## Abstract

Practice strategies are ways to practice with new subject matter after initial instruction or self-study. To help students acquire (mathematical) problem-solving skills, two practice strategies are generally effective: practicing through worked examples and practicing through retrieval practice. 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. To better understand what strategy works under which conditions, we propose to integrate two existing perspectives that were recently put forward into one new model. In this model, we argue that the optimal practice strategy depends on both the complexity of the learning task and on the time between the last practice opportunity and the test (i.e., the retention interval). We propose a preregistered multi-classroom experiment to test this model. More specifically, we plan to use a 2 (Task Complexity: simple vs. complex) x 2 (Practice Strategy: worked examples vs. retrieval practice) x 2 (Retention Interval: 5 minutes vs. 1 week) between-subjects design, with 22 participants per cell (N = 176). We also

plan to perform a Bayesian 2 x 2 x 2 ANCOVA on participants’ problem-solving

performance to test the three-way interaction effect of task complexity, practice strategy, and retention interval (Hypothesis 1), the two-way interaction effect of task complexity and practice strategy after 5 minutes (Hypothesis 2), and the two-way interaction effect of task complexity and practice strategy after 1 week (Hypothesis 3). During our Round Table presentation, we will discuss (a) any questions we have about received reviewers’ comments, (b) the viability and value of the theoretical integration we propose, and/or (c) our first ideas

on analysing the moderating qualities of (initial retrieval) effort and initial retrieval success.

Keywords: worked examples, retrieval practice, (mathematical) problem-solving, task complexity, retention interval

plan to perform a Bayesian 2 x 2 x 2 ANCOVA on participants’ problem-solving

performance to test the three-way interaction effect of task complexity, practice strategy, and retention interval (Hypothesis 1), the two-way interaction effect of task complexity and practice strategy after 5 minutes (Hypothesis 2), and the two-way interaction effect of task complexity and practice strategy after 1 week (Hypothesis 3). During our Round Table presentation, we will discuss (a) any questions we have about received reviewers’ comments, (b) the viability and value of the theoretical integration we propose, and/or (c) our first ideas

on analysing the moderating qualities of (initial retrieval) effort and initial retrieval success.

Keywords: worked examples, retrieval practice, (mathematical) problem-solving, task complexity, retention interval

Original language | English |
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Publication status | Published - 17 Mar 2022 |

Event | ICO National Spring School 2022 - Online, Utrecht, Netherlands Duration: 17 Mar 2022 → 18 Mar 2022 https://sites.google.com/view/ico-nss-2022/home-1 |

### Conference

Conference | ICO National Spring School 2022 |
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Abbreviated title | ICO ISS 2022 |

Country/Territory | Netherlands |

City | Utrecht |

Period | 17/03/22 → 18/03/22 |

Internet address |