# Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Emergence of MA

#### 1.2. The Aims of the Current Study

## 2. Method

#### 2.1. Participants

#### 2.2. Materials

#### 2.2.1. Measures of Socioeconomic Status and Cognitive Ability

#### Northern Ireland Multiple Deprivation Measure

#### Parental Education

#### Verbal and Non-Verbal Intelligence

#### Order Working Memory (WM) Task

#### Daily Event Task

#### 2.2.2. Measures of Basic Numerical Skills at the Start of the First School Year

#### Number Ordering2

#### Counting

#### Non-Symbolic Addition

#### Number Comparison

#### Number Line Task

#### Mathematics Performance

#### Mathematical Anxiety

#### 2.3. Procedure

#### 2.4. Power Analysis

## 3. Results

#### 3.1. Concurrent MA and Math Performance at T3

#### 3.2. Longitudinal Relations between T1 and T2 Basic Skills and T3 Math Performance

#### 3.3. Longitudinal Relations between T1 and T2 Basic Skills and MA at T3

#### 3.4. Longitudinal Relations between Formal Mathematical Skills at Different Time Points and between Formal Mathematics Skills and MA

#### 3.5. Indirect Effects of Early Formal Math Skills on T3 MA

## 4. Discussion

#### 4.1. Limitations and Future Directions

#### 4.2. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | The original sample consisted of ninety children at T1. At T2, two of the children moved schools, and one further participant was withdrawn from the study. At T3, a further 27 children did not take part in the study. Three of these children moved to another school. The remaining 24 children did not take part because their parent(s) did not give consent for their child to take part. The children who did not take part at T3 were not all from the same class (children in the study came from eight different classes across four different schools); the number of children from each of the eight classes who did not take part in the study at T3 ranged from 1–5. Despite the high drop-out rate in the study, children who dropped out did not differ from the final sample in their basic characteristics (see Table S1 in Supplementary Materials). |

2 | Reaction time data was recorded for only three tasks (number comparison, daily events, and number ordering at T2). We did not analyse these results further, as reliability estimates for RT for young children tend to be lower than those for accuracy. |

3 | Due to high attrition rates at Time 3, our final sample size was slightly smaller than this. |

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**Figure 1.**Theoretical model demonstrating the potential mediational effects of mathematical performance at T2 and T3 on the relationship between T1 mathematical performance and MA measured at T3.

**Figure 2.**Theoretical model demonstrating the potential mediational effect of mathematical performance at T3 on the relationship between T2 mathematical performance and math anxiety measured at T3.

**Table 1.**Descriptive statistics for the mathematical anxiety and mathematical performance measures and p-values for Kolmogorov-Smirnov normality tests.

Mean (SD) | Range | D | |
---|---|---|---|

Parental education (Median) | 5 | 0–6 | <0.001 |

Deprivation (Median) | 10.09 | 1.85–62.91 | <0.001 |

Vocabulary (T1) | 15.93 (7.03) | 7–32 | 0.030 |

Block design (T1) | 24.40 (3.37) | 16–30 | 0.011 |

OPQ (T1) | 44.12 (7.18) | 26–56 | 0.200 |

Order WM (T1) | 9.93 (4.36) | 1–16 | <0.001 |

Order WM (T2) | 11.23 (4.34) | 1–19 | <0.001 |

Daily events (T1) | 0.66 (.12) | 0.46–0.96 | <0.001 |

Daily events (T2) | 0.77 (.12) | 0.46–1 | 0.003 |

Number ordering (T1) | 0.85 (.28) | 0–1 | <0.001 |

Number ordering (T2) | 0.76 (.20) | 0.38–1 | <0.001 |

Counting (T1) | 0.20 (2.72) | −8.21–3 | <0.001 |

Counting (T2) | 0.32 (1.83) | −9.28–1 | <0.001 |

Non-symbolic addition (T1) | 0.56 (0.11) | 0.30–0.88 | 0.002 |

Non-symbolic addition (T2) | 0.66 (0.14) | 0.33–0.96 | 0.178 |

Number comparison (T1) | 0.71 (0.19) | 0.40–1 | 0.008 |

Number comparison (T2) | 0.97 (0.04) | 0.75–1 | <0.001 |

Number line estimation (T1) | 199.36 (78.52) | 64–453 | 0.023 |

Number line estimation (T2) | 120.24 (42.82) | 42.222 | 0.200 |

CMAQ-R | 34.30 (13.30) | 16–70 | 0.200 |

EES-AMAS | 19.53 (9.18) | 9–39 | <0.001 |

Math Performance at T1 | 23.24 (4.88) | 1–28 | <0.001 |

Math Performance at T2 (raw score) | 21.74 (4.71) | 7–29 | 0.001 |

Math Performance at T3 (raw score) | 27.43 (7.15) | 13–40 | 0.200 |

Math Performance at T3 (standardised score) | 106.10 (11.49) | 86–130 | 0.200 |

**Table 2.**Pearson’s and Bayesian correlations between math anxiety and both overall math performance and performance on the different domains of the math performance assessment at T3.

Math Anxiety | |||
---|---|---|---|

r | BF_{10} | BF_{01} | |

Formal math performance (Raw) | −0.31 * | 5.380 | 0.186 |

Counting and understanding number | −0.35 ** | 12.434 | 0.080 |

Knowing and using number facts | −0.30 * | 4.418 | 0.226 |

Calculating | −0.28 * | 3.210 | 0.312 |

Understanding shape | −0.07 | 0.263 | 3.807 |

Measuring | −0.07 | 0.267 | 3.748 |

Handling data | −0.08 | 0.289 | 3.464 |

**Table 3.**Zero-order correlations (controlling for IQ and SES) between math anxiety and performance at T3 and the measures at T1 and T2.

Formal Math Performance (T3) | Math Anxiety (T3) | |||||
---|---|---|---|---|---|---|

r | BF_{10} | BF_{01} | r | BF_{10} | BF_{01} | |

OPQ (T1) | 0.21 | 1.03 | 0.97 | 0.01 | 0.15 | 6.55 |

Order WM (T1) | 0.28 * | 3.23 | 0.31 | 0.07 | 0.11 | 8.89 |

Order WM (T2) | 0.30 * | 4.62 | 0.22 | 0.08 | 0.11 | 9.41 |

Daily events (T1) | 0.41 ** | 62.23 | 0.02 | −0.12 | 0.40 | 2.47 |

Daily events (T2) | 0.39 ** | 30.95 | 0.03 | −0.01 | 0.17 | 6.01 |

Number ordering (T1) | 0.25 | 1.73 | 0.58 | 0.13 | 0.09 | 11.45 |

Number ordering (T2) | 0.49 *** | 663.18 | <0.01 | −0.35 ** | 13.56 | 0.07 |

Counting (T1) | 0.44 *** | 143.21 | <0.01 | −0.24 | 1.67 | 0.60 |

Counting (T2) | 0.20 | 0.95 | 1.05 | −0.17 | 0.63 | 1.60 |

Non-symbolic addition (T1) | 0.23 | 1.39 | 0.72 | −0.22 | 1.26 | 0.79 |

Non-symbolic addition (T2) | 0.45 *** | 197.52 | <0.01 | −0.22 | 1.15 | 0.87 |

Number comparison (T1) | 0.14 | 0.49 | 2.05 | −0.37 ** | 20.90 | 0.05 |

Number comparison (T2) | 0.32 * | 6.25 | 0.16 | −0.04 | 0.21 | 4.87 |

Number line estimation (T1) | 0.35 ** | 12.60 | 0.08 | 0.12 | 0.38 | 2.61 |

Number line estimation (T2) | 0.16 | 0.60 | 1.67 | 0.07 | 0.26 | 3.83 |

Formal math performance (T1) | 0.47 ** | 340.31 | <0.001 | 0.02 | 0.15 | 6.79 |

Formal math performance (T2) | 0.58 ** | 28,939.12 | <0.001 | −0.19 | 0.82 | 1.22 |

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## Share and Cite

**MDPI and ACS Style**

O’Connor, P.A.; Morsanyi, K.; McCormack, T.
Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School. *J. Intell.* **2023**, *11*, 211.
https://doi.org/10.3390/jintelligence11110211

**AMA Style**

O’Connor PA, Morsanyi K, McCormack T.
Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School. *Journal of Intelligence*. 2023; 11(11):211.
https://doi.org/10.3390/jintelligence11110211

**Chicago/Turabian Style**

O’Connor, Patrick A., Kinga Morsanyi, and Teresa McCormack.
2023. "Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School" *Journal of Intelligence* 11, no. 11: 211.
https://doi.org/10.3390/jintelligence11110211