### Fostering Germane Load Through Self-Explanation Prompting In Calculus Instruction

Cecep Anwar Hadi Firdos Santosa^{(1*)}, Sufyani Prabawanto

^{(2)}, Indiana Marethi

^{(3)}

(1) Universitas Sultan Ageng Tirtayasa

(2) Indonesia University of Education

(3) Universitas Sultan Ageng Tirtayasa

(*) Corresponding Author

#### Abstract

The purpose of this research was to investigate the effect of self-explanation prompting to students’ germane load while studying mathematics in the multivariable calculus course. This research employed a quasi-experimental method with matching-only posttest-only control group design. The subject of the research consists of 72 first-year mathematics education undergraduate students. The results indicated that there was no significant difference in students’ germane load between students who implemented worked-example with self-explanation prompting and students who implemented worked-example without self-explanation prompting. However, it was revealed that the students' germane load was categorized high in both classes. It indicates that the worked-example method could foster students' germane load. Nonetheless, these results cannot be evidence that self-explanation prompting is capable to foster students' germane load. However, there is an association between germane load and learning objectives. When students achieve the learning objectives, then its learning method is able to foster the germane load. To assess the learning objectives, the posttest was arranged. The results stated that students who implemented the worked-example method with self-explanation prompting had better test scores than students who implemented the worked-example method without self-explanation prompting. This result was sufficient to provide evidence that the use of worked-example with self-explanation prompting could foster students’ germane load students in the multivariable calculus course.

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Baddeley, A. (1992). Working Memory. Science, 255, 556–559.

Baddeley, A. (2003). Working memory: looking back and looking forward. Nature Reviews. Neuroscience, 4(10), 829–39.

Baddeley, A. (2010, March 23). Working memory. Current Biology, 20(4), 136–140.

Baddeley, A. (2012). Working memory: theories, models, and controversies. Annual Review of Psychology, 63, 1–29.

Berthold, K., Röder, H., Knörzer, D., Kessler, W., & Renkl, A. (2011). The double-edged effects of explanation prompts. Computers in Human Behavior, 27(1), 69–75.

Bokosmaty, S., Sweller, J., & Kalyuga, S. (2015). Learning Geometry Problem Solving by Studying Worked Examples: Effects of Learner Guidance and Expertise. American Educational Research Journal, 52(2), 307–333.

Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24–34.

Clark, R. C., Nguyen, F., & Sweller, J. (2011). Efficiency in Learning; Evidence-Based Guidlines to Manage Cognitive Load. New York: John Wiley and Son Ltd.

Debue, N., & Leemput, C. van de. (2014). What does germane load mean? An empirical contribution to the cognitive load theory. Frontiers in Psychology, 5(October), 1–12.

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to Design and Evaluate Research in Education (8th ed.). New York: McGraw-Hill.

Hausmann, R. G. M., Nokes, T. J., VanLehn, K., & Gershman, S. (2009). The Design of Self-explanation Prompts : The Fit Hypothesis. In 31st Annual Conference of the Cognitive Science Society Cognitive Science (pp. 2626–2631).

Hefter, M. H., Renkl, A., Riess, W., Schmid, S., Fries, S., & Berthold, K. (2015). Effects of a training intervention to foster precursors of evaluativist epistemological understanding and intellectual values. Learning and Instruction, 39, 11–22.

Hodds, M., Alcock, L., & Inglis, M. (2014). Self-Explanation Training Improves Proof Comprehension. Journal for Research in Mathematics Education, 45(1), 62–101.

Hu, F.-T., Ginns, P., & Bobis, J. (2015). Getting the point: Tracing worked examples enhances learning. Learning and Instruction, 35, 85–93.

Jamieson, S. (2004). Likert scales: how to (ab)use them. Medical Education, 38, 1212–1218.

Job, P., & Schneider, M. (2014). Empirical positivism, an epistemological obstacle in the learning of calculus. ZDM - International Journal on Mathematics Education, 46(4), 635–646.

Kalyuga, S. (2011). Cognitive Load Theory: How Many Types of Load Does It Really Need? Educational Psychology Review, 23(1), 1–19.

Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Procedia - Social and Behavioral Sciences, 8(5), 173–180.

Khateeb, M. (2008). Cognitive Load Theory and Mathematics Education. (Thesis). University of New South Wales.

Leahy, W., & Sweller, J. (2008). The Imagination Effect Increases with an Increased Intrinsic Cognitive Load. Applied Cognitive Psychology, 22(2008), 273–283.

Martínez-Planell, R., Gonzalez, A. C., DiCristina, G., & Acevedo, V. (2012). Students’ conception of infinite series. Educational Studies in Mathematics, 81(2), 235–249.

Mattys, S. L., Barden, K., & Samuel, A. G. (2014). Extrinsic cognitive load impairs low-level speech perception. Psychonomic Bulletin and Review, 21(3), 748–754.

Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63(2), 81–97.

Moore, R. C. (1994). Making the Transition to Formal Proof. Journal of Educational Studies in Mathematics, 27, 249–266.

Moru, E. K. (2009). Epistemological obstacles in coming to understand the limit of a function at undergraduate level: A case from the national university of lesotho. International Journal of Science and Mathematics Education.

Norman, G. (2010). Likert scales, levels of measurement and the “laws.” Advance in Health Science Education, 15, 625–632.

Nursyahidah, F., & Albab, I. U. (2017). Investigating Student Difficulties on Integral Calculus Based on Critical Thinking Aspects. Jurnal Riset Pendidikan Matematika, 4(2), 211–218.

Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics.

Paas, F., & Gog, T. Van. (2006). Optimising worked example instruction : Different ways to increase germane cognitive load. Learning and Instruction, 16(411), 87–91.

Paas, F., & Kester, L. (2006). Learner and information characteristics in the design of powerful learning environments. Applied Cognitive Psychology, 20(3), 281–285.

Peterson, L. R., & Peterson, M. J. (1959). Journal of Experimental Psychology, 58(3), 193–198.

Purcell, E. J., Varberg, D., & Rigdon, S. E. (2007). Calculus (9th Editio). New Jersey: Prentice-Hall Inc.

Rau, M. a, Aleven, V., & Rummel, N. (2015). Successful Learning With Multiple Graphical Representations and Self-Explanation Prompts. Journal of Educational Psychology, 107(1), 30–46.

Renkl, A. (2017). Learning from worked-examples in mathematics: students relate procedures to principles. ZDM, 1–14.

Retnowati, E., Ayres, P., & Sweller, J. (2010). Worked example effects in individual and group work settings. Educational Psychology, 30(February 2015), 349–367.

Rittle-Johnson, B., Loehr, A. M., & Durkin, K. (2017). Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. Zdm, 0(0123456789), 0.

Roelle, J., Hiller, S., Berthold, K., & Rumann, S. (2017). Example-based learning: The benefits of prompting organization before providing examples. Learning and Instruction, 49, 1–12.

Rourke, A., & Sweller, J. (2009). The worked-example effect using ill-defined problems: Learning to recognise designers’ styles. Learning and Instruction, 19(2), 185–199.

Salden, R. J. C. M., Koedinger, K. R., Renkl, A., Aleven, V., & McLaren, B. M. (2010). Accounting for Beneficial Effects of Worked Examples in Tutored Problem Solving. Educational Psychology Review, 22(4), 379–392.

Santosa, C. A. H. F. (2013). Mengatasi Kesulitan Mahasiswa ketika Melakukan Pembuktian Matematis Formal. Jurnal Pengajaran MIPA, 18(2), 152–160.

Santosa, C. A. H. F., Suryadi, D., & Prabawanto, S. (2016). Pengukuran efisiensi kognitif matematis di perguruan tinggi. In Seminar Nasional Matematika dan Pendidikan Matematika. Cirebon: Fakultas Keguruan dan Ilmu Pendidikan, Universitas Swadaya Gunung Jati.

Santosa, C. A. H. F., Suryadi, D., Prabawanto, S., & Syamsuri. (n.d.). The role of worked-example in enhancing students’ self-explanation and cognitive efficiency in calculus instruction. Jurnal Riset Pendidikan Matematika.

Stewart, J. (2012). Calculus. (L. Covello, L. Neustaetter, J. Staller, & M. Ross, Eds.) (Seventh Ed). Belmont: Brooks/Cole.

Sweller, J. (2008). Human Cognitive Architecture. In J. M. Spector, M. D. Merril, J. J. G. van Merriënboer, & M. P. Driscoll (Eds.), Handbook of Research on Educational Communications and Technology (pp. 369–381). New York: Lawrence Erlbaum Associates.

Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22(2), 123–138.

Sweller, J. (2011). Cognitive Load Theory. In J. P. Mestre & B. H. Ross (Eds.), The Psychology of Learning and Cognition in Education (pp. 37–74). Waltham: Elsevier.

Sweller, J., & Sweller, S. (2006). Natural information processing systems. Evolutionary Psychology, 4, 434–458.

Tall, D. (2008). The Transition to Formal Thinking in Mathematics, 20(2), 5–24.

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.

Van Loon-Hillen, N., Van Gog, T., & Brand-Gruwel, S. (2012). Effects of worked examples in a primary school mathematics curriculum. Interactive Learning Environments, 20(1), 89–99.

Yanuarto, W. N. (2016). Students ’ Awareness on Example and Non-Example Learning in Geometry Class. International Electronic Journal Of Mathematics Education, 11(10), 3511–3519.

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