Abstract
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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Notes
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.
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Acknowledgments
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
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DOI: https://doi.org/10.1007/s11251-012-9207-8