Sity Rahmy Maulida, Endah Retnowati, Fitria Mardika, Rozi Fitriza


This research examined: (1) the effectiveness of learning through a goal-free problem strategy compared with learning through a goal-given problem strategy with regard to transfer ability, reasoning, or cognitive load; (2) the effectiveness of learning collaboratively compared with learning individually with regard to transfer ability, reasoning, or cognitive load; and (3) interaction between learning strategy (goal-free or goal-given) and setting (collaborative or Individual) in terms of transfer ability, reasoning, or cognitive load. The experiment was conducted using a 2 (setting: collaborative vs. Individual) x 2 (strategy: goal-free vs. goal-given) factorial design; posttest-only control-group. The results of the data analysis supported hypothesis that the students who learned by goal-free problems strategy led to be better in terms of near and far transfer scores than students who learned by the goal-given strategy. The goal-free problems strategy was also proved to be more effective in terms of students' reasoning in near and far transfer tests rather than the goal-given problems strategy. Collaborative learning more effectively minimizes cognitive load during acquisition and near transfer test phase than students learn individually, also effectively facilitating students in terms of the near transfer only than students in individual learning. There was a significant interaction effect between the learning setting factor and strategy factor in terms of near transfer ability and reasoning in the near transfer test. Simple effect test showed that learning collaboratively by goal-given strategy was significantly more effective in terms of near transfer ability and students’ reasoning in the near transfer test, and learning individually by goal-free strategy was significantly more effective in terms of near transfer ability and students’ reasoning in near transfer test.


Goal-Free Problem; Cognitive Load; Collaborative Learning

Full Text:


DOI: https://doi.org/10.15548/mej.v6i2.4564
Abstract views : 368 times
PDF : 174 times


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(5), 370–376. https://doi.org/10.1016/j.sbspro.2010.12.052

Ayres, P. L. (1993). Why goal-free problems can facilitate learning. Contemporary Educational Psychology, 18(3), 376–381.

Ayres, P., & Sweller, J. (1990). Locus of difficulty in multistage mathematics problems. The American Journal of Psychology, 167–193.

Brodie, K. (2009). Teaching mathematical reasoning in secondary school classrooms. Springer Science & Business Media.

Buehner, M., Krumm, S., & Pick, M. (2005). Reasoning= working memory≠ attention. Intelligence, 33(3), 251–272.

Cindy, E. H. S. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235–266.

Clark, R. C., Nguyen, F., & Sweller, J. (2011). Efficiency in learning: Evidence-based guidelines to manage cognitive load. John Wiley & Sons.

Cresswell, J. W. (2013). Research design: qualitative, quantitative, and mixed methods aproaches (4th ed.). Sage Publication.

Hinsz, V. B., Vollrath, D. A., & Tindale, R. S. (1997). The emerging conceptualization of groups as information processors. Psychological Bulletin, 121(1), 43–64. https://doi.org/10.1037/0033-2909.121.1.43

Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: a response to Kirschner, Sweller, and. Educational Psychologist, 42(2), 99–107.

Kalyuga, S. (2007). Enhancing instructional efficiency of interactive e-learning environments: A cognitive load perspective. Educational Psychology Review, 19(3), 387–399. https://doi.org/10.1007/s10648-007-9051-6

Kirschner, F., Paas, F., & Kirschner, P. A. (2009). A cognitive load approach to collaborative learning: United brains for complex tasks. Educational Psychology Review, 21(1), 31–42. https://doi.org/10.1007/s10648-008-9095-2

Kyllonen, P. C., & Christal, R. E. (1990). Reasoning ability is (little more than) working-memory capacity?! Intelligence, 14(4), 389–433.

Mamede, S., Schmidt, H. G., & Norman, G. R. (2006). Innovations in problem-based learning: What can we learn from recent studies? Advances in Health Sciences Education, 11(4), 403–422. https://doi.org/10.1007/s10459-006-9018-2

Nazir, M. (2014). Metode penelitian. Ghalia Indonesia.

Oberauer, K., Süß, H. M., Wilhelm, O., & Wittman, W. W. (2003). The multiple faces of working memory: Storage, processing, supervision, and coordination. Intelligence, 31(2), 167–193. https://doi.org/10.1016/S0160-2896(02)00115-0

Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77(3), 272.

Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1–4.

Paas, F., Renkl, A., & Sweller, J. (2004). Cognitive load theory: Instructional implications of the interaction between information structures and cognitive architecture. Instructional Science, 321/2, 1–8.

Paas, Fred, van Gog, T., & Sweller, J. (2010). Cognitive load theory: New conceptualizations, specifications, and integrated research perspectives. Educational Psychology Review, 22(2), 115–121. https://doi.org/10.1007/s10648-010-9133-8

Raaijmakers, S. F., Baars, M., Schaap, L., Paas, F., & Van Gog, T. (2017). Effects of performance feedback valence on perceptions of invested mental effort. Learning and Instruction, 51, 36–46.

Retnowati, E., Ayres, P., Sweller, J., Retnowati, E., Ayres, P., & Sweller, J. (2016). Journal of Educational Psychology Can Collaborative Learning Improve the Effectiveness of Worked Examples in Learning Mathematics ? Can Collaborative Learning Improve the Effectiveness of Worked Examples in Learning Mathematics ? Journal of Educational Psychology. http://dx.doi.org/10.1037/edu0000167

Retnowati, E. S., & Murdanu. (2015). Efektivitas Goal-Free Problems Dalam Pembelajaran Matematika Kolaboratif Ditinjau Dari Muatan Kognitif dan Kemampuan Transfer Pengetahuan. Yogyakarta State University.

Sweller, J., Ayres, P., & Kalyuga, S. (2011). Measuring cognitive load. In Cognitive load theory (pp. 71-85). Springer, New York, NY.

Sweller, John. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1016/0364-0213(88)90023-7

Watson, J. M., & Moritz, J. B. (2001). Development of reasoning associated with pictographs: Representing, interpreting, and predicting. Educational Studies in Mathematics, 48(1), 47–81.

Webb, N. M. (2009). The teacher’s role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 79(1), 1–28. https://doi.org/10.1348/000709908X380772

Wirth, J., & Leutner, D. (2008). Self-regulated learning as a competence: Implications of theoretical models for assessment methods. Zeitschrift Für Psychologie/Journal of Psychology, 216(2), 102.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Ruang Jurnal Program Studi Tadris Matematika
Fakultas Tarbiyah dan Keguruan
Universitas Islam Negeri Imam Bojol Padang
email: mej.uinibpadang@gmail.com


Lisensi Creative Commons
Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi-NonKomersial 4.0 Internasional.