To promote student learning in a relearning situation in university-level mathematics, we developed the learning method TAU (Think Ask Understand). TAU provides support (i.e. a role script) for students’ interaction during a collaborative problem-solving phase at the beginning of the learning process, while content-related instruction is delayed until a subsequent phase. As the contents targeted in university-level mathematics are complex, withholding instruction will most likely result in students’ failure to solve problems, even in relearning situations. However, there is reason to believe (e.g. Kapur, Instr Sci 38(6):523–550, 2009) that due to their collaborative grappling with the contents, students will be better prepared to benefit from the subsequent instruction phase and thus ultimately learn more than students who receive instruction right at the beginning. In a four-week, in vivo experiment with 76 students, we compared TAU to a direct instruction condition (i.e. a condition in which students received instruction right at the beginning). Post-test analyses showed a significant interaction effect between condition and week: Students in the TAU condition outperformed students in the direct instruction condition in all weeks but the first. The results suggest that the more students were familiarized with TAU, the better their learning outcomes became. Our process data further indicate that students collaborated fruitfully in accordance with the role script and increasingly internalized the script. This collaboration may then have paved the way for increased learning from the subsequent instruction. Our results provide evidence that delaying instruction can also promote learning in relearning situations and at the university level. Moreover, our findings call into question whether all support must be delayed; the primary issue may not be whether or not to provide support, but rather when to provide which kind of support.
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Productive Failure and guided discovery learning have in common that both approaches put students in a self-determined learning situation. However, the two approaches have different foci: Guided discovery learning emphasizes the discovery aspect, that is, learners reveal underlying concepts or models by running experiments and interpreting their data (e.g. de Jong and van Joolingen 1998). In contrast, Productive Failure emphasizes the two consecutive phases with a self-determined learning situation in the first phase and instruction in the second phase (e.g. Kapur 2009).
As only 8 students worked with regrouped partners, a statistical analysis was not feasible. These students either worked with a different partner for only one session due to the absence of their partner in that session, or they changed their partner for all subsequent sessions. Twenty-six students worked in stable dyads.
Not all students were absent in the same session or sessions. 6 students only participated in the first session, 10 students missed one of the four sessions, and 1 student missed two sessions. Therefore, a statistical comparison of students who attended all sessions and students who missed sessions was not feasible.
Due to rounding errors the sum is not 100%.
The decrease of the inter-rater agreement for session 4 might be caused by the increase of implicitly structured interaction, which increases the room for interpretation when coding the data.
Berg, K. F. (1993). Structured cooperative learning and achievement in a high school mathematics class. Paper presented at the Annual Meeting of the American Educational Research Association, Atlanta, GA.
Beutelspacher, A., & Danckwerts, R. (2005). Neuorientierung der universitären Lehrerausbildung im Fach Mathematik für das gymnasiale Lehramt (Forschungs- und Entwicklungsprojekt) [New orientation of mathematics teacher education at the university (research project)]. Gießen/Siegen: Universität, Mathematisches Institut. Retrieved July 1st, 2011 from http://www.uni-siegen.de/fb6/didaktik/tkprojekt/downloads/t-projekt-vorstudie_lang.pdf.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68, 179–201.
Dillenbourg, P., & Jermann, P. (2007). Designing integrative scripts. In F. Fischer, I. Kollar, H. Mandl, & J. Haake (Eds.), Scripting computer-supported communication of knowledge. Cognitive, computational, and educational perspectives (pp. 275–301). New York: Springer.
Diziol, D., & Rummel, N. (2010). How to design support for collaborative e-learning: A framework of relevant dimensions. In B. Ertl (Ed.), E-collaborative knowledge construction: learning from computer-supported and virtual environments (pp. 162–179). Hershey, PA: IGI Global.
Diziol, D., Walker, E., Rummel, N., & Koedinger, K. (2010). Using intelligent tutor technology to implement adaptive support for student collaboration. Educational Psychology Review, 22(1), 89–102.
Friedrich, H. F. (1992). Vermittlung von reduktiven Textverarbeitungsstrategien durch Selbstinstruktion [teaching reductionist strategies for text processing by self-instruction]. In: H. Mandl & H. F. Friedrich (Eds.), Lern-und Denkstrategien. Analyse und Intervention [strategies for learning and thinking. Analysis and Intervention] (pp. 193–211). Göttingen: Hogrefe.
Friedrich, H. F., & Mandl, H. (1997). Analyse und Förderung selbstgesteuerten Lernens [analysis and facilitation of self-directed learning]. In F. E. Weinert & H. Mandl (Eds.), Psychologie der Erwachsenenbildung (Enzyklopädie der Psychologie, Pädagogische Psychologie) [psychology of adult education (Encyclopedia of psychology, educational psychology)] (pp. 237–293). Göttingen: Hogrefe.
Hammann, M. (2003). Aus Fehlern lernen (learning from mistakes). Unterricht Biologie (Biology Education), 27(288), 31–35.
Hythecker, V. I., Dansereau, D. F., & Rocklin, T. R. (1988). An analysis of the processes influencing the structured dyadic learning environment. Educational Psychologist, 23(1), 23–37.
Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424.
Kapur, M. (2009). Productive failure in mathematical problem solving. Instructional Science, 38(6), 523–550.
Kapur, M. (2010). A further study of productive failure in mathematical problem-solving: Unpacking the design components. Instructional Science, 39(4), 561–579.
Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science (this issue).
Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. The Journal of the Learning Sciences, 21(1), 45–83.
Kapur, M., & Rummel, N. (2009). The assistance dilemma in CSCL. In: A. Dimitracopoulou, C. O’Malley, D. Suthers, & P. Reimann (Eds.), Computer supported collaborative learning practices-CSCL2009 community events proceedings, Vol 2 (pp. 37–42). Berlin: International Society of the Learning Sciences.
Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. Gilbert, S. Fiske, & G. Lindzey (Eds.), Handbook of social psychology (4th ed., Vol. 1, pp. 233–265). Boston: McGraw-Hill.
Kenny, D. A., Kashy, D. A., & Cook, W. L. (2006). Dyadic data analysis. New York: Guilford Press.
King, A. (2007). Scripting collaborative learning processes: A cognitive perspective. In F. Fischer, I. Kollar, H. Mandl, & J. M. Haake (Eds.), Scripting computer-supported collaborative learning: Cognitive, computational, and educational perspectives (pp. 13–37). New York: Springer.
Kneser, C., & Plötzner, R. (2001). Collaboration on the basis of complementary domain knowledge: Observed dialogue structures and their relation to learning success. Learning and Instruction, 11(1), 53–83.
Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19(3), 239–264.
Koedinger, K. R., Aleven, V., Roll, I., & Baker, R. (2009). In vivo experiments on whether supporting metacognition in intelligent tutoring systems yields robust learning. In D. J. Hacker, J. Dunlosky, & A. C. Graesser (Eds.), Handbook of metacognition in education (pp. 897–964). New York: Routledge.
Kollar, I., Fischer, F., & Slotta, J. D. (2007). Internal and external scripts in computer-supported collaborative inquiry learning. Learning & Instruction, 17(6), 708–721.
Mullins, D., Rummel, N., & Spada, H. (2011). Are two heads always better than one? Differential effects of collaboration on students’ computer-supported learning in mathematics. International Journal of Computer-Supported Collaborative Learning, 6(3), 421–443.
O’Donnell, A. M. (1999). Structuring dyadic interaction through scripted cooperation. In A. M. O’Donnell & A. King (Eds.), Cognitive perspectives on peer learning (pp. 179–196). Mahwah, NJ: Lawrence Erlbaum Associates.
PSLC (2011). Learnlab. Pittsburgh science of learning center. Retrieved September 2nd, 2011, from http://learnlab.org.
Renkl, A. (2008a). Kooperatives Lernen (collaborative learning). In: W. Schneider, & M. Hasselhorn (Eds.), Handbuch Psychologie, Bd. Pädagogische Psychologie (Manual of psychology, Vol. Educational psychology, pp. 84–94). Göttingen. Hogrefe.
Renkl, A. (2008b). Lehren und Lernen im Kontext der Schule (Teaching and learning in the school context). In A. Renkl (Ed.), Lehrbuch Pädagogische Psychologie (Textbook educational psychology) (pp. 109–153). Bern: Huber.
Roll, I., Aleven, V., & Koedinger, K. R. (2009). Helping students know ‘further’–increasing the flexibility of students’ knowledge using symbolic invention tasks. In: N. A. Taatgen, & H. van Rijn (Eds.), Proceedings of the 31st annual conference of the cognitive science society (pp. 1169–1174). Austin, TX: Cognitive Science Society.
Roll, I., Aleven, V., & Koedinger, K. R. (2011). Outcomes and mechanisms of transfer in invention activities. In: L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Proceedings of the 33rd Annual Meeting of the Cognitive Science Society (pp. 2824–2829). Boston: Cognitive Science Society.
Roll, I., Holmes, N. G., Day, J, & Bonn, D. (2012). Using metacognitive scaffolding to improve the inquiry process and its outcomes in guided invention activities. Instructional Science (this issue).
Salomon, G., & Globerson, T. (1989). When teams do not function the way they ought to. International Journal of Educational Research, 13, 89–100.
Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475–522.
Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129–184.
Slavin, R. E. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Educational Psychology, 21(1), 43–69.
Slavin, R. E. (2006). Educational psychology (8th ed.). Boston: Pearson/Allyn & Bacon.
Teasley, S. D. (1995). The role of talk in children’s peer collaborations. Developmental Psychology, 31(2), 207–220.
van Joolingen, W. R., de Jong, T., Lazonder, A. W., Savelsbergh, E. R., & Manlove, S. (2005). Co-Lab: research and development of an online learning environment for collaborative scientific discovery learning. Computers in Human Behavior, 21, 671–688.
VanLehn, K., Siler, S., Murray, C., Yamauchi, T., & Baggett, W. B. (2003). Why do only some events cause learning during human tutoring? Cognition and Instruction, 21(3), 209–249.
Walker, E., Rummel, N., & Koedinger, K. (2011). Designing automated adaptive support to improve student helping behaviors in a peer tutoring activity. International Journal of Computer Supported Collaborative Learning. doi:10.1007/s11412-011-9111-2.
Westermann, K., & Rummel, N. (2012). New evidence on productive failure building on students' prior knowledge is key! Paper to be presented at the International Conference of the Learning Sciences (ICLS) 2012, Sydney, Australia.
Wiedmann, M., Wiley, J., & Rummel, N. (2012). How does group composition affect learning in invention paradigms? Instructional Science (this issue).
We would like to thank Professor Spada (Institute of Psychology, University of Freiburg, Germany) as well as Professor Goette and Dipl.-Math. Martin Franzen (Institute of Mathematics, University of Freiburg, Germany) for their support and collaboration. The project was funded by Verband der Freunde der Universität Freiburg e.V. and Alumni Freiburg e.V.
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Westermann, K., Rummel, N. Delaying instruction: evidence from a study in a university relearning setting. Instr Sci 40, 673–689 (2012). https://doi.org/10.1007/s11251-012-9207-8
- Assistance dilemma
- Productive failure
- Collaboration script