# Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Meaning in Mathematics Classroom Content

#### 2.1. Conceptual Structure

#### 2.2. Representation Systems

#### 2.3. Sense

## 3. Methodology

#### Data Analysis

## 4. Results

#### 4.1. Conceptual Structure: Strategies

#### 4.2. Conceptual Structure: Contents

#### 4.3. Representation Systems

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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School | Type | Group | Participants |
---|---|---|---|

1 | Public | A | 16 |

B | 15 | ||

2 | Partnership | C | 26 |

3 | Partnership | D | 25 |

F | 23 |

Content | Description |
---|---|

Part-whole (equal parts) | Students use of pictures of pizzas divided into equal pieces |

Part-whole (inequal parts) | Students use of pictures of pizzas divided in pieces of diferent size |

Fraction | Students express fractions in their simbolic form (for example, 1/3) |

Multiplication | Students multiply natural numbers to solve the task |

Division | Students use division of natural numbers to solve the task |

Addition | Students include additions in their procedure of solving the task |

Decimal numbers | Students use decimal numbers to express the quantity of pizza who eat each boy or girl |

Comparison of natural numbers | Students compare natural numbers (usually the number of pieces made) to solve the task |

Grouping | Students perform distributions |

Category | Description | Variation | Description |
---|---|---|---|

Within | Students relate the respective quantities (number of girls’ pizzas to number of boys’ pizzas and number of boys to number of girls) and subsequently compare the results | Pre-within | Students compare the quantities of a given feature or magnitude, but fail to compare the results to solve the task posed |

Between | Students relate non-uniform quantities (number of pizzas to number of people) and subsequently compare the results. | Incomplete between | Students relate non-uniform quantities while failing to compare the results to reach a solution |

Unitisa-tion | Students identify four units (seven girls, three boys, three pizzas, one pizza) and create a new unit, the ratio for the comparison. | Use of written language to explain the procedure deployed | |

Pieces | Students divide the pizzas into the same number of pieces, calculate the number of pieces for the girls and the number for the boys and compare those quantities. | Incomplete pieces | Students divide the pizzas into the same number of pieces but take the procedure no further |

Other | Students use a procedure not classifiable under any of the categories established |

Representation | Description |
---|---|

Graphic | Use of pictures or charts |

Symbolic-numerical | Use of numerical or algebraic symbols |

Verbal | Use of written language to explain the procedure followed |

Strategy | No. Students |
---|---|

One strategy only | |

Within | 0 |

Pre-within | 12 |

Between | 12 |

Incomplete between | 13 |

Unitisation | 6 |

Pieces | 17 |

Incomplete pieces | 7 |

Other | 15 |

Combination of strategies | |

Pre-within and incomplete between | 10 |

Pre-within and unitisation | 2 |

Pre-within and pieces | 2 |

Pre-within and incomplete pieces | 3 |

Pre-within and other | 1 |

Incomplete between and incomplete pieces | 2 |

Graphic | Symbolic-Numerical | Verbal | All Three | |
---|---|---|---|---|

Graphic | 12 | - | ||

Symbolic-numerical | 4 (4) | 3 | - | |

Verbal | 43 (28) | 10 (10) | 7 | |

26 (6) | ||||

Total | 85 | 39 | 33 |

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**MDPI and ACS Style**

Castro-Rodríguez, E.; Ferreira, M.; Montoro, A.B.; Ruiz-Hidalgo, J.F.
Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task. *Mathematics* **2022**, *10*, 1339.
https://doi.org/10.3390/math10081339

**AMA Style**

Castro-Rodríguez E, Ferreira M, Montoro AB, Ruiz-Hidalgo JF.
Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task. *Mathematics*. 2022; 10(8):1339.
https://doi.org/10.3390/math10081339

**Chicago/Turabian Style**

Castro-Rodríguez, Elena, Marisel Ferreira, Ana B. Montoro, and Juan F. Ruiz-Hidalgo.
2022. "Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task" *Mathematics* 10, no. 8: 1339.
https://doi.org/10.3390/math10081339