THEOREMS (The Original Research of Mathematics), 4(2), 179–184. https://doi.org/10.31949/th.v4i2.1683.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4.
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 1–32. https://doi.org/10.1016/0364-0213(88)90023-7.
van de Pol, J., Volman, M., Oort, F., & Beishuizen, J. (2015). The effects of scaffolding in the classroom: support contingency and student independent working time in relation to student achievement, task effort and appreciation of support. Instructional Science, 43(5), 615–641. https://doi.org/10.1007/s11251-015-9351-z.
Van MerriëNboer, J. J. G. (2013). Perspectives on problem solving and instruction. Computers & Education, 64, 153–160. https://doi.org/10.1016/j.compedu.2012.11.025.
Van Merrienboer, J. J. G., Kester, L., & Paas, F. (2006). Teaching complex rather than simple tasks: Balancing intrinsic and germane load to enhance transfer of learning. Applied Cognitive Psychology: The Official Journal of the Society for Applied Research in Memory and Cognition, 20(3), 343–352. https://doi.org/10.1002/acp.1250.
Van Merriënboer, J. J. G., Kirschner, P. A., & Kester, L. (2003). Taking the load off a learner’s mind: Instructional design for complex learning. Educational Psychologist, 38(1), 5–13. https://doi.org/10.1207/S15326985EP3801_2.
Widyatiningtyas, R., Kusumah, Y. S., Sumarmo, U., & Sabandar, J. (2015). The impact of problem-based learning approach to senior high school students’ mathematics critical thinking ability. Indonesian Mathematical Society Journal on Mathematics Education, 6(2), 30–38. https://doi.org/10.22342/jme.6.2.2165.107-116.
Wilder, S. (2015). Impact of problem-based learning on academic achievement in high school: a systematic review. Educational Review, 67(4), 414–435. https://doi.org/10.1080/00131911.2014.974511.
Yew, E. H. J., & Goh, K. (2016). Problem-based learning: An overview of its process and impact on learning. Health Professions Education, 2(2), 75–79. https://doi.org/10.1016/j.hpe.2016.01.004.
Zwaal, W. (2019). Assessment for problem-based learning. Research in Hospitality Management, 9(2), 77–78. https://doi.org/10.1080/22243534.2019.1689696.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
