# Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1–6

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Theoretical Framework of the MathPro Test

#### 1.2. Core Number Domain

#### 1.3. Memory Domain

#### 1.4. Visual-Spatial Domain

#### 1.5. Reasoning Domain

#### 1.6. Selection of the MathPro Test Tasks

#### 1.7. The Aim of This Study

## 2. Materials and Methods

#### 2.1. MathPro Subtests

#### 2.2. MathPro Subtests

#### 2.2.1. Dots Magnitude Comparison

#### 2.2.2. Single and Multidigit Number Magnitude Comparison

#### 2.2.3. Screen Keyboard Use

#### 2.2.4. Numbers Dictation

#### 2.2.5. Next Number

#### 2.2.6. Previous Number

#### 2.2.7. Subitizing

#### 2.2.8. Enumeration

#### 2.2.9. Addition Facts Retrieval

#### 2.2.10. Multiplication Facts Retrieval

#### 2.2.11. Mental Calculations

#### 2.2.12. Number Lines 0–100

#### 2.2.13. Number Lines 0–1000

#### 2.2.14. Squares

#### 2.2.15. Building Blocks

#### 2.2.16. Word Problems

#### 2.2.17. Calculation Principles

#### 2.2.18. Numerical Patterns

#### 2.3. MathPro Test Advantages

#### 2.4. Standardized Test in Mathematics

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Descriptive Analyses

#### 3.2. Internal Consistency

#### 3.3. Grade and Difficulty Effects

#### 3.4. Correlations with the Standardized Math Test

#### 3.5. Comparison of MD Versus Typically Achieving Students

^{2}= 0.40). Indeed, MD students performed significantly less accurately than TAs in numbers dictation, subitizing, enumeration, addition facts retrieval, number lines 0–100, building blocks and numerical patterns. They were also slower in the single-digit numbers comparison, i.e., the sole task where their speed was measured (Table 8).

^{2}= 0.30). MD students performed significantly lower than TAs in single digit numbers comparison, multidigit numbers comparison, numbers dictation, previous numbers, subitizing, mental calculations, number lines 0–100, word problems and numerical patterns (Table 8). The MANCOVA run for the reaction time controlling for the general speed showed a significant global group effect (F(3, 84) = 4.532, p = 0.005 and η

^{2}= 0.14). The MD students were significantly slower than TAs in addition facts retrieval.

^{2}= 0.56). MD students significantly underperformed on multidigit numbers comparison, numbers dictation, mental calculations, number lines 0–100 and 0–1000, squares, word problems and calculation principles (Table 8). The MANCOVA run on speed measures controlling for the general motor speed failed to show a significant global effect of the group (F(8, 82) = 1.896 and p = 0.064) as MD students were significantly slower than TAs in multidigit numbers comparison only (Table 8).

^{2}= 0.34) and the grade (F (36, 494) = 3.890, p < 0.001 and η

^{2}= 0.22) but not of the group × grade interaction (F (36, 494) = 1.378 and p = 0.079). MD students performed significantly more poorly than TAs in dots comparison, multidigit numbers comparison, numbers dictation, multiplication facts retrieval, mental calculations, number lines 0–100 and 0–1000, squares, building blocks, word problems, calculation principles and numerical patterns (Table 9). The MANCOVA run on speed measures controlling for the general motor speed showed a significant global effect of the group (F (8, 263) = 3.451, p = 0.001 and η

^{2}= 0.10), the Grade (F (16, 528) = 4.596, p < 0.001 and η

^{2}= 0.12) but not of the group × grade interaction (F (16, 528) = 0.987 and p = 0.469). Indeed, MD students were significantly slower than TA students in multidigit numbers comparison, enumeration, addition and multiplication facts (Table 9).

## 4. Discussion

#### 4.1. The Core Number Domain Measures

#### 4.2. The Memory Domain Measures

#### 4.3. The Reasoning Domain Measures

#### 4.4. The Visual-Spatial Domain Measures

#### 4.5. The Difficulties in Children with MD

#### 4.6. Limitations and Future Perspectives

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Difficulty Effects for Grades 1, 2, 3

#### Appendix A.1.1. Multidigit Numbers Comparison

^{2}= 0.07) and their RTs were shorter for two-digit numbers (3819 ± 916) than for three-digit numbers ((4489 ± 1827), F (1, 97) = 17.369, p < 0.001 and η

^{2}= 0.16). Grade 3 students’ AC were similarly high for the two- and three-digit numbers (0.90 ± 0.18 and 0.91 ± 0.18, respectively) and non-significantly (F (2,202) = 2.155 and p = 0.119) lower for the four-digit numbers (0.87 ± 0.22). RTs increased with the size of the number (F (2,202) = 63.878, p < 0.001 and η

^{2}= 0.39: two-, three- and four-digit, 3275 ± 520, 3455 ± 657 and 4506 ± 1522, respectively).

#### Appendix A.1.2. Numbers Dictation

#### Appendix A.1.3. Next Numbers

^{2}= 0.36) better for single-digit numbers (0.64 ± 0.36) than two-digit numbers (0.36 ± 0.40).

#### Appendix A.1.4. Previous Numbers

^{2}= 0.07) for single-digit numbers (0.65 ± 0.38) than for two-digit numbers (0.42 ± 0.41).

#### Appendix A.1.5. Enumeration

^{2}= 0.10) for the smaller group of dots (0.75 ± 0.28) than for the larger (0.67 ± 0.34).

#### Appendix A.1.6. Addition Facts Retrieval

^{2}= 0.04) for the smaller sums (0.84 ± 0.25) than for the larger (0.81 ± 0.28).

#### Appendix A.1.7. Mental Calculations

^{2}= 0.72) with the increased difficulty (easy (0.74 ± 0.31), medium (0.59 ± 0.33) and difficult (0.25 ± 0.30)).

## References

- Ancker, J.S.; Kaufman, D. Rethinking health numeracy: A multidisciplinary literature review. J. Am. Med. Inf. Assoc.
**2007**, 14, 713–721. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rivera-Batiz, F.L. Quantitative literacy and the likelihood of employment among young adults in the United States. J. Hum. Resour.
**1992**, 27, 313–328. [Google Scholar] [CrossRef] - Parsons, S.; Bynner, J. Does Numeracy Matter More? National Research and Development Centre for Adult Literacy and Numeracy: London, UK, 2005; p. 44. [Google Scholar]
- Szücs, D. Subtypes and co-morbidity in mathematical learning disabilities: Multi-dimensional study of verbal and visual memory processes is key to understanding. Prog. Brain Res.
**2016**, 227, 277–304. [Google Scholar] - Geary, D.C. Role of Cognitive Theory in the Study of Learning Disability in Mathematics. J. Learn. Disabil.
**2005**, 38, 305–307. [Google Scholar] [CrossRef] [PubMed] - Geary, D.C. Mathematics and learning disabilities. J. Learn. Disabil.
**2004**, 37, 4–15. [Google Scholar] [CrossRef] - Gersten, R.; Clarke, B.; Jordan, N.C.; Newman-Gonchar, R.; Haymond, K.; Wilkins, C. Universal Screening in Mathematics for the Primary Grades: Beginnings of a Research Base. Except. Child.
**2012**, 78, 423–445. [Google Scholar] [CrossRef] [Green Version] - Lewis, K.E.; Fisher, M.B. Taking stock of 40 years of research on mathematical learning disability: Methodological issues and future directions. J. Res. Math. Educ.
**2016**, 47, 338–371. [Google Scholar] [CrossRef] - Murphy, M.M.; Mazzocco, M.M.M.; Hanich, L.B.; Early, M.C. Cognitive characteristics of children with mathematics learning disability (MD) vary as a function of the cutoff criterion used to define MD. J. Learn. Disabil.
**2007**, 40, 458–478. [Google Scholar] [CrossRef] [Green Version] - Bartelet, D.; Ansari, D.; Vaessen, A.; Blomert, L. Cognitive subtypes of mathematics learning difficulties in primary education. Dev. Disabil. Res. Rev.
**2014**, 35, 657–670. [Google Scholar] [CrossRef] - Ashkenazi, S.; Black, J.M.; Abrams, D.A.; Hoeft, F.; Menon, V. Neurobiological underpinnings of math and reading learning disabilities. J. Learn. Disabil.
**2013**, 46, 549–569. [Google Scholar] [CrossRef] [Green Version] - Fias, W.; Menon, V.; Szucs, D. Multiple components of developmental dyscalculia. Trends Neurosci. Educ.
**2013**, 2, 43–47. [Google Scholar] [CrossRef] [Green Version] - Skagerlund, K.; Träff, U. Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes with Different Cognitive Profiles and Deficits. J. Learn. Disabil.
**2016**, 49, 36–50. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Karagiannakis, G.; Baccaglini-Frank, A.; Papadatos, Y. Mathematical learning difficulties subtypes classification. Front. Hum. Neurochir.
**2014**, 8, 57. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Schneider, M.; Beeres, K.; Coban, L.; Merz, S.; Schmidt, S.S.; Stricker, J.; De Smedt, B. Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Dev. Sci.
**2017**, 20, e12372. [Google Scholar] [CrossRef] - Schwenk, C.; Sasanguie, D.; Jörg-Tobias, K.; Kempe, S.; Doebler, P.; Holling, H. (Non-) symbolic magnitude processing in children with mathematical difficulties: A meta-analysis. Res. Dev. Disabil.
**2017**, 64, 152–167. [Google Scholar] [CrossRef] - Moeller, K.; Neuburger, S.; Kaufmann, L.; Landerl, K.; Nuerk, H.-C. Basic number processing deficits in developmental dyscalculia: Evidence from eye-tracking. Cogn. Dev.
**2009**, 24, 371–386. [Google Scholar] [CrossRef] - Schleifer, P.; Landerl, K. Subitizing and counting in typical and atypical development. Dev. Sci.
**2011**, 14, 280–291. [Google Scholar] [CrossRef] - Ashkenazi, S.; Mark-Zigdon, N.; Henik, A. Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness? Dev. Sci.
**2013**, 16, 35–46. [Google Scholar] [CrossRef] - Landerl, K.; Bevan, A.; Butterworth, B. Developmental dyscalculia and basic numerical capacities: A study of 8–9-year-old students. Cognition
**2004**, 93, 99–125. [Google Scholar] [CrossRef] - Lyons, I.M.; Beilock, S.L. Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition
**2011**, 121, 256–261. [Google Scholar] [CrossRef] - Garnett, K.; Fleischner, J.E. Automatization and basic fact performance of normal and learning disabled children. Learn. Disabil. Q.
**1983**, 6, 223–230. [Google Scholar] [CrossRef] [Green Version] - Geary, D.C.; Hoard, M.K.; Hamson, C.O. Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. J. Exp. Child Psychol.
**1999**, 74, 213–239. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mussolin, C.; Noël, M.-P. Specific retrieval deficit from long-term memory in children with poor arithmetic facts abilities. Open Psychol. J.
**2008**, 1, 26–34. [Google Scholar] [CrossRef] [Green Version] - De Visscher, A.; Noël, M.-P. The detrimental effect of interference in multiplication facts storing: Typical development and individual differences. J. Exp. Psychol. Gen.
**2014**, 143, 2380–2400. [Google Scholar] [CrossRef] [PubMed] - De Visscher, A.; Noël, M.P. Arithmetic facts storage deficit: The hypothesis of hypersensitivity-to-interference in memory. Dev. Sci.
**2014**, 17, 434–442. [Google Scholar] [CrossRef] [PubMed] - Holmes, V.M.; McGregor, J. Rote memory and arithmetic fact processing. Mem. Cog.
**2007**, 35, 2041–2051. [Google Scholar] [CrossRef] [Green Version] - Friso-van den Bos, I.; van der Ven, S.H.G.; Kroesbergen, E.H.; van Luit, J.E.H. Working memory and mathematics in primary school children: A meta-analysis. Educ. Res. Rev.
**2013**, 10, 29–44. [Google Scholar] [CrossRef] - Peng, P.; Namkung, J.; Barnes, M.; Sun, C. A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. J. Educ. Psychol.
**2016**, 108, 455–473. [Google Scholar] [CrossRef] - Swanson, H.L.; Jerman, O. Math Disabilities: A Selective Meta-Analysis of the Literature. Rev. Educ. Res.
**2006**, 76, 249–274. [Google Scholar] [CrossRef] - Van Garderen, D. Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. J. Learn. Disabil.
**2006**, 39, 496–506. [Google Scholar] [CrossRef] - Osmon, D.C.; Smerz, J.M.; Braun, M.M.; Plambeck, E. Processing abilities associated with math skills in adult learning disability. J. Clin. Exp. Neuropsyc.
**2006**, 28, 84–95. [Google Scholar] [CrossRef] [PubMed] - Crollen, V.; Noël, M.-P. How does space interact with numbers? In Visual-Spatial Ability in STEM Education. Transforming Research into Practice; Khine, M.S., Ed.; Springer International Publishing: Cham, Switzerland, 2017; pp. 241–263. [Google Scholar]
- Rourke, B.P. Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. J. Learn. Disabil.
**1993**, 26, 214–226. [Google Scholar] [CrossRef] [PubMed] - Rourke, B.P.; Conway, J.A. Disabilities of arithmetic and mathematical reasoning: Perspectives from neurology and neuropsychology. J. Learn. Disabil.
**1997**, 30, 34–46. [Google Scholar] [CrossRef] [PubMed] - Rourke, B.P.; Finlayson, M.A.J. Neuropsychological significance of variations in patterns of academic performance: Verbal and visual-spatial abilities. J. Abnorm. Child Psychol.
**1978**, 6, 121–133. [Google Scholar] [CrossRef] [PubMed] - Mammarella, I.C.; Giofrè, D.; Ferrara, R.; Cornoldi, C. Intuitive geometry and visuospatial working memory in children showing symptoms of nonverbal learning disabilities. Child Neuropsychol.
**2013**, 19, 235–249. [Google Scholar] [CrossRef] [Green Version] - Mammarella, I.C.; Lucangeli, D.; Cornoldi, C. Spatial working memory and arithmetic deficits in children with nonverbal learning difficulties (NLD). J. Learn. Disabil.
**2010**, 43, 455–468. [Google Scholar] [CrossRef] [Green Version] - Crollen, V.; Vanderclausen, V.; Allaire, F.; Pollaris, A.; Noël, M.-P. Spatial and numerical processing in children with non-verbal learning disabilities. Dev. Disabil. Res. Rev.
**2015**, 47, 61–72. [Google Scholar] [CrossRef] - Hubbard, E.M.; Piazza, M.; Pinel, P.; Dehaene, S. Interactions between number and space in parietal cortex. Nat. Rev. Neurosci.
**2005**, 6, 435–448. [Google Scholar] [CrossRef] - Szucs, D.; Devine, A.; Soltesz, F.; Nobes, A.; Gabriel, F. Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex
**2013**, 49, 2674–2688. [Google Scholar] [CrossRef] [Green Version] - Schneider, M.; Merz, S.; Stricker, J.; De Smedt, B.; Torbeyns, J.; Verschaffel, L.; Luwel, K. Associations of Number Line Estimation with Mathematical Competence: A Meta-analysis. Child Dev.
**2018**, 89, 1467–1484. [Google Scholar] [CrossRef] - Fuchs, L.S.; Compton, D.L.; Fuchs, D.; Paulsen, K.; Bryant, J.D.; Hamlett, C.L. The Prevention, Identification, and Cognitive Determinants of Math Difficulty. J. Educ. Psychol.
**2005**, 97, 493–513. [Google Scholar] [CrossRef] - Nunes, T.; Bryant, P.; Evans, D.; Bell, D.; Gardner, S.; Gardner, J.; Carraher, J. The contribution of logical reasoning to the learning of mathematics in primary school. Br. J. Dev. Psychol.
**2007**, 25, 147–166. [Google Scholar] [CrossRef] - Fuchs, L.S.; Fuchs, D.; Compton, D.L.; Powell, S.R.; Seethaler, P.M.; Capizzi, A.M.; Schatschneider, C.; Fletcher, J.M. The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. J. Educ. Psychol.
**2006**, 98, 29–43. [Google Scholar] [CrossRef] - Green, C.T.; Bunge, S.A.; Chiongbian, V.B.; Barrow, M.; Ferrer, E. Fluid reasoning predicts future mathematical performance among children and adolescents. J. Exp. Child Psychol.
**2017**, 157, 125–143. [Google Scholar] [CrossRef] [Green Version] - Deary, I.; Strand, S.; Smith, P.; Fernandes, C. Intelligence and Educational Achievement. Intelligence
**2007**, 35, 13–21. [Google Scholar] [CrossRef] - Morsanyi, K.; Devine, A.; Nobes, A.; Szucs, D. The link between logic, mathematics and imagination: Evidence from children with developmental dyscalculia and mathematically gifted children. Dev. Sci.
**2013**, 16, 542–553. [Google Scholar] [CrossRef] - Karagiannakis, G.; Baccaglini-Frank, A.; Roussos, P. Detecting strengths and weaknesses in learning mathematics through a model classifying mathematical skills, Aust. J. Learn. Disabil.
**2017**, 21, 115–141. [Google Scholar] - Gunderson, E.A.; Ramirez, G.; Beilock, S.L.; Levine, S.C. The relation between spatial skill and early number knowledge: The role of the linear number line. Dev. Psychol.
**2012**, 48, 1229–1241. [Google Scholar] [CrossRef] [Green Version] - Simms, V.; Clayton, S.; Cragg, L.; Gilmore, C.; Johnson, S. Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills. J. Exp. Child Psychol.
**2016**, 145, 22–33. [Google Scholar] [CrossRef] [Green Version] - Schneider, M.; Grabner, R.H.; Paetsch, J. Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. J. Educ. Psychol.
**2009**, 101, 359–372. [Google Scholar] [CrossRef] [Green Version] - Reigosa-Crespo, V.; Valdés-Sosa, M.; Butterworth, B.; Estévez, N.; Rodríguez, M.; Santos, E.; Torres, P.; Suárez, R.; Lage, A. Basic numerical capacities and prevalence of developmental dyscalculia: The Havana Survey. Dev. Psychol.
**2012**, 48, 123–135. [Google Scholar] [CrossRef] [PubMed] [Green Version] - World Health Organization. World Medical Association Declaration of Helsinki. Ethical principles for medical research involving human subjects. Bull. World Health Org.
**2001**, 79, 373–374. [Google Scholar] - Gebuis, T.; Reynvoet, B. Generating nonsymbolic number stimuli. Behav. Res. Methods
**2011**, 43, 981–986. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Desmet, L.; Grégoire, L.; Mussolin, C. Developmental changes in the comparison of decimal fractions. Learn. Instr.
**2010**, 20, 521–523. [Google Scholar] [CrossRef] [Green Version] - Noël, M.-P.; Turconi, E. Assessing number transcoding in children. Eur. J. Psychol. Appl.
**1999**, 49, 295–302. [Google Scholar] - Siegler, R.S.; Opfer, J.E. The Development of Numerical Estimation: Evidence for Multiple Representations of Numerical Quantity. Psychol. Sci.
**2003**, 14, 237–243. [Google Scholar] [CrossRef] - Siegler, R.S.; Booth, J.L. Development of numerical estimation in young children. Child Dev.
**2004**, 75, 428–444. [Google Scholar] [CrossRef] - Opfer, J.E.; Siegler, R.S. Representational change and children’s numerical estimation. Cogn. Psychol.
**2007**, 55, 169–195. [Google Scholar] [CrossRef] - Carpenter, T.P.; Moser, J.M. The development of addition and subtraction problem—solving skills. In Addition and Subtraction: A Cognitive Perspective; Carpenter, T.P., Moser, J.M., Romberg, T.P., Eds.; Lawrence Erlbaum Associates: Hillsdale, NJ, USA, 1982; pp. 9–25. [Google Scholar]
- Vergnaud, G. Multiplicative structures. In Acquisition of Mathematical Concepts and Processes; Lesh, R., Landau, M., Eds.; Academic Press: New York, NY, USA, 1983; pp. 127–174. [Google Scholar]
- Dudal, P. Leerlingvolgsysteem: Wiskunde-Toetsen 1-6 [Student Monitoring System: Mathematics-Tests 1–6]; Garant: Leuven, Belgium, 2000. [Google Scholar]
- IBM Corp. IBM SPSS Statistics for Macintosh, Version 25.0; IBM Corp.: Armonk, NY, USA, 2017. [Google Scholar]
- Streiner, D.L. Starting at the beginning: An introduction to coefficient alpha and internal consistency. J. Pers. Assess.
**2003**, 80, 99–103. [Google Scholar] [CrossRef] - Brankaer, C.; Ghesquière, P.; De Smedt, B. Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test). Behav. Res. Methods
**2016**, 49, 1361–1373. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nosworthy, N.; Bugden, S.; Archibald, L.E.; Ansari, D. A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children’s Arithmetic Competence. PLoS ONE
**2013**, 8, e67918. [Google Scholar] [CrossRef] - Halberda, J.; Mazzocco, M.M.M.; Feigenson, L. Individual differences in non-verbal number acuity correlate with maths achievement. Nature
**2008**, 455, 665–668. [Google Scholar] [CrossRef] - Butterworth, B. Dyscalculia Screener; InferNelson: London, UK, 2003. [Google Scholar]
- Gebuis, T.; Kadosh, R.C.; Gevers, W. Sensory-intergration system rather than approximate number system underlies numerosity processing: Acritical review. Acta Psychol.
**2016**, 171, 17–35. [Google Scholar] [CrossRef] - De Smedt, B.; Noël, M.-P.; Gilmore, C.; Ansari, D. How do symbolic and non-symbolic numerical magnitude processing relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends Neurosci. Educ.
**2013**, 2, 48–55. [Google Scholar] [CrossRef] [Green Version] - Russell, R.L.; Ginsburg, H.P. Cognitive analysis of children’s mathematical difficulties. Cogn. Instr.
**1984**, 1, 217–244. [Google Scholar] [CrossRef] - Jiménez, J.E.; Garcia, A.I. Is IQ-achievement discrepancy relevant in the definition of arithmetic learning disabilities? Learn. Disabil. Q.
**1999**, 22, 291–301. [Google Scholar] - Jordan, N.C.; Oettinger, T. Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. J. Learn. Disabil.
**1997**, 30, 624–634. [Google Scholar] [CrossRef] - Fuchs, L.S.; Fuchs, D. Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities. J. Learn. Disabil.
**2002**, 35, 564–574. [Google Scholar] [CrossRef] - Geary, D.C.; Hoard, M.K.; Bailey, D.H. Fact Retrieval Deficits in Low Achieving Children and Children with Mathematical Learning Disability. J. Learn. Disabil.
**2012**, 45, 291–307. [Google Scholar] [CrossRef] [Green Version] - Noël, M.P.; Rousselle, L. Developmental Changes in the Profiles of Dyscalculia: An Explanation Based on a Double Exact-and-Approximate Number Representation Model. Front. Hum. Neurosci.
**2011**, 5, 165. [Google Scholar] [CrossRef] [Green Version] - Geary, D.; Hoard, M.K.; Nugent, L.; Byrd-Craven, J. Development of Number Line Representations in Children with Mathematical Learning Disability. Dev. Neuropsychol.
**2008**, 33, 277–299. [Google Scholar] [CrossRef] [Green Version] - Temple, C.M. Digit dyslexia: A category-specific disorder in developmental dyscalculia. Cogn. Neuropsychol.
**1989**, 6, 93–116. [Google Scholar] [CrossRef] - Sullivan, K.S.; Macaruso, P.; Sokol, S.M. Remediation of Arabic numeral processing in a case of developmental dyscalculia. Neuropsychol. Rehabil.
**1996**, 6, 27–53. [Google Scholar] [CrossRef]

**Figure 7.**Squares subtest screenshots. (

**a**) contain only whole squares; (

**b**) contain a combination of whole squares and half-square triangles; (

**c**) quarter-square triangles are also included.

**Figure 11.**Difficulty level × grade interaction on (

**a**) single-digits number comparison, (

**b**) number dictation, (

**c**) subitizing, (

**d**) building blocks, (

**e**) numerical patterns and (

**f**) number lines.

Grade | Sex | Sum | |
---|---|---|---|

Boys | Girls | ||

1 | 50 | 56 | 106 |

2 | 55 | 43 | 98 |

3 | 52 | 50 | 102 |

4 | 55 | 56 | 111 |

5 | 52 | 40 | 92 |

6 | 56 | 57 | 113 |

Sum | 320 | 302 | 622 |

Domain | |||
---|---|---|---|

Core Number | Memory | Reasoning | Visual-Spatial |

1. Dots comparison 2. Single-digit numbers comparison 8. Subitizing | 5. Numbers dictation 6. Νext number 7. Previous number 9. Enumeration 10. Addition facts retrieval 11. Multiplication facts retrieval | 3. Multidigit numbers comparison 12. Mental calculations 17. Word problems 18. Calculation principles 19. Numerical patterns | 13. Number lines 0–100 14. Number lines 0–1000 15. Squares 16. Building blocks |

Subtests | Grade 1 | Grade 2 | Grade 3 | Grades 4–6 |
---|---|---|---|---|

1. Dots comparison | 30 | 30 | 30 | 30 |

2. Single-digit numbers comparison | 24 | 24 | 24 | 24 |

3. Multidigit numbers comparison | 0 | 6 | 9 | 12 |

4. Screen keyboard use | 10 | 10 | 10 | 10 |

5. Numbers dictation * | 30 | 30 | 30 | 30 |

6. Next number * | 12 | 18 | 18 | 18 |

7. Previous number * | 12 | 18 | 18 | 18 |

8. Subitizing | 20 | 20 | 20 | 20 |

9. Enumeration | 14 | 14 | 14 | 14 |

10. Addition facts retrieval | 12 | 12 | 12 | 12 |

11. Multiplication facts retrieval | 0 | 0 | 14 | 14 |

12. Mental calculations | 0 | 12 | 24 | 24 |

13. Number lines 0–100 | 22 | 22 | 22 | 22 |

14. Number lines 0–1000 | 0 | 0 | 22 | 22 |

15. Squares | 0 | 0 | 10 | 10 |

16. Building blocks | 8 | 8 | 8 | 8 |

17. Word problems * | 0 | 10 | 18 | 18 |

18. Calculation principles * | 0 | 0 | 15 | 15 |

19. Numerical patterns * | 18 | 18 | 18 | 18 |

Individual Measures | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

M | SD | M | SD | M | SD | M | SD | M | SD | M | SD | |

Dots comparison (AC) | 0.55 | 0.13 | 0.60 | 0.10 | 0.62 | 0.10 | 0.63 | 0.09 | 0.69 | 0.08 | 0.67 | 0.09 |

Single-digit numbers comparison (AC) | 0.95 | 0.06 | 0.97 | 0.39 | 0.98 | 0.05 | 0.99 | 0.03 | 0.98 | 0.05 | 0.98 | 0.04 |

Single-digit numbers comparison (RT) | 3113 | 437 | 2799 | 385 | 2515 | 354 | 2337 | 205 | 2211 | 314 | 2153 | 187 |

Multidigit numbers comparison (AC) | - | - | 0.85 | 0.18 | 0.88 | 0.14 | 0.80 | 0.13 | 0.87 | 0.12 | 0.90 | 0.12 |

Multidigit numbers comparison (RT) | - | - | 4027 | 944 | 3512 | 503 | 3075 | 360 | 2903 | 444 | 2749 | 285 |

Screen keyboard use (AC) | 0.96 | 0.01 | 0.98 | 0.01 | 0.98 | 0.01 | 0.99 | 0.01 | 0.99 | 0.01 | 0.99 | 0.01 |

Screen keyboard use (RT) | 4234 | 792 | 3621 | 523 | 3204 | 399 | 2850 | 275 | 2682 | 350 | 2484 | 259 |

Numbers dictation (AC) | 0.36 | 0.14 | 0.63 | 0.20 | 0.79 | 0.17 | 0.90 | 0.16 | 0.93 | 0.12 | 0.95 | 0.12 |

Numbers dictation (RT) | 3670 | 1339 | 3890 | 862 | 2487 | 491 | 2679 | 600 | 2539 | 438 | 2243 | 404 |

Next number (AC) | 0.50 | 0.35 | 0.64 | 0.28 | 0.83 | 0.25 | 0.91 | 0.09 | 0.92 | 0.02 | 0.95 | 0.12 |

Next number (RT) | 5682 | 1779 | 5513 | 1384 | 3605 | 889 | 3569 | 596 | 3169 | 519 | 2772 | 370 |

Previous number (AC) | 0.53 | 0.37 | 0.73 | 0.24 | 0.87 | 0.21 | 0.94 | 0.12 | 0.95 | 0.14 | 0.97 | 0.07 |

Previous number (RT) | 5942 | 2079 | 5189 | 1115 | 3259 | 610 | 3244 | 510 | 2957 | 439 | 2618 | 347 |

Subitizing (AC) | 0.64 | 0.20 | 0.74 | 0.16 | 0.79 | 0.14 | 0.85 | 0.11 | 0.87 | 0.11 | 0.87 | 0.12 |

Enumeration (AC) | 0.71 | 0.29 | 0.81 | 0.23 | 0.85 | 0.18 | 0.92 | 0.13 | 0.92 | 0.13 | 0.89 | 0.15 |

Enumeration (RT) | 11830 | 6553 | 8387 | 1850 | 7529 | 1550 | 6623 | 1263 | 6115 | 1250 | 5431 | 1024 |

Addition facts retrieval (AC) | 0.82 | 0.25 | 0.91 | 0.19 | 0.94 | 0.14 | 0.98 | 0.04 | 0.98 | 0.04 | 0.96 | 0.13 |

Addition facts retrieval (RT) | 8178 | 4130 | 5402 | 1847 | 4343 | 2617 | 3343 | 778 | 3030 | 606 | 2568 | 428 |

Multiplication facts retrieval (AC) | - | - | - | - | 0.80 | 0.24 | 0.92 | 0.14 | 0.95 | 0.058 | 0.92 | 0.16 |

Multiplication facts retrieval (RT) | - | - | - | - | 8550 | 3598 | 6186 | 2214 | 4992 | 1539 | 4333 | 2190 |

Mental calculations (AC) | - | - | 0.53 | 0.27 | 0.63 | 0.23 | 0.80 | 0.19 | 0.85 | 0.14 | 0.84 | 0.15 |

Number lines 0–100 (PAE) | 17.24 | 8.12 | 8.42 | 4.29 | 6.48 | 2.81 | 5.14 | 1.62 | 4.73 | 1.49 | 4.59 | 1.68 |

Number lines 0–1000 (PAE) | - | - | - | - | 11.02 | 6.49 | 7.75 | 4.42 | 5.97 | 3.08 | 5.37 | 2.99 |

Squares (AC) | - | - | - | - | 0.59 | 0.23 | 0.68 | 0.17 | 0.73 | 0.16 | 0.77 | 0.16 |

Building blocks (AC) | 0.58 | 0.27 | 0.78 | 0.26 | 0.81 | 0.23 | 0.86 | 0.19 | 0.91 | 0.14 | 0.93 | 0.12 |

Word problems (AC) | - | - | 0.44 | 0.30 | 0.36 | 0.24 | 0.54 | 0.29 | 0.68 | 0.31 | 0.81 | 0.18 |

Calculation principles (AC) | - | - | - | - | 0.22 | 0.22 | 0.33 | 0.23 | 0.36 | 0.18 | 0.51 | 0.28 |

Numerical patterns (AC) | 0.21 | 0.16 | 0.38 | 0.18 | 0.45 | 0.17 | 0.52 | 0.20 | 0.58 | 0.21 | 0.60 | 0.20 |

Measure | Cronbach’s α | Internal Consistency Level |
---|---|---|

Numbers dictation (AC) | 0.95 | Good or excellent |

Screen keyboard use (RT) | 0.94 | |

Calculation principles (AC) | 0.92 | |

Number lines 0–100 (PAE) | 0.92 | |

Next number (AC) | 0.87–0.93 | |

Word problems (AC) | 0.86–0.93 | |

Previous number (AC) | 0.84–0.93 | |

Single-digit numbers comparison (RT) | 0.82–0.93 | |

Multidigit numbers comparison (RT) | 0.81–0.90 | |

Numerical patterns (AC) | 0.89 | |

Numbers dictation (RT) | 0.56–0.89 | |

Enumeration (RT) | 0.88 | |

Addition facts retrieval (AC) | 0.88 | |

Number lines 0–1000 (PAE) | 0.88 | |

Multiplication facts retrieval (AC) | 0.86 | |

Mental calculations (AC) | 0.85–0.87 | |

Multiplication facts retrieval (RT) | 0.85 | |

Enumeration (AC) | 0.85 | |

Addition facts retrieval (RT) | 0.84 | |

Building blocks (AC) | 0.79 | Acceptable |

Subitizing (AC) | 0.78 | |

Next number (RT) | 0.66–0.78 | |

Previous number (RT) | 0.57–0.74 | |

Squares (AC) | 0.66 | Poor |

Screen calculator use (AC) | 0.62 | |

Single-digit numbers comparison (AC) | 0.57 | |

Multidigit numbers comparison (AC) | 0.44–0.55 | |

Dots comparison (AC) | 0.42 | Unacceptable |

Grade | η^{2} | Difficulty | η^{2} | Grade × Difficulty | η^{2} | |
---|---|---|---|---|---|---|

Dots comparison (AC) | F_{5,541} = 15.93 *** | 0.13 | ^{1} F_{3.678,1989} = 102.10 *** | 0.09 | p = 0.062 | |

Single-digit numbers comparison (AC) | F_{5,615} = 10.72 *** | 0.08 | F_{1,615} = 67.37 *** | 0.18 | p = 0.298 | |

Single-digit numbers comparison (RT) | F_{5,615} = 136.60 *** | 0.53 | F_{1,615} = 252.30 *** | 0.29 | F_{5,615} = 7.11 *** | 0.06 |

Multidigit numbers comparison ^{4} (AC) | F_{2,312} = 17.30 *** | 0.10 | ^{2} F_{31.664,519} = 206.34 *** | 0.40 | ^{2} F_{3.328,519} = 23.45 *** | 0.13 |

Multidigit numbers comparison ^{4} (RT) | F_{2,311} = 21.72 *** | 0.12 | ^{1} F_{1.775,552} = 63.06 *** | 0.17 | p = 0.407 | |

Numbers dictation (AC) | F_{5,614} = 242.84 *** | 0.66 | ^{1} F_{3.234,1986} = 654.23 *** | 0.52 | ^{1} F_{16.17,1986} = 107.85 *** | 0.47 |

Numbers dictation ^{4} (RT) | F_{2,300} = 27.54 *** | 0.16 | ^{1} F_{2.652,796} = 4.74 ** | 0.02 | ^{1} F_{5.304,796} = 6.03 *** | 0.04 |

Next number ^{3} (AC) | F_{3,413} = 8.72 *** | 0.06 | ^{1} F_{1.781,734} = 37.84 ** | 0.08 | ^{1} F_{5.343,734} = 5.08 ** | 0.04 |

Next number ^{4} (RT) | F_{2,304} = 20.01 *** | 0.17 | p = 0.972 | F_{2,304} = 5.49 ** | 0.04 | |

Previous number ^{3} (AC) | F_{3,413} = 9.72 *** | 0.07 | ^{1} F_{1.700,702} = 34.55 ** | 0.08 | ^{1} F_{5.101,702} = 7.06 * | 0.05 |

Previous number ^{4} (RT) | F_{2,306} = 18.64 *** | 0.11 | p = 0.516 | F_{2,306} = 9.93 ** | 0.06 | |

Subitizing (AC) | F_{5,614} = 41.622 *** | 0.25 | ^{2} F_{2.802,1721} = 458.88 *** | 0.43 | ^{2} F_{14.012,1721} = 4.984 *** | 0.04 |

Enumeration (AC) | F_{5,616} = 17.67 *** | 0.13 | F_{1,616} = 74.64 *** | 0.11 | F_{5,616} = 2.60 * | 0.02 |

Enumeration ^{5} (RT) | F_{4,500} = 8.74 *** | 0.07 | p = 0.216 | p = 0.584 | ||

Addition facts retrieval (AC) | F_{5,615} = 15.36 *** | 0.11 | p = 0.219 | p = 0.099 | ||

Addition facts retrieval ^{5} (RT) | F_{4,510} = 5.32 *** | 0.04 | p = 0.991 | p = 0.773 | ||

Multiplication facts retrieval ^{3} (AC) | F_{3,412} = 15.95 *** | 0.10 | F_{1,412} = 13.02 *** | 0.03 | p = 0.783 | |

Multiplication facts retrieval ^{4} (RT) | F_{2,412} = 19.49 *** | 0.13 | p = 0.799 | p = 0.087 | ||

Mental calculations (AC) | F_{3,413} = 31.64 *** | 0.19 | ^{1} F_{1.745,721} = 219.09 *** | 0.35 | ^{1} F_{5.236,721} = 8.34 *** | 0.06 |

Number line tasks ^{6} (PAE) | F_{5,611} = 147.55 *** | 0.55 | ||||

Squares (AC) | F_{3,413} = 33.04 *** | 0.20 | ||||

Building blocks (AC) | F_{3,412} = 21.75 *** | 0.14 | F_{1,412} = 1216.52 *** | 0.75 | F_{3,412} = 9.84 *** | 0.07 |

Word problems ^{3} (AC) | F_{5,610} = 37.71 *** | 0.24 | F_{1,610} = 230.76 *** | 0.27 | F_{5,610} = 6.86 *** | 0.05 |

Calculation principles (AC) | F_{3,403} = 61.69 *** | 0.32 | F_{2,806} = 335.39 *** | 0.45 | F_{6,806} = 9.07 *** | 0.06 |

Numerical patterns (AC) | F_{3,403} = 25.23 *** | 0.16 | ^{1} F_{1.791,722} = 511.78 *** | 0.60 | ^{1} F_{5.374,722} = 15.36 *** | 0.10 |

^{1}Huynh–Feldt correction;

^{2}Greenhouse–Geisser correction;

^{3}grades 3–6;

^{4}grades 4–6;

^{5}grades 2–6;

^{6}includes both number line 0–100 and 0–1000 tasks.

**Table 7.**Person correlation coefficients between the MathPro index score and the standardized math test.

Grade | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Dots comparison (AC) | 0.124 | 0.278 ** | 0.299 ** | 0.201 * | 0.009 | 0.052 |

Single-digit numbers comparison (AC) | 0.087 | 0.097 | 0.100 | 0.010 | 0.107 | 0.187 |

Single-digit numbers comparison (RT) | 0.257 ** | 0.022 | 0.020 | 0.051 | 0.009 | 0.093 |

Multidigit numbers comparison (AC) | - | 0.385 ** | 0.368 ** | 0.538 ** | 0.289 ** | 0.192 * |

Multidigit numbers comparison (RT) | - | 0.181 | 0.252 * | 0.158 | 0.166 | 0.075 |

Numbers dictation (AC) | 0.283 ** | 0.439 ** | 0.403 ** | 0.206* | 0.307 ** | 0.148 |

Numbers dictation (RT) | - | - | 0.035 | 0.169 | 0.023 | 0.036 |

Next number (AC) | 0.256 ** | 0.305 ** | 0.094 | 0.106 | 0.187 | 0.042 |

Next number (RT) | - | - | 0.057 | 0.137 | 0.182 | 0.024 |

Previous number (AC) | 0.303 ** | 0.478 ** | 0.109 | 0.167 | 0.141 | 0.086 |

Previous number (RT) | 0.100 | 0.028 | 0.072 | 0.042 | ||

Subitizing (AC) | 0.288 ** | 0.263 ** | 0.152 | 0.013 | 0.184 | 0.095 |

Enumeration (AC) | 0.382 ** | 0.249 * | 0.014 | 0.152 | 0.126 | 0.154 |

Enumeration (RT) | - | - | 0.235 * | 0.017 | 0.179 | 0.184 |

Addition facts retrieval (AC) | 0.434 ** | 0.260 ** | 0.162 | 0.313 ** | 0.006 | 0.034 |

Addition facts retrieval (RT) | - | 0.315 ** | 0.180 | 0.287 ** | 0.373 ** | 0.288 ** |

Multiplication facts retrieval (AC) | - | - | 0.278 ** | 0.336 ** | 0.008 | 0.062 |

Multiplication facts retrieval (RT) | - | - | - | 0.161 | 0.433 ** | 0.192 * |

Mental calculations (AC) | 0.573 ** | 0.439 ** | 0.495 ** | 0.460 ** | 0.325 ** | |

Number lines 0–100 (PAE) | 0.374 ** | 0.476 ** | 0.430 ** | 0.292 ** | 0.434 ** | 0.274 ** |

Number lines 0–1000 (PAE) | - | - | 0.569 ** | 0.488 ** | 0.414 ** | 0.394 ** |

Squares (AC) | - | - | 0.365 ** | 0.433 ** | 0.277 ** | 0.319 ** |

Building blocks (AC) | 0.446 ** | 0.185 | 0.219* | 0.327 ** | 0.004 | 0.196 ** |

Word problems (AC) | - | 0.518 ** | 0.391 ** | 0.613 ** | 0.335 ** | 0.495 ** |

Calculation principles (AC) | - | - | 0.364 ** | 0.425 ** | 0.411 ** | 0.189 |

Numerical patterns (AC) | 0.521 ** | 0.477 ** | 0.298 ** | 0.509 ** | 0.462 ** | 0.475 ** |

MathPro index score | 0.595 ** | 0.604 ** | 0.568 ** | 0.627 ** | 0.637 ** | 0.472 ** |

Individual Measures | Grade 1 | Grade 2 | Grade 3 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

TA | MD | F_{1,103} | Sig | TA | MD | F_{1,91} | Sig | TA | MD | F_{1,93} | Sig | |

n = 20 | n = 83 | n = 75 | n = 16 | n = 73 | n = 20 | |||||||

M (SD) | M (SD) | M (SD) | M (SD) | M (SD) | M (SD) | |||||||

Dots comparison (AC) | 0.55 (0.13) | 0.54 (0.11) | 0.047 | 0.829 | 0.60 (0.01) | 0.57 (0.01) | 1.30 | 0.256 | 0.63 (0.01) | 0.60 (0.01) | 1.152 | 0.286 |

Single-digit numbers comparison (AC) | 0.95 (0.07) | 0.94 (0.05) | 0.077 | 0.782 | 0.98 (0.03) | 0.95 (0.06) | 9.19 | 0.003 | 0.98 (0.04) | 0.98 (0.03) | 0.305 | 0.582 |

Single-digit numbers comparison (RT) | 3324 (390) | 3050 (421) | 7.286 | 0.008 | 2788 (493) | 2807 (376) | 0.385 | 0.537 | 2490 (367) | 2583 (380) | 0.132 | 0.717 |

Multidigit numbers comparison (AC) | - | - | - | - | 0.88 (0.17) | 0.71 (0.21) | 11.43 | 0.001 | 0.92 (0.12) | 0.78 (0.15) | 17.318 | <0.001 |

Multidigit numbers comparison (RT) | - | - | - | - | 4229 (1052) | 3991 (920) | 1.044 | 0.310 | 3421 (464) | 3832 (596) | 10.036 | 0.002 |

Numbers dictation (AC) | 0.38 (0.13) | 0.31 (0.15) | 4.34 | 0.040 | 0.66 (0.21) | 0.53 (0.18) | 5.47 | 0.022 | 0.83 (0.14) | 0.69 (0.19) | 12.198 | 0.001 |

Numbers dictation (RT) | - | - | - | - | - | - | - | - | 3242 (610) | 3407 (746) | 0.175 | 0.676 |

Next number (AC) | 0.53 (0.34) | 0.39 (0.34) | 2.76 | 0.100 | 0.65 (0.29) | 0.63 (0.22) | 0.058 | 0.810 | 0.83 (0.03) | 0.82 (0.03) | 0.029 | 0.866 |

Next number (RT) | - | - | - | - | - | - | - | - | 3572 (800) | 3838 (1268) | 0.526 | 0.470 |

Previous number (AC) | 0.56 (0.35) | 0.44 (0.40) | 1.84 | 0.179 | 0.76 (0.23) | 0.60 (0.27) | 6.13 | 0.015 | 0.87 (0.20) | 0.82 (0.28) | 0.775 | 0.381 |

Previous number (RT) | - | - | - | - | - | - | - | - | 3239 (644) | 3361 (581) | 0.143 | 0.706 |

Subitizing | 0.66 (0.20) | 0.54 (0.18) | 6.32 | 0.014 | 0.75 (0.13) | 0.66 (0.24) | 5.02 | 0.028 | 0.79 (0.12) | 0.78 (0.12) | 0.236 | 0.628 |

Enumeration (AC) | 0.76 (0.24) | 0.52 (0.32) | 14.34 | <0.001 | 0.82 (0.22) | 0.75 (0.29) | 1.11 | 0.295 | 0.84 (0.18) | 0.85 (0.21) | 0.016 | 0.901 |

Enumeration (RT) | - | - | - | - | - | - | - | - | 7431 (1547) | 7874 (1847) | 0.607 | 0.438 |

Addition facts retrieval (AC) | 0.88 (0.18) | 0.66 (0.34) | 15.31 | <0.001 | 0.92 (0.19) | 0.85 (0.25) | 1.55 | 0.216 | 0.94 (0.13) | 0.95 (0.08) | 0.075 | 0.784 |

Addition facts retrieval (RT) | - | - | - | - | 5177 (1667) | 6816 (2390) | 12.113 | 0.001 | 4096 (1428) | 5444 (5187) | 3.347 | 0.071 |

Multiplication facts retrieval (AC) | - | - | - | - | - | - | - | - | 0.82 (0.22) | 0.75 (0.25) | 1.320 | 0.254 |

Mental calculations (AC) | - | - | - | - | 0.59 (0.25) | 0.30 (0.25) | 17.52 | <0.001 | 0.66 (0.23) | 0.52 (0.18) | 5.408 | 0.022 |

Number lines 0–100 (PAE) | 15.67 (7.46) | 23.21 (8.37) | 15.51 | <0.001 | 7.7 (3.88) | 11.24 (4.65) | 10.85 | 0.002 | 5.77 (1.79) | 8.92 (4.40) | 22.374 | <0.001 |

Number lines 0–1000 (PAE) | - | - | - | - | - | - | - | - | 8.82 (4.81) | 16.13 (6.69) | 27.984 | <0.001 |

Squares (AC) | - | - | - | - | - | - | - | - | 0.62 (0.21) | 0.45 (0.23) | 9.514 | 0.003 |

Building blocks (AC) | 0.63 (0.25) | 0.46 (0.29) | 7.39 | 0.008 | 0.79 (0.27) | 0.72 (0.26) | 0.82 | 0.368 | 0.83 (0.23) | 0.77 (0.18) | 1.029 | 0.313 |

Word problems (AC) | - | - | - | - | 0.49 (0.30) | 0.23 (0.26) | 10.85 | 0.001 | 0.40 (0.25) | 0.28 (0.16) | 3.743 | 0.041 |

Calculation principles (AC) | - | - | - | - | - | - | - | - | 0.26 (0.24) | 0.09 (0.09) | 7.801 | 0.006 |

Numerical patterns (AC) | 0.25 (0.15) | 0.08 (0.09) | 21.95 | <0.001 | 0.42 (0.18) | 0.28 (0.16) | 6.78 | 0.011 | 0.46 (0.17) | 0.41 (0.15) | 1.240 | 0.268 |

Individual Measures | TA | MD | F_{1,278} | Sig |
---|---|---|---|---|

n = 212 | n = 76 | |||

M (SD) | M (SD) | |||

Dots comparison (AC) | 0.67 (0.09) | 0.64 (0.09) | 5.287 | 0.022 |

Single-digit numbers comparison (AC) | 0.99 (0.04) | 0.99 (0.03) | 0.103 | 0.749 |

Single-digit numbers comparison (RT) | 2239 (244) | 2226 (290) | 3.466 | 0.064 |

Multidigit numbers comparison (AC) | 0.88 (0.11) | 0.79 (0.14) | 28.790 | <0.001 |

Multidigit numbers comparison (RT) | 2885 (352) | 3009 (478) | 4.31 | 0.039 |

Numbers dictation (AC) | 0.94 (0.12) | 0.87 (0.17) | 14.752 | <0.001 |

Numbers dictation (RT) | 4079 (593) | 4211 (811) | 0.694 | 0.405 |

Next number (AC) | 0.93 (0.11) | 0.91 (0.17) | 2.395 | 0.123 |

Next number (RT) | 3125 (543) | 3310 (724) | 3.653 | 0.057 |

Previous number (AC) | 0.96 (0.11) | 0.95 (0.07) | 0.591 | 0.443 |

Previous number (RT) | 2936 (488) | 2961 (578) | 0.333 | 0.564 |

Subitizing (AC) | 0.87 (0.11) | 0.85 (0.12) | 3.725 | 0.055 |

Enumeration (AC) | 0.92 (0.11) | 0.90 (0.16) | 1.949 | 0.164 |

Enumeration (RT) | 5935 (1209) | 6392 (1480) | 5.238 | 0.023 |

Addition facts retrieval (AC) | 0.98 (0.05) | 0.96 (0.06) | 1.073 | 0.301 |

Addition facts retrieval (RT) | 2878 (598) | 3237 (902) | 14.173 | <0.001 |

Multiplication facts retrieval (AC) | 0.96 (0.08) | 0.90 (0.17) | 7.244 | 0.008 |

Multiplication facts retrieval (RT) | 4990 (2215) | 5827 (2165) | 6.403 | 0.012 |

Mental calculations (AC) | 0.87 (0.12) | 0.72 (0.21) | 54.627 | <0.001 |

Number lines 0–100 (PAE) | 4.50 (1.33) | 5.68 (2.06) | 30.571 | <0.001 |

Number lines 0–1000 (PAE) | 5.42 (2.93) | 9.43 (4.58) | 70.988 | <0.001 |

Squares (AC) | 0.77 (0.16) | 0.66 (0.18) | 24.387 | <0.001 |

Building blocks (AC) | 0.92 (0.14) | 0.86 (0.19) | 8.479 | 0.004 |

Word problems (AC) | 0.75 (0.24) | 0.48 (0.28) | 60.986 | <0.001 |

Calculation principles (AC) | 0.44 (0.24) | 0.31 (0.24) | 13.964 | <0.001 |

Numerical patterns (AC) | 0.62 (0.20) | 0.47 (0.16) | 30.403 | <0.001 |

Domain | Subtests | Criterion | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 |
---|---|---|---|---|---|---|---|---|

Core | Dots comparison (AC) ^{α} | STMC | ✓ | ✓ | ✓ | |||

MD-TA | ✓ | ✓ | ✓ | |||||

Single-digit numbers comparison (AC) ^{α} | STMC | |||||||

MDC | ✓ | |||||||

Single-digit numbers comparison (RT) | STMC | ✓ | ||||||

MD-TA | ✓ | |||||||

Subitizing | STMC | ✓ | ✓ | |||||

MD-TA | ✓ | ✓ | ||||||

Memory | Numbers dictation (AC) | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | |

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

Numbers dictation (RT) ^{α} | STMC | |||||||

MD-TA | ||||||||

Next number (AC) | STMC | ✓ | ✓ | |||||

MD-TA | ||||||||

Next number (RT) ^{α} | STMC | |||||||

MD-TA | ||||||||

Previous number (AC) | STMC | ✓ | ✓ | |||||

MD-TA | ||||||||

Previous number (RT) ^{α} | STMC | |||||||

MD-TA | ||||||||

Enumeration (AC) | STMC | ✓ | ✓ | |||||

MD-TA | ✓ | |||||||

Enumeration (RT) | STMC | ✓ | ||||||

MD-TA | ✓ | ✓ | ✓ | |||||

Addition facts retrieval (AC) | STMC | ✓ | ✓ | ✓ | ||||

MD-TA | ✓ | |||||||

Addition facts retrieval (RT) | STMC | ✓ | ✓ | ✓ | ✓ | |||

MD-TA | ✓ | ✓ | ✓ | ✓ | ||||

Multiplication facts retrieval (AC) | STMC | ✓ | ✓ | |||||

MD-TA | ✓ | ✓ | ✓ | |||||

Multiplication facts retrieval (RT) | STMC | ✓ | ✓ | |||||

MD-TA | ✓ | ✓ | ✓ | |||||

Reasoning | Multidigit numbers comparison (AC) ^{α} | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | |

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | |||

Multidigit numbers comparison (RT) | STMC | ✓ | ||||||

MD-TA | ✓ | ✓ | ✓ | ✓ | ||||

Mental calculations | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | ||

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | |||

Word problems | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | ||

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | |||

Calculation principles | STMC | ✓ | ✓ | ✓ | ||||

MD-TA | ✓ | ✓ | ✓ | ✓ | ||||

Numerical patterns | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | |||

Visual-spatial | Number lines 0–100 | STMC | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

MD-TA | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

Number lines 0–1000 | STMC | ✓ | ✓ | ✓ | ✓ | |||

MD-TA | ✓ | ✓ | ✓ | ✓ | ||||

Squares ^{α} | STMC | ✓ | ✓ | ✓ | ✓ | |||

MD-TA | ✓ | ✓ | ✓ | ✓ | ||||

Building blocks | STMC | ✓ | ✓ | ✓ | ✓ | |||

MD-TA | ✓ | ✓ | ✓ | ✓ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Karagiannakis, G.; Noël, M.-P.
Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1–6. *Behav. Sci.* **2020**, *10*, 126.
https://doi.org/10.3390/bs10080126

**AMA Style**

Karagiannakis G, Noël M-P.
Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1–6. *Behavioral Sciences*. 2020; 10(8):126.
https://doi.org/10.3390/bs10080126

**Chicago/Turabian Style**

Karagiannakis, Giannis, and Marie-Pascale Noël.
2020. "Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1–6" *Behavioral Sciences* 10, no. 8: 126.
https://doi.org/10.3390/bs10080126