# The Relationship between Interleaving and Variability Effects: A Cognitive Load Theory Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Cognitive Load Theory

- Novel, secondary information can be acquired either by randomly generating it during problem solving and testing it for effectiveness or, more efficiently, by obtaining it from other people.
- If that information is to be used subsequently, it can be stored in long-term memory for subsequent use. Long-term memory has no known capacity or duration limits [14].
- When environmental signals indicate that it is needed, information can be transferred from long-term memory back to working memory to generate appropriate action. Unlike when processing novel information, working memory has no known limits when processing familiar information retrieved from long-term memory [15].
- Extraneous cognitive load is imposed by suboptimal instructional designs that artificially and unnecessarily increase element interactivity. Altering the design of instruction can reduce or eliminate extraneous cognitive load.

## 3. Explanations of the Interleaving Effect

#### 3.1. Interleaving and the Discrimination Hypothesis

#### 3.2. Relations between the Interleaving Effect and the Variability Effect

## 4. Present Study

#### Power Analysis and Ethics Approval

## 5. Experiment 1

#### 5.1. Method

#### 5.1.1. Participants

#### 5.1.2. Materials

#### 5.1.3. Procedure

#### 5.1.4. Scoring

#### 5.2. Results

#### 5.2.1. Mathematics Working Memory Test

_{p}

^{2}= 0.006, and the storage scores, F(3, 139) = 0.17, MSE = 39.42, p = 0.92, η

_{p}

^{2}= 0.004, the effect of group was not significant. Following these non-significant ANOVAs, Bayes analyses were calculated to provide grounds for accepting the null hypothesis. For the storage scores, BF

_{01}= 22.2, suggesting the data were about 22 times more likely under the null hypothesis compared to the alternative hypothesis. Similarly, for the processing scores, BF

_{01}= 19.6, suggesting the data were 20 times more likely under the null hypothesis compared to the alternative hypothesis. These results indicate that there was no evidence of working memory resource depletion differences between the groups.

#### 5.2.2. Language Working Memory Test

_{p}

^{2}= 0.015, and BF

_{01}= 12.2, suggesting the data were about 12 times more likely under the null hypothesis compared to the alternative hypothesis. For the storage scores, the effect of group was again not significant, F(3, 139) = 1.18, MSE = 19.37, p = 0.32, η

_{p}

^{2}= 0.025, and BF

_{01}= 6.90, suggesting the data were about seven times more likely under the null hypothesis compared to the alternative hypothesis. Again, there were no significant working memory resource depletion differences found between the groups.

#### 5.2.3. Post-Tests

_{p}

^{2}= 0.010, and BF

_{01}= 10, suggesting the data were about 10 times more likely under the null hypothesis than the alternative hypothesis. For the language post-test, the effect of group also was not significant, F(3, 139) = 1.04, MSE = 4.81, p = 0.38, η

_{p}

^{2}= 0.022, and BF

_{01}= 10, suggesting the data were about 10 times more likely under the null hypothesis than the alternative hypothesis.

#### 5.3. Discussion

## 6. Experiment 2

#### 6.1. Method

#### 6.1.1. Participants

#### 6.1.2. Materials

#### 6.1.3. Procedure

#### 6.1.4. Scoring

#### 6.2. Results

#### 6.2.1. Working Memory Test: Processing

^{2}= 0.024, and BF

_{01}= 1.43, suggesting the data were slightly above one time more likely under the null hypothesis compared to the alternative hypothesis. The effect of testing time was not significant, F(1, 111) = 0.44, MSE = 56.15, p = 0.51, partial η

^{2}= 0.004, and BF

_{01}= 5, suggesting the data were about five times more likely under the null hypothesis compared to the alternative hypothesis. The Design $\times $ Testing Time interaction was also not significant, F(1, 111) = 0.86, MSE = 56.15, p = 0.36, partial η

^{2}= 0.008, and BF

_{01}= 20, suggesting the data were about 20 times more likely under the null hypothesis compared to the alternative hypothesis.

#### 6.2.2. Working Memory Test: Storage

^{2}= 0.057, and BF

_{01}= 5.2. The effect of testing time was significant, F(1, 111) = 8.28, MSE = 33.61, p = 0.005, partial η

^{2}= 0.069, and BF

_{01}= 1.4. The interaction Design $\times $ Testing Time was also significant, F(1, 111) = 13.39, MSE = 33.61, p < 0.001, partial η

^{2}= 0.108, and BF

_{01}= 4.8. The Bayes factors were more than 1, which was due to the large sample size and relatively small effect size.

_{iff}= 1.41, p < 0.001, d = 1.08, and BF

_{01}= 0.01 (suggesting the data were about 100 times more likely under the alternative hypothesis). For the delayed testing groups, there was no significant difference between the interleaved and blocked designs, t(57) = 0.72, SED

_{iff}= 1.63, p = 0.48, d = 0.56, and BF

_{01}= 142.9 (suggesting the data were about 143 times more likely under the null hypothesis than the alternative hypothesis).

#### 6.2.3. Post-Test

^{2}= 0.041, and BF

_{01}= 1.3, indicating that the interleaved design outperformed the blocked design, showing an interleaving effect. The effect of testing time was significant, F(1, 111) = 4.09, MSE = 13.07, p = 0.046, partial η

^{2}= 0.036, and BF

_{01}= 1.7, indicating that groups with immediate testing outperformed those with delayed testing. Again, the Bayes factor values above 1 are due to the large sample size and relatively small effect size. The interaction between design and testing time was not significant, F(1, 111) = 0.09, MSE = 0.31, p = 0.76, η

_{p}

^{2}= 0.001, and BF

_{01}= 3.3 (suggesting the data were about three times more likely under the null hypothesis than the alternative hypothesis).

#### 6.3. Discussion

## 7. General Discussion

#### Limitations and Future Directions

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Sample of Mathematics Material Used in Experiment 1

## Appendix B. Sample of Language Material Used in Experiment 1 (Translated from the Original Bahasa Indonesia)

Paragraph | Summary |

One of the benefits of coconut is to prevent premature aging and relieve diarrhoea. The relevant part is coconut water. The water in coconut fruit contains cytokinin hormones that prevent premature aging, while the minerals, amino acids, and enzymes it contains are useful for relieving diarrhoea. | This paragraph describes the benefits of coconut water to prevent premature aging and relieve diarrhoea. |

The content of cytokinin in coconut water serves to regulate the growth, development, and aging of cells. The cytokinin content in coconut water has anti-aging, anti-carcinogenic, and anti-thrombotic effects. | This paragraph describes the content of cytokinin as anti-aging, anti-carcinogenic, and anti-thrombotic effects. |

Coconut water is useful when you have diarrhoea because it can replace the fluid lost from the gastrointestinal tract. This is because coconut water contains amino acids, enzymes, minerals, and fatty acids that result in coconut water having high osmolarity. In addition, coconut water also contains low amounts of sodium chloride as well as high amounts of sugars and amino acids. It has a balanced composition of fluids to prevent dehydration during diarrhoea. | This paragraph describes the content of coconut water in the form of minerals with the right composition that can restore body fluids lost during diarrhoea. |

**What are the benefits of coconut water for the body?**

Answer | Explanation |

Coconut fruit has benefits for the body. One part is that coconut water can prevent premature aging and relieve diarrhoea. Coconut water contains cytokinins that have anti-aging, anti-carcinogenic, and anti-thrombotic benefits. The content of coconut water in the form of minerals with the right composition can restore body fluids lost during diarrhoea. | The answer consists of four sentences, namely: The main idea of all three paragraphs; Summary of the first paragraph; Summary of the second paragraph; Summary of the third paragraph |

## Appendix C. Sample of Type A Problem Used in Experiment 2

## Appendix D. Sample of Type B Problem Used in Experiment 2

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Day 1 | MMLL | LLMM | MLML | LMLM |
---|---|---|---|---|

30 min | Mathematics A | Language A | Mathematics A | Language A |

30 min | Mathematics B | Language B | Language A | Mathematics A |

15 min | Mathematics Working Memory Test for all groups | |||

30 min | Language A | Mathematics A | Mathematics B | Language B |

30 min | Language B | Mathematics B | Language B | Mathematics B |

15 min | Language Working Memory Test for all groups | |||

Day 2 | All groups | |||

30 min | Mathematics Post-Test | |||

30 min | Language Post-Test |

**Table 2.**Experiment 1: means (and standard deviations) of mathematics and language working memory scores.

Group | Processing | Storage |
---|---|---|

Mathematics Working Memory | ||

MMLL | 22.75 (2.98) | 19.67 (5.39) |

LLMM | 22.94 (2.61) | 19.14 (6.12) |

MLML | 22.26 (4.02) | 19.59 (5.98) |

LMLM | 22.70 (3.24) | 18.76 (7.39) |

Language Working Memory | ||

MMLL | 20.72 (3.15) | 21.89 (5.01) |

LLMM | 21.31 (1.55) | 21.03 (3.72) |

MLML | 21.21 (3.05) | 22.85 (5.21) |

LMLM | 21.54 (1.92) | 22.51 (3.47) |

**Table 3.**Experiment 1: means (and standard deviations) of mathematics and language post-test scores.

Group | Mathematics Post-Test | Language Post-Test |
---|---|---|

MMLL | 8.14 (3.78) | 6.72 (2.25) |

LLMM | 8.00 (4.38) | 7.28 (1.75) |

MLML | 7.64 (4.60) | 6.97 (2.28) |

LMLM | 8.00 (4.32) | 6.41 (2.43) |

Interleaved Design | Blocked Design | |||
---|---|---|---|---|

Immediate Testing | Delayed Testing | Immediate Testing | Delayed Testing | |

20 min | Introduction of basic concepts | |||

3 min | Mathematics A | Mathematics A | Mathematics A | Mathematics A |

3 min | Mathematics B | Mathematics B | Mathematics A | Mathematics A |

3 min | Mathematics A | Mathematics A | Mathematics A | Mathematics A |

20 min | Rest | Rest | ||

3 min | Mathematics B | Mathematics B | Mathematics B | Mathematics B |

3 min | Mathematics A | Mathematics A | Mathematics B | Mathematics B |

3 min | Mathematics B | Mathematics B | Mathematics B | Mathematics B |

20 min | Rest | Rest | ||

15 min | Mathematics Working Memory Test for all groups | |||

20 min | Mathematics Post-Test for all groups |

Group | Processing | Storage |
---|---|---|

1. Interleaved with immediate testing | 42.39 (6.86) | 44.32 (6.92) |

2. Interleaved with delayed testing | 42.77 (6.36) | 45.17 (4.11) |

3. Blocked with immediate testing | 41.39 (6.84) | 51.07 (2.83) |

4. Blocked with delayed testing | 39.17 (9.50) | 44.00 (7.86) |

Groups | Post-Test |
---|---|

1. Interleaved with immediate testing | 3.07 (1.82) |

2. Interleaved with delayed testing | 2.50 (1.87) |

3. Blocked with immediate testing | 2.45 (1.85) |

4. Blocked with delayed testing | 1.67 (1.59) |

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## Share and Cite

**MDPI and ACS Style**

Chen, O.; Retnowati, E.; Castro-Alonso, J.C.; Paas, F.; Sweller, J.
The Relationship between Interleaving and Variability Effects: A Cognitive Load Theory Perspective. *Educ. Sci.* **2023**, *13*, 1138.
https://doi.org/10.3390/educsci13111138

**AMA Style**

Chen O, Retnowati E, Castro-Alonso JC, Paas F, Sweller J.
The Relationship between Interleaving and Variability Effects: A Cognitive Load Theory Perspective. *Education Sciences*. 2023; 13(11):1138.
https://doi.org/10.3390/educsci13111138

**Chicago/Turabian Style**

Chen, Ouhao, Endah Retnowati, Juan Cristobal Castro-Alonso, Fred Paas, and John Sweller.
2023. "The Relationship between Interleaving and Variability Effects: A Cognitive Load Theory Perspective" *Education Sciences* 13, no. 11: 1138.
https://doi.org/10.3390/educsci13111138