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Learning subtraction strategies with interleaved practice

Numerous studies show that primary school students rarely use subtraction strategies flexibly and adaptively. To foster students’ ability to use subtraction strategies flexibly and adaptively, interleaved practice seems to be a promising approach because it supports students in abstracting the specific application conditions of different subtraction strategies by studying various tasks alternately. However, empirical results on interleaving mathematical tasks are inconsistent. The concrete implementation of interleaved practice seems to be crucial. According to the discriminative-contrast hypothesis, comparison processes are expected to be underlying learning mechanisms explaining the advantage of interleaved over blocked practice. However, primary school students might especially need further instructional support to use the evoked comparison processes.
In our previous study on subtraction strategies in primary school mathematics, we therefore implemented interleaved practice that included additional instructional support (simultaneous presentation, comparison prompts, self-explanation prompts), which had a remarkable effect on students’ strategy proficiency compared to blocked practice. Instructional support, however, was provided but not systematically varied. Thus, the extent to which the interleaved presentation and the additional forms of support contributed to the observed learning effect is unclear. The current project aims at investigating whether adding additional instructional support can increase the effectiveness of interleaved learning in primary school mathematics and thus enhance students’ lasting learning. In three experiments, third graders will be taught to use different number-based subtraction strategies adaptively. The experimental conditions vary only with the order of strategies and additional forms of instructional support. To investigate the (lasting) learning effect, students in all conditions will be tested at three points of measurement: immediately after the treatment, 8 weeks, and 4 months later. In Experiment 1 (N = 292), we will investigate whether an increasing interleaved practice of subtraction strategy is more beneficial than a ‘pure’ form of interleaved or blocked practice for third graders’ proficiency in subtraction strategies and whether including self-explanation prompts also contributes to students’ strategy proficiency. Based on the ‘best’ interleaved learning condition from Experiment 1 (most likely increasing interleaved practice with self-explanation prompts), Experiment 2 (N = 242) will explore whether presenting the tasks simultaneously instead of sequentially in (increasing) interleaved practice can boost students’ strategy proficiency and lasting learning. Experiment 3 (N = 242) investigates if including comparison prompts in (increasing) interleaved practice with a simultaneous task presentation positively affects students’ subtraction strategy proficiency sustainably.

Keywords: interleaved practice; subtraction strategies; strategy proficiency; mathematics; primary school instruction

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Nemeth, L., & Lipowsky, F. (2023). The role of prior knowledge and need for cognition for the effectiveness of interleaved and blocked practice. European Journal of Psychology of Education

Nemeth, L., Scheitz, N., Hollmann, N., Borromeo Ferri, R., & Lipowsky, F. (2023). Mix it up! Verschachteltes Lernen ist oft nachhaltiger. mathematik lehren, 238, 25–28.

Richter, T., Berger, R., Ebersbach, M., Eitel, A., Endres, T., Borromeo Ferri, R., Hänze, M., Lachner, A., Leutner, D., Lipowsky, F., Nemeth, L., Renkl, A., Roelle, J., Rummer R., Scheiter, K., Schweppe J., von Aufschnaiter, C., & Vorholzer, A. (2022). How to promote lasting learning in schools: Theoretical approaches and an agenda for research. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie/German Journal of Developmental Psychology and Educational Psychology, 54(4), 135–141. (open access) 

Nemeth, L., Werker, K., Arend, J., & Lipowsky, F. (2021). Fostering the acquisition of subtraction strategies with interleaved practice: An intervention study with German third graders. Learning and Instruction, 71, 101354.

Nemeth, L., Werker, K., Arend, J., Vogel, S., & Lipowsky, F. (2019). Interleaved learning in elementary school mathematics: Effects on the flexible and adaptive use of subtraction strategies. Frontiers in Psychology, 10, 86.

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