Jurnal Riset Pendidikan Matematika


self-explanation, mathematical cognitive efficiency, mental effort, worked-example.

Document Type



This research was aimed to investigate the effect of students' self-explanation to their achievement, mental effort, and cognitive efficiency while studying mathematics, particularly in integral topics. This research used a static-group comparison design implemented to first-year undergraduate students. The subject of the study consists of 64 first year undergraduate students in one of the universities in Banten province, Indonesia. The students were divided into two classrooms, experimental and control. Experimental classroom received worked-example method whereas control classroom studying without worked-example method. Instruments used in this research include achievement tests, rating scale mental effort, deviation model of cognitive efficiency, and teaching materials in the form of worked-example. The results show that the implementation of self-explanation through worked-example helps students get a higher achievement, lower mental effort, and better cognitive efficiency compared to students who get instruction without worked-example method. The research also reveals the important role of worked-example in enhancing the ability of students' self-explanation.

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Almeida, D. (2003). Engendering proof attitudes : can the genesis of mathematical knowledge teach us anything? International Journal of Mathematical Education in Science and Technology, 34(4), 479-488. doi:http://doi.org/10.1080/0020739031000108574

Ayres, P., & Paas, F. (2012). Cognitive load theory: new directions and challenges. Applied Cognitive Psychology, 26(6), 827-832. doi:http://doi.org/10.1002/acp.2882

Baddeley, A. (1992). Working memory. Science, 255, 556-559. doi:http://doi.org/10.1126/science.1736359

Baddeley, A. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology, 49(1), 5-28.

Baddeley, A. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417-423. http://doi.org/10.1016/S1364-6613(00)01538-2

Baddeley, A. (2003). Working memory: Looking back and looking forward. Nature Reviews: Neuroscience, 4(10), 829-39. doi:http://doi.org/10.1038/nrn1201

Baddeley, A. (2010). Working memory. Current Biology, 20(4), 136-140. http://doi.org/10.1016/j.cub.2009.12.014

Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63, 1-29. doi:http://doi.org/10.1146/annurev-psych-120710-100422

Baddeley, A. D., & Larsen, J. D. (2007). The phonological loop: Some answers and some questions. The Quarterly Journal of Experimental Psychology, 60(4), 512-518. doi:http://doi.org/10.1080/17470210601147663

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. doi:http://doi.org/10.3102/0002831214549450

Cohen, D. (1995). Crossroads in mathematics: Standards for introductory college mathematics before calculus. Memphis, TN: AMATYC, State Technical Institute at Memphis.

Durkin, K. (2011). The self-explanation effect when learning mathematics: A meta-analysis. In Conference on Building and Educatioan Science: Investigating Mechanisms (pp. 1-5). Washington, DC: Society for Research on Educational Effectivenss Spring 2011.

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York, NY: McGraw-Hill.

Fukawa-Connelly, T. (2012). Classroom sociomathematical norms for proof presentation in undergraduate in abstract algebra. The Journal of Mathematical Behavior, 31(3), 401-416. doi:http://doi.org/10.1016/j.jmathb.2012.04.002

Harel, G., & Kaput, J. (2002). The role of conceptual entities and their symbols in building advance mathematical concepts. In D. Tall (Ed.), Advanced mathematical thinking (pp. 83-94). New York, NY: Kluwer Academic Publisher.

Hodds, M., Alcock, L., & Inglis, M. (2014). Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 45(1), 62-101. doi:http://doi.org/10.5951/jresematheduc.45.1.0062

Hoffman, B. (2012). Cognitive efficiency: A conceptual and methodological comparison. Learning and Instruction, 22(2), 133-144. doi:http://doi.org/10.1016/j.learninstruc.2011.09.001

Hsu, H.-Y., & Silver, E. A. (2014). Cognitive complexity of mathematics instructional tasks in a Taiwanese classroom: An examination of task sources. Journal for Research in Mathematics Education, 45(4), 460-496. doi:http://doi.org/10.5951/jresematheduc.45.4.0460

Inam, A. (2016). Euclidean geometry's problem solving based on metacognitive in aspect of awareness. International Electronic Journal of Mathematics Education, 11(7), 2319-2331.

Intaros, P., Inprasitha, M., & Srisawadi, N. (2014). Students' problem solving strategies in problem solving-mathematics classroom. Procedia - Social and Behavioral Sciences, 116, 4119-4123. doi:http://doi.org/10.1016/j.sbspro.2014.01.901

Kalyuga, S. (2011). Cognitive load theory: How many types of load does it really need? Educational Psychology Review, 23(1), 1-19. doi:http://doi.org/10.1007/s10648-010-9150-7

Khateeb, M. (2008). Cognitive load theory and mathematics education (Unpub;ished master's theses). University of New South Wales, New South Wales.

Kline, R. B. (2011). Principles and practice of structural equation modelling (3rd ed.). New York, NY: Guilford Press.

Kyungbin, K., Kumalasari, C. D., & Howland, J. L. (2011). Self-explanation prompts on problem-solving performance in an interactive learning environment. Journal of Interactive Online Learning, 10(2), 96-112.

Lockwood, E., Ellis, A. B., & Lynch, A. G. (2016). Mathematicians' example-related activity when exploring and proving conjectures. International Journal of Research in Undergraduate Mathematics Education, 2(2), 165-196. doi:http://doi.org/10.1007/s40753-016-0025-2

Lopez, O. S. (2007). Classroom diversification: a strategic view of educational productivity. Review of Educational Research, 77(1), 28-80.

McCrory, R., & Stylianides, A. J. (2014). Reasoning and proving in mathematics textbooks for prospective elementary teachers. International Journal of Educational Research, 64, 119-131. doi:http://doi.org/10.1016/j.ijer.2013.09.003

Miller, S. (2001). Workload measures. Iowa City, IA: National Advanced Driving Simulator.

Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27, 249-266. doi:http://doi.org/10.1007/BF01273731

NCTM. (2009). Focus in high school mathematics: reasoning and sense making. Reston, VA: Author. doi: http://doi.org/10.5951/mathteacher.106.8.0635

Norman, G. (2010). Likert scales, levels of measurement and the "laws." Advance in Health Science Education, 15, 625-632. Retrieved from http://www.fammed.ouhsc.edu/research/FMSRE%25

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. doi:http://doi.org/http://dx.doi.org/10.21831/jrpm.v4i2.15507

Paas, F. G. W. C., & Merrienboer, J. J. G. van. (1994). Instructional control of cognitive load in the training of complex cognitive tasks. Educational Psychology Review, 6(4), 351-371.

Paas, F. G. W. C., & Merrienboer, J. J. G. van. (1993). The efficiency of instructional conditions: an approach to combine mental effort and performance measures. Human Factors, 35(4), 737-743.

Pachman, M., Sweller, J., & Kalyuga, S. (2014). Effectiveness of combining worked examples and deliberate practice for high school geometry. Applied Cognitive Psychology, 28, 685-692. doi:http://doi.org/10.1002/acp.3054

Rach, S., & Heinze, A. (2016). The transition from school to university in mathematics: which influence do school-related variables have? International Journal of Science and Mathematics Education, 1-21. doi:http://doi.org/10.1007/s10763-016-9744-8

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. doi:http://doi.org/10.1037/a0037211

Rukavina, S., Zuvic-butorac, M., Ledic, J., Milotic, B., & Jurdana-sepic, R. (2012). Developing positive attitude towards science and mathematics through motivational classroom experiences. Science Education International, 23(1), 6-19.

Santosa, C. A. H. F. (2013). Mengatasi kesulitan mahasiswa ketika melakukan pembuktian matematis formal. Jurnal Pengajaran MIPA, 18(2), 152-160. Retrieved from http://journal.fpmipa.upi.edu/index.php/jpmipa/article/viewFile/3/3

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.

Schmeck, A., Opfermann, M., Gog, T. van, Paas, F., & Leutner, D. (2015). Measuring cognitive load with subjective rating scales during problem solving : Differences between immediate and delayed ratings. Instructional Science, 43(1), 93-114. doi:http://doi.org/10.1007/s11251-014-9328-3

Sriraman, B. (2004). The characteristics of mathematical creativity. Mathematics Educator, 14(1), 19-34.

Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. doi:http://doi.org/10.3102/00028312033002455

Stylianides, G. J. (2014). Textbook analyses on reasoning and proving: significance and methodological challenges. International Journal of Educational Research, 64, 63-70. doi:http://doi.org/10.1016/j.ijer.2014.01.002

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, NY: Lawrence Erlbaum Associates.

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). Oxford, UK: Academic Press.

Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory: explorations in the learning sciences, instructional systems and performance technologies. London, UK: Springer.

Syamsuri, Purwanto, Subanji, & Irawati, S. (2017). Using APOS theory framework: Why did students unable to construct a formal proof? International Journal on Emerging Mathematics Education, 1(2), 135-146. doi:http://doi.org/http://dx.doi.org/10.12928/ijeme.v1i2.5659

Syamsuri, & Santosa, C. A. H. F. (2017). Karakteristik pemahaman mahasiswa dalam mengonstruksi bukti matematis. Jurnal Review Pembelajaran Matematika, 2(2). 131-143.

Tall, D. (2011). Perceptions, operations and proof in undergraduate mathematics. The De Morgan Journal, 1(1), 19-27.

Tuovinen, J. E., & Paas, F. (2004). Exploring multidimensional approaches to the efficiency of instructional conditions. Instructional Science, 32, 133-152. doi:http://doi.org/10.1023/B:TRUC.0000021813.24669.62

White, P., & Mitcelmore, M. (1996). Conceptual knowledge in introductory calculus. Journal for Research in Mathematics Education, 79-95.

Widyanti, A., Johnson, A., & Waard, D. De. (2010). Pengukuran beban kerja mental dalam searching task dengan metode rating scale mental effort (RSME). J@ti Undip: Jurnal Teknik Industri, V(1), 1-6.

Wilhelm, A. G. (2015). Mathematics teachers' enactment of cognitively demanding tasks: investigating links to teachers' knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636-674.