## Abstract

Introduction: Successful implementation of effective practice strategies (e.g., studying worked examples, retrieval practice) could help to improve mathematics performance. However, it is not yet fully understood when each practice strategy should be used, despite the practical value of this knowledge for mathematics textbook authors, teachers, and students. Building upon two existing perspectives on what works when, we proposed that the optimal practice strategy could depend on both the complexity of the learning task (i.e., task complexity) and the time between the last practice opportunity and the test (i.e., retention interval). Method: We conducted a multi-classroom experiment to test this proposition. More specifically, we used a 2 (Task Complexity: simple vs. complex) x 2 (Practice Strategy: studying worked example vs. retrieval practice) x 2 (Retention Interval: 5 minutes vs. 1 week) between-subjects design with students’ problem-solving performance as the dependent variable (N = 166).

Results: Although there was no evidence for the hypothesised three-way interaction effect (H1), there was evidence for the hypothesised two-way interaction effect of practice strategy and retention interval (H2), independent of task complexity: After 5 minutes, students studying worked examples slightly outperformed those practicing retrieval, but after 1 week, students practicing retrieval considerably outperformed those studying worked examples. Discussion: Findings imply that, as soon as a ‘basic’ level of understanding has been established (e.g., through instruction and study of a limited number of worked examples), practicing retrieval pays off, even for relatively complex tasks.

Results: Although there was no evidence for the hypothesised three-way interaction effect (H1), there was evidence for the hypothesised two-way interaction effect of practice strategy and retention interval (H2), independent of task complexity: After 5 minutes, students studying worked examples slightly outperformed those practicing retrieval, but after 1 week, students practicing retrieval considerably outperformed those studying worked examples. Discussion: Findings imply that, as soon as a ‘basic’ level of understanding has been established (e.g., through instruction and study of a limited number of worked examples), practicing retrieval pays off, even for relatively complex tasks.

Original language | English |
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Publication status | Published - 11 May 2023 |

Event | ICO International Spring School 2023 - Blankenberge, Belgium Duration: 8 May 2023 → 12 May 2023 https://sites.google.com/view/ico-iss2023/homepage |

### Conference

Conference | ICO International Spring School 2023 |
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Abbreviated title | ICO ISS2023 |

Country/Territory | Belgium |

City | Blankenberge |

Period | 8/05/23 → 12/05/23 |

Internet address |