The Compound Area of Quadrilaterals and Triangles: A Worked Example Based Learning Design
DOI:
https://doi.org/10.31764/jtam.v7i1.11678Keywords:
Worked example, Compound area, Cognitive load.Abstract
Complex yet hierarchical mathematical material in fact does not mean that the process of schema acquisition and accommodation in long-term memory is easy. For an instance, year seven students learn to solve problems related to the compound area of quadrilaterals and triangles. This problem may be categorized as a well-structured problem, therefore, it might be procedurally obvious to reach the solution, for those who have possessed sufficient prior knowledge of the aspects of the shapes. This study aims to discuss instructional strategy for novices when learning to solve problems like these. Based on a cognitive load theory, the strategy of worked example could be applied effectively for novices. The design of the worked example must be presented in such a way it could minimize extraneous cognitive load. The composite shapes of quadrilateral and triangles might be challenging to be described in an integrated format to avoid the split attention effect. This paper shows how this can be done by using techniques, such as (1) number sequences of the solution steps; (2) different colors for prompting attention resource; (3) less wording, more procedure application; and (4) consistency of layout within overall material. In order to apply these, the instructional designers should follow ADD steps, (1) Analyze the learning content, arrange them accordingly; (2) Design one worked example, evaluate its accuracy and niche; and (3) Develop into several worked example pairs. Two worked example with paired problems have been successfully developed and declare valid. Eventually, it might be suggested that comprehensive consideration when designing worked example that contain pictures should reflects how students use their cognitive resource during learning.References
Ayres, P., & Sweller, J. (2012). The split-attention principle in multimedia learning. In The Cambridge Handbook of Multimedia Learning (Second Edi, pp. 206–226). Cambridge University Press. https://doi.org/10.1017/CBO9781139547369.011
Azizah, N., & Retnowati, E. (2017). Desain Worked Example untuk Mengajarkan Matematika pada Siswa Disabilitas Netra. Seminar Matematika Dan Pendidikan Matematika Uny, 517–524. http://seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/full/M-76.pdf
Cardellini, L. (2014). Problem solving: How can we help students overcome cognitive difficulties. Journal of Technology and Science Education, 4(4), 237–249. https://doi.org/10.3926/jotse.121
Chen, O., Castro-Alonso, J. C., Paas, F., & Sweller, J. (2018). Undesirable difficulty effects in the learning of high-element interactivity materials. Frontiers in Psychology, 9(1483), 1–7. https://doi.org/10.3389/fpsyg.2018.01483
Chen, O., & Kalyuga, S. (2020). Cognitive Load Theory, Spacing Effect, and Working Memory Resources Depletion: Implications for Instructional Design. In Form, Function, and Style in Instructional Design: Emerging Research and Opportunities (pp. 1–25). IGI Global.
Kalyuga, S. (2010). Schema acquisition and sources of cognitive load. Cognitive Load Theory, 48–64. https://doi.org/10.1017/CBO9780511844744.005
Kalyuga, S. (2011). Cognitive Load Theory: How Many Types of Load Does It Really Need? Educational Psychology Review, 23(1), 1–19. https://doi.org/10.1007/s10648-010-9150-7
Kim, Y. R. (2013). Effects of Worked Examples on Far Transfer. In Foreign Affairs (Vol. 91, Issue 5). University of North Carolina.
Manson, E., & Ayres, P. (2021). Investigating how errors should be flagged and worked examples structured when providing feedback to novice learners of mathematics. Educational Psychology, 41(2), 153–171. https://doi.org/10.1080/01443410.2019.1650895
Paas, F., Tuovinen, J. E., Tabbers, H., & Van Gerven, P. W. M. (2010). Cognitive load measurement as a means to advance cognitive load theory. Educational Psychologist, 38(1), 63–71. https://doi.org/10.1207/S15326985EP3801_8
Paas, F., & van Merriënboer, J. J. G. (2020). Cognitive-Load Theory: Methods to Manage Working Memory Load in the Learning of Complex Tasks. Current Directions in Psychological Science, 29(4), 394–398. https://doi.org/10.1177/0963721420922183
Renkl, A. (2014). Toward an instructionally oriented theory of example-based learning. Cognitive Science, 38(1), 1–37. https://doi.org/10.1111/cogs.12086
Renkl, A., & Atkinson, R. K. (2010). Learning from worked-out examples and problem solving. In Cognitive Load Theory (pp. 89–108). United States of America by Cambridge University Press. https://doi.org/10.1017/CBO9780511844744.007
Retnowati, E., & Marissa. (2018). Designing worked examples for learning tangent lines to circles. Interbational Conference on Mathematics, Science and Education, 983(1). https://doi.org/10.1088/1742-6596/983/1/012124
Retnowati, Endah. (2014). Psychology of mathematics learning: Constructing knowledge. In UNY Press. UNY Press. http://staff.uny.ac.id/sites/default/files/lain-lain/endah-retnowati-spd-med-phd/book1psychology-math-learningedit1.pdf
Retnowati, Endah, Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(3), 349–367. https://doi.org/10.1080/01443411003659960
Rodiawati, A., & Retnowati, E. (2019). How to Design Worked Examples for Learning Patterns in Mathematics. Journal of Physics: Conference Series, 1320(1). https://doi.org/10.1088/1742-6596/1320/1/012045
Rohman, H. M. H., & Retnowati, E. (2018). How to teach geometry theorems using worked examples: A cognitive load theory perspective. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012104
Sweller, J. (2011). Cognitive Load Theory. In H. G. Bower (Ed.), Psychology of Learning and Motivation: Advances in Research and Theory (1st ed., Vol. 55, pp. 37–76). Elsevier Inc. https://doi.org/10.1016/B978-0-12-387691-1.00002-8
Sweller, J. (2019). Cognitive load theory and educational technology. Educational Technology Research and Development, 68(1), 1–16. https://doi.org/10.1007/s11423-019-09701-3
Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive Load Theory, Explorations in the learning sciences, instructional systems and performance technologies. In Recenti Progressi in Medicina (Vol. 82, Issue 1). Springer Science+Business Media. http://www.springer.com/series/8640
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019a). Cognitive Architecture and Instructional Design: 20 Years Later. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019b). Cognitive Architecture and Instructional Design: 20 Years Later. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
van Gog, T., Kester, L., & Paas, F. (2011). Effects of worked examples, example-problem, and problem-example pairs on novices’ learning. Contemporary Educational Psychology, 36(3), 212–218. https://doi.org/10.1016/j.cedpsych.2010.10.004
Van Merriënboer, J. J. G., & Sweller, J. (2005). Cognitive load theory and complex learning: Recent developments and future directions. In Educational Psychology Review (Vol. 17, Issue 2). https://doi.org/10.1007/s10648-005-3951-0
Widyastuti, B. W., & Retnowati, E. (2021). Effects of Worked Example on Experts’ Procedural Skills in Solving Geometry Problems. Proceedings of the 7th International Conference on Research, Implementation, and Education of Mathematics and Sciences (ICRIEMS 2020), 528(Icriems 2020), 338–343. https://doi.org/10.2991/assehr.k.210305.049
Wirzberger, M., Herms, R., Esmaeili Bijarsari, S., Eibl, M., & Rey, G. D. (2018). Schema-related cognitive load influences performance, speech, and physiology in a dual-task setting: A continuous multi-measure approach. Cognitive Research: Principles and Implications, 3(1). https://doi.org/10.1186/s41235-018-0138-z
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