Email this article 
LEARNING GOAL-FREE PROBLEMS: COLLABORATIVELY OR INDIVIDUALLY?
Endah Retnowati, Universitas Negeri Yogyakarta, Indonesia
Paul Ayres, University of New South Wales, Australia
Murdanu Murdanu, Universitas Negeri Yogyakarta, Indonesia
Abstract
Goal-free is a learning strategy to present a problem without specific questions, in contrary to a goal-given problem. This research examined the goal-free effects during mathematics collaborative learning measured by cognitive load ratings and transfer performance. An experiment was conducted in authentic mathematics classrooms employing a factorial design with 2 problem presentations (goal-free vs. goal-given problems) ´ 2 learning environments (collaboratively vs. individually) using a Geometry topic. This consisted of four consecutive phases: introductory, acquisition, near and far transfer tests. 111 seventh graders (Average: 12.8 y.o.) who were novices, participated voluntary. The findings showed that students who learned by goal-free problems had significantly higher far-transfer scores than when the goal was given. Interestingly, in the acquisition phase, the students in goal-free problems experienced significantly higher cognitive load than their counterparts. Further, it was found that overall, individuals scored significantly higher in a far-transfer test than those who learned collaboratively; however, during the acquisition phase individuals experienced significantly higher cognitive load than collaborative learning. No pattern of interaction effects was indicated. Overall, it was concluded that goal-free problems may be learned either collaborativelly or individually. Nevertheless, the goal-free problems stimulated higher cognitive load during learning, which seemed to have a positive influence.
Keywords
Full Text:
PDFReferences
Ayres, P. (2006). Impact of reducing intrinsic cognitive load on learning in a mathematical domain. Applied Cognitive Psychology, 20(3), 287-298. doi:10.1002/acp.1245.
Ayres, P. (1993). Why goal-free problems can facilitate learning. Contemporary Educational Psychology, 18(3), 376-381. doi:10.1006/ceps.1993.1027.
Ayres, P., & Sweller, J. (1990). Locus of difficulty in multistage mathematics problems. American Journal of Psychology, 103(2), 167-193. doi:10.2307/1423141.
Bhowmick, S., Chandra, A., Harper, J. S., & Sweetin, V. (2015). Collaborative learning using a project across multiple business courses: A cognitive load and knowledge convergence approach. Decision Sciences Journal of Innovative Education, 13(2), 197-219. doi:10.1111/dsji.12060
Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347-362. doi:10.1037/0022-0663.79.4.347.
Cowan, N. (2000). The magical number 4 in short-termmemory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–185. doi: 10.1017/s0140525x01003922.
Daniels, H. (2001). Vygotsky and pedagogy. London and New York: Routledge Falmer.
Hesse, F., Care, E., Buder, J., Sassenberg, K., & Griffin, P. (2014). A framework for teachable collaborative problem solving skills. In P. Griffin & E. Care (Eds.), Assessment and teaching of 21st century skills (pp. 37-56). Dordrecht: Springer Science+Business Media. doi:10.1007/978-94-017-9395-7_2.
Hung, W. (2013). Team-based complex problem solving: A collective cognition perspective. Educational Technology Research and Development, 61(3), 365-384. doi:10.1007/s11423-013-9296-3.
Johnson, D. W., & Johnson, R. T. (2002). Learning together and alone: Overview and meta-analysis. Asia Pacific Journal of Education, 22(1), 95-105. doi:10.1080/0218879020220110
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. doi:10.1207/s15326985ep4102_1.
Mayer, R. (1999). The promise of educational psychology: Teaching for meaningful learning (Vol. 2). USA: Merill - Prentice Hall.
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. doi:10.1037/h0043158
Paas, F., Renkl, A., & Sweller, J. (2004). Cognitive load theory: Instructional implications of the interaction between information structures and cognitive architecture. Instructional Science, 32(1-2), 1-8. doi:10.1023/B:TRUC. 0000021806. 17516.d0.
Paas, F., Tuovinen, J. E., van Merrienboer, J., & Darabi, A. (2005). A motivational perspective on the relation between mental effort and permormance: Optimizing learner involvement in instruction. Educational Tecnology, Research and Development, 53(3), 25-35. doi:10.1007/BF02504795.
Retnowati, E. (2009). Toward the improvement of group learning using goal-free problems. Proceedings International Seminar on Education: Responding to Global Education Challenges, 248-261.
Retnowati, E., Ayres, P., & Sweller, J. (2016). Can collaborative learning improve the effectiveness of worked examples in learning mathematics? Journal of Educational Psychology, 109(5), 666-679. doi:10.1037/edu0000167.
Retnowati, E., Ayres, P., & Sweller, J. (2018). Collaborative learning effects when students have complete or incomplete knowledge. Applied Cognitive Psychology, 32(6), 681-692. doi:10.1002/acp.3444.
Retnowati, E., Fathoni, Y., & Chen, O. (2018). Mathematics problem solving skill acquisition: Learning by Problem Posing or by Problem Solving? Cakrawala Pendidikan, 37(1), 1-10. doi:10.21831/cp.v37i1.18787
Sweller, J. (2009). Cognitive basis of human creativity. Educational Psychology Review, 21(1), 11-19. doi:10.1007/s10648-008-9091-6.
Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22(2), 123- 138. doi:10.1007/s10648-010-9128-5.
Sweller, J. (2004). Instructional design consequences of an analogy between evolution by natural selection and human cognitive architecture. Instructional Science, 32(1-2), 9-31. doi:10.1023/B:TRUC.0000021808.72598.4d.
Sweller, J., & Chandler, P. (1994). Why some material is difficult to learn? Cognition and Instruction, 12(3), 185-233. doi:10.1207/s1532690xci1203_1.
Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. New York, NY: Springer. doi:10.1007/978-1-4419-8126-4
Sweller, J., van Merrienboer, J. J., & Paas, F. G. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251-296. doi:10.1023/A:1022193728205.
Sweller, J., van Merrienboer, J. J. G. & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31 (2), 261-292. doi:10.1007/s10648-019-09465-5.
van Gog, T., & Paas, F. (2008). Instructional efficiency: Revisiting the original construct in educational research. Educational Psychologist, 43(1), 16-26. doi:10.1080/00461520701756248.
Webb, N. M., & Mastergeorge, A. (2003). Promoting effective helping behavior in peer-directed group. International Journal of Educational Research, 39(1-2), 73-97. doi:10.1016/S0883-0355(03)00074-0.
Youssef-Shalala, A., Ayres, P., Schubert, C., & Sweller, J. (2014). Using a general-problem solving strategy to promote transfer. Journal of Experimental Psychology: Applied, 20(3), 215-231. doi:10.1037/xap0000021.
DOI: https://doi.org/10.21831/cp.v38i3.26914
Refbacks
- There are currently no refbacks.
Social Media:
Jurnal Cakrawala Pendidikan by Lembaga Pengembangan dan Penjaminan Mutu Pendidikan UNY is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://journal.uny.ac.id/index.php/cp/index.
