# Personal Need for Structure and Fractions in Mathematical Education

^{*}

*Eur. J. Investig. Health Psychol. Educ.*

**2022**,

*12*(5), 448-457; https://doi.org/10.3390/ejihpe12050033

## Abstract

**:**

## 1. Introduction

#### 1.1. Previous Research

- (a)
- The practical perspective: the ability to deal effectively with these concepts improves the ability to understand and handle situations and problems in the real world.
- (b)
- The psychological perspective: rational numbers provide a rich environment for development and expansion of the mental structures necessary for continued intellectual development.
- (c)
- The mathematical perspective: rational-number understandings create the foundation upon which elementary algebraic operations can later be based.

#### 1.2. Personal Need for Structure and Mathematics

#### 1.3. Research

- The application fraction test in Slovak language and Slovak conditions;
- The analysis mistakes of students;
- The relationship research between mathematical knowledge and cognitive individual variable. Mathematical knowledge is presented by knowledge of fractions, cognitive-individual variable is differentiated as personal need for structure (PNS).

## 2. Materials and Methods

#### 2.1. PNS Scale

#### 2.2. Knowledge of Fractions as a Variable

- (a)
- Mathematical structures: a set of concepts is organized by mathematics;
- (b)
- Educational structures: a set of concepts is organized by a teacher, textbook, or curriculum;
- (c)
- Cognitive structures: a set of concepts is organized by a pupil.

**IRT model**

## 3. Results

^{2}(1) =23.89, p < 0.001) is highly significant. Therefore, the unidimensional model fits significantly better than the correlated traits model. However, comparing the unidimensional model to the correlated traits model, using the AIC and BIC reveals that the correlated traits model may be preferable: M3: AIC = 5559.3, BIC = 5763.0; M4: AIC = 5537.4, BIC = 5744.3. Therefore, in agreement with previous studies [2,19], the PNS scale measures two distinct but related components of the need for structure construct.

**DIF**

**Estimates of parameters**

^{2}(29) = 95.89, p < 0.001) is highly significant. Therefore, the unidimensional model fits significantly better than the bifactor model.

^{2}(170) = 245.45; χ

^{2}/df = 1.44) would suggest rejection of the model, but RMSEA value based on this statistic (RMSEA = 0.05) suggests a reasonably fair approximate fit.

**DIF**

**Estimates of parameters**

**Person score**

**Reliability**

**Analysis of the dependence of fractions knowledge and PNS**

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Factor loading, parameter estimates, the goodness of item fit statistics for correlated traits model.

Items | Factor Loading | Item Parameter Estimates | Item Fit Statistics | |||||||
---|---|---|---|---|---|---|---|---|---|---|

b2 | b3 | b4 | b5 | b6 | a | $\mathbf{S}-{\mathit{\chi}}^{2}$ | df | p | ||

Factor 1: Desire for Structure (DFS) | ||||||||||

P3 | 0.73 | −2.70 | −2.34 | −1.32 | −0.24 | 0.69 | 1.07 | 49.64 | 37 | 0.080 |

P4 | 0.62 | −3.19 | −2.45 | −1.69 | −0.49 | 0.68 | 0.79 | 55.01 | 40 | 0.057 |

P6 (reversed) | 0.57 | −2.26 | −1.28 | −0.24 | 0.96 | 2.13 | 0.70 | 59.86 | 51 | 0.185 |

P10 | 0.69 | −2.52 | −1.79 | −0.40 | 0.73 | 1.92 | 0.96 | 45.56 | 37 | 0.158 |

Factor 2: Response to Lack of Structure (RLS) | ||||||||||

P1 | 0.53 | −4.06 | −3.46 | −2.09 | −0.06 | 1.49 | 0.62 | 34.20 | 33 | 0.410 |

P2 (reversed) | 0.48 | −2.90 | −1.23 | −0.40 | 1.03 | 2.22 | 0.55 | 63.10 | 51 | 0.119 |

P7 | 0.52 | −3.35 | −2.23 | −0.86 | 0.86 | 2.63 | 0.60 | 46.17 | 38 | 0.170 |

P8 | 0.70 | −2.74 | −1.82 | −0.96 | −0.10 | 0.59 | 0.98 | 45.51 | 41 | 0.290 |

P9 | 0.61 | −2.65 | −1.28 | −0.38 | 0.85 | 1.67 | 0.76 | 49.83 | 49 | 0.440 |

P11 (reversed) | 0.50 | −2.39 | −0.80 | 0.60 | 1.84 | 3.11 | 0.58 | 43.00 | 46 | 0.599 |

P12 | 0.70 | −2.49 | −1.43 | −0.60 | 0.47 | 1.51 | 0.97 | 50.96 | 41 | 0.137 |

**Table 2.**The percentage success rate for resolution of the tasks of the fractions test, factor loading, item difficulty, and goodness of item fit for the Rasch model.

Task | % | Factor Loading | Difficulty (SE) | ${\mathit{\chi}}^{2}\left(160\right)$ | p |
---|---|---|---|---|---|

A1 | 75.3 | 0.22 | −1.15 (0.19) | 306.50 | 0.000 |

A2 | 84.6 | 0.81 | −1.71 (0.23) | 81.20 | 1.000 |

A3 | 80.3 | 0.73 | −1.43 (0.21) | 111.10 | 0.999 |

A4 | 70.4 | 0.78 | −0.90 (0.18) | 103.84 | 1.000 |

A5 | 90.7 | 0.59 | −2.24 (0.29) | 103.57 | 1.000 |

A6 | 71.6 | 0.28 | −0.96 (0.18) | 189.32 | 0.056 |

A7 | 85.8 | 0.47 | −1.80 (0.24) | 132.90 | 0.942 |

B1 | 63.6 | 0.79 | −0.59 (0.17) | 103.08 | 1.000 |

B2 | 74.1 | 0.40 | −1.09 (0.19) | 157.85 | 0.533 |

B3 | 77.2 | 0.70 | −1.25 (0.20) | 114.99 | 0.997 |

B4 | 61.1 | 0.77 | −0.49 (0.17) | 111.78 | 0.999 |

B5 | 79.6 | 0.25 | −1.39 (0.21) | 288.30 | 0.000 |

B7 | 74.7 | 0.48 | −1.12 (0.19) | 139.64 | 0.876 |

C2 | 37.0 | 0.68 | 0.53 (0.17) | 177.71 | 0.160 |

C3 | 32.1 | 0.70 | 0.75 (0.18) | 135.15 | 0.924 |

C4 | 25.3 | 0.65 | 1.10 (0.20) | 114.03 | 0.998 |

C5 | 5.6 | 0.69 | 2.79 (0.35) | 106.67 | 1.000 |

C6 | 8.0 | 0.56 | 2.43 (0.31) | 286.29 | 0.000 |

C7 | 1.9 | 0.72 | 3.79 (0.55) | 73.15 | 1.000 |

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**MDPI and ACS Style**

Švecová, V.; Rybanský, Ľ.; Pavlovičová, G.
Personal Need for Structure and Fractions in Mathematical Education. *Eur. J. Investig. Health Psychol. Educ.* **2022**, *12*, 448-457.
https://doi.org/10.3390/ejihpe12050033

**AMA Style**

Švecová V, Rybanský Ľ, Pavlovičová G.
Personal Need for Structure and Fractions in Mathematical Education. *European Journal of Investigation in Health, Psychology and Education*. 2022; 12(5):448-457.
https://doi.org/10.3390/ejihpe12050033

**Chicago/Turabian Style**

Švecová, Valéria, Ľubomír Rybanský, and Gabriela Pavlovičová.
2022. "Personal Need for Structure and Fractions in Mathematical Education" *European Journal of Investigation in Health, Psychology and Education* 12, no. 5: 448-457.
https://doi.org/10.3390/ejihpe12050033