## Methods

### Participants

### Measurement Variables and Instruments

#### Clinical and Sociodemographic Variables

#### FSIQ Assessment

#### Mathematical Competence

#### Mathematical Problem Solving (MPI)

#### Neurocognitive Variables

### Statistical Analysis

#### Description of the Sample

#### Mathematical Performance (Strategy and Accuracy) as a Function of ASD Status

#### Relationship of Mathematical Strategy and Accuracy in ASD and Non-ASD Groups

#### Mathematical Strategy and Various Neurocognitive Domains in ASD and non-ASD Groups

## Results

### Description of the Sample

ASD (N = 26) | non-ASD (N = 26) | Statistics | p | Effect size | |
---|---|---|---|---|---|

Sex (males) | 23 (88.4%) | 23 (88.4%) | χ ^{2}(2) = 0.00 | 1.000 | Φ = 0.00 |

Age (years) | 9.35 (2.06) [6.25–12.92] | 9.41 (1.96) [6.25–12.42] | t (50) = − 0.10 | .922 | d = − 0.03 |

Parental SES | χ ^{2}(4) = 4.56 | .336 | V = 0.30 | ||

V (High level) | 5 (19.2%) | 9 (34.6%) | |||

IV (High-middle level) | 8 (30.8%) | 8 (30.8%) | |||

III (Middle level) | 8 (30.8%) | 3 (11.5%) | |||

II (Low-middle level) | 4 (15.4%) | 3 (11.5%) | |||

I (Low level) | 1 (3.8%) | 3 (11.5%) | |||

Mathematical competence | |||||

TEMA-3 score | 54.00 (13.15) [26- 72] | 62.81 (10.19) [41–72] | t (50) = -2.70 | .009** | d = − 0.75 |

Mathematical age | 7.56 (1.10) [5.50–9.00] | 8.38 (0.93) [6.50–9.00] | t (50) = − 2.89 | .006** | d = − 0.81 |

WISC-FSIQ | 89.88 (11.78) [70–115] | 102.00 (10.98) [81—130] | t (50) = − 3.84 | < .001** | d = − 1.06 |

Executive functions | |||||

Working memory | 89.85 (12.47) [69–117] | 100.54 (11.56) [79–122] | t (50) = − 3.19 | .002** | d = − 0.89 |

Response set | 7.62 (3.44) [2—14] | 8.71 (3.04) [4–14] | t (50) = − 1.09 | .281 | d = − 0.34 |

Inhibition | 6.62 (3.31) [1–14] | 9.31 (3.80) [1–15] | t (50) = − 2.72 | .009** | d = − 0.75 |

Verbal comprehension | 89.81 (19.29) [45–130] | 104.96 (11.84) [86–133] | t (50) = − 3.41 | .001** | d = − 0.95 |

Social perception | |||||

Affect recognition | 7.50 (3.34) [1–18] | 9.92 (1.94) [7–13] | t (50) = -3.20 | .002** | d = − 0.89 |

Theory of mind | 16.31 (6.79) [0–26] | 22.54 (2.52) [17–26] | U = 126.50 | < .001** | η ^{2} = 0.29 |

### Mathematical Performance (Strategy and Accuracy) as a Function of ASD Status

MPI median score | ASD (N = 26) | Non-ASD (N = 26) | Statistics | p | Effect size | ||
---|---|---|---|---|---|---|---|

1.98 (1.34), range:1–4 | 2.35 (1.38), range: 1–4 | t (50) = 0.44 | .339 | d = − 0.27 | |||

Accuracy (out of 1) | 0.35 (0.38), range:0–1 | 0.50 (0.28), range: 0.13–1 | t (50) = − 1.62 | .112 | d = − 0.45 | ||

Level of accuracy | Observed | Expected | Observed | Expected | |||

0–25% | 15 (57%) | 10.5 (40.4%) | 6 (23%) | 10.5 (40.4%) | Fisher’s = 8.57 | .034* | V = 0.41 |

26–50% | 3 (11.5%) | 7 (26.9%) | 11 (42.3%) | 7 (26.9%) | |||

51–75% | 3 (11.5%) | 3.5(13.5%) | 4 (15.4%) | 3.5 (13.5%) | |||

76–100% | 5 (19.2%) | 5 (19.2%) | 5 (19.2%) | 5 (19.2%) |

^{2}= 0.02. Likewise, interactions of group (ASD/non-ASD) with the rest of covariates were not significant, indicating that ASD status did not moderate the effect of age and FSIQ on strategy.

^{2}= 0.01. Interactions between ASD status and covariates were not statistically significant.

^{2}= 0.29] and accuracy [F (1,26) = 8.65; p = 0.008, η

^{2}= 0.30]. In both models (strategy and accuracy), the regression coefficient for the main effect of ASD group had positive sign, whereas its interaction with FSIQ was negative (values not shown). This suggests that, within the average-FSIQ level, strategy and accuracy are better in the ASD group, and less sensitive to variations in FSIQ than for non-ASD children.

### Relationship of Mathematical Strategy and Accuracy in ASD and non-ASD Groups

^{2}= 0.29]. Adjusted marginal means of MPI were 1.30 (SE = 0.22) among poorer performers, vs. 2.90 (SE = 0.27) for the rest. This indicates that the worst performing ASD children use mostly incorrect strategies (MPI = 1) (e.g. providing a random number as a solution, or performing addition of the data instead of multiplication).

^{2}= 0.04].

### Mathematical Strategy and Various Neurocognitive Domains in ASD and Non-ASD Groups

Neurocognitive variables | ASD (N = 26) | Non-ASD (N = 26) | ||
---|---|---|---|---|

Spearman´s ρ | p | Spearman´s ρ | p | |

Executive function | ||||

Response set | .52 | .016* | .26 | .252 |

Inhibition | .44 | .024* | .14 | .505 |

Working memory | .30 | .141 | .17 | .407 |

Verbal comprehension | .34 | .086 | − .10 | .637 |

Social perception | ||||

Affect recognition | .11 | .603 | − .07 | .746 |

Theory of mind | .70 | < .001** | .28 | .164 |

^{2}= 0.19] inhibition [F (1,24) = 4.34, p = 0.050, η

^{2}= 0.17] and ToM [F (1,24) = 5.08, p = 0.035, η

^{2}= 0.20]. Conversely, for non-ASD children, there were no significant differences between poorer performers and all others regarding any of the explored neurocognitive domains (Table 4).

Neurocognitive variables | ASD (N = 26) | Non-ASD (N = 26) | ||||||
---|---|---|---|---|---|---|---|---|

≤ 25% (n = 15) Mean (SE) | > 25% (n = 11) Mean (SE) | F (1, 24); p | Effect size | ≤ 25% (n = 6) Mean (SE) | > 25% (n = 20) Mean (SE) | F (1, 24); p | Effect size | |

Executive functions | ||||||||

Working memory | 86.85 (3.48) | 93.93 (4.36) | F = 1.12; p = .302 | η ^{2} = 0.05 | 99.53 (5.40) | 100.84 (2.63) | F = 0.04; p = .841 | η ^{2} = 0.00 |

Response set | 6.28 (1.27) | 8.84 (1.20) | F = 1.522; p = .235 | η ^{2} = 0.09 | 10.05 (1.72) | 8.63 (0.63) | F = 0.68; p = .423 | η ^{2} = 0.04 |

Inhibition | 4.82 (1.06) | 9.07 (1.33) | F = 4.34; p = .050* | η ^{2} = 0.17 | 10.78 (1.67) | 8.86 (0.81) | F = 0.93; p = .346 | η ^{2} = 0.04 |

Verbal comprehension | 83.81 (3.32) | 97.98 (4.16) | F = 4.94; p = .037* | η ^{2} = 0.19 | 105.47 (4.57) | 104.81 (2.23) | F = 0.01; p = .905 | η ^{2} = 0.00 |

Social perception | ||||||||

Affect recognition | 7.78 (1.15) | 7.12 (1.44) | F = 0.08; p = .706 | η ^{2} = 0.00 | 10.09 (0.95) | 9.87 (0.46) | F = 0.04; p = .844 | η ^{2} = 0.00 |

Theory of mind | 13.50 (1.54) | 20.13 (1.92) | F = 5.08; p = .035* | η ^{2} = 0.20 | 23.06 (0.97) | 22.38 (0.47) | F = 0.34; p = .561 | η ^{2} = 0.02 |