Instructional Science

, Volume 40, Issue 4, pp 673–689 | Cite as

Delaying instruction: evidence from a study in a university relearning setting

  • Katharina WestermannEmail author
  • Nikol Rummel


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.


Assistance dilemma Productive failure Collaboration script Mathematics University 



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.


  1. 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.Google Scholar
  2. 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
  3. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  4. de Jong, T., & van Joolingen, W. R. (1998). Scientific discovery learning with computer simulations of conceptual domains. Review of Educational Research, 68, 179–201.Google Scholar
  5. 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.Google Scholar
  6. 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.CrossRefGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. 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.Google Scholar
  9. 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.Google Scholar
  10. Hammann, M. (2003). Aus Fehlern lernen (learning from mistakes). Unterricht Biologie (Biology Education), 27(288), 31–35.Google Scholar
  11. 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.CrossRefGoogle Scholar
  12. Kapur, M. (2008). Productive failure. Cognition and Instruction, 26(3), 379–424.CrossRefGoogle Scholar
  13. Kapur, M. (2009). Productive failure in mathematical problem solving. Instructional Science, 38(6), 523–550.CrossRefGoogle Scholar
  14. Kapur, M. (2010). A further study of productive failure in mathematical problem-solving: Unpacking the design components. Instructional Science, 39(4), 561–579.CrossRefGoogle Scholar
  15. Kapur, M. (2012). Productive failure in learning the concept of variance. Instructional Science (this issue).Google Scholar
  16. Kapur, M., & Bielaczyc, K. (2012). Designing for productive failure. The Journal of the Learning Sciences, 21(1), 45–83.CrossRefGoogle Scholar
  17. 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.Google Scholar
  18. 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.Google Scholar
  19. Kenny, D. A., Kashy, D. A., & Cook, W. L. (2006). Dyadic data analysis. New York: Guilford Press.Google Scholar
  20. 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.CrossRefGoogle Scholar
  21. 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.CrossRefGoogle Scholar
  22. Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19(3), 239–264.CrossRefGoogle Scholar
  23. 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.Google Scholar
  24. Kollar, I., Fischer, F., & Slotta, J. D. (2007). Internal and external scripts in computer-supported collaborative inquiry learning. Learning & Instruction, 17(6), 708–721.CrossRefGoogle Scholar
  25. 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.CrossRefGoogle Scholar
  26. 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.Google Scholar
  27. PSLC (2011). Learnlab. Pittsburgh science of learning center. Retrieved September 2nd, 2011, from
  28. 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.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. 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.Google Scholar
  32. 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).Google Scholar
  33. Salomon, G., & Globerson, T. (1989). When teams do not function the way they ought to. International Journal of Educational Research, 13, 89–100.CrossRefGoogle Scholar
  34. Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475–522.CrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. 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.CrossRefGoogle Scholar
  37. Slavin, R. E. (2006). Educational psychology (8th ed.). Boston: Pearson/Allyn & Bacon.Google Scholar
  38. Teasley, S. D. (1995). The role of talk in children’s peer collaborations. Developmental Psychology, 31(2), 207–220.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. 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.CrossRefGoogle Scholar
  41. 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.Google Scholar
  42. 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.Google Scholar
  43. Wiedmann, M., Wiley, J., & Rummel, N. (2012). How does group composition affect learning in invention paradigms? Instructional Science (this issue).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Institute of Educational ResearchRuhr-Universität BochumBochumGermany

Personalised recommendations