Appendix

Table A1Characteristics of Studies Examining the Associations between Mathematics or Number Sense Performance, and Executive FunctioningAuthors & year N Mean

Age (months)

Maths measures

Inhibition measures

Shifting measures

Verbal updating measures

Visuospatial updating measures

PL measures VSSP measures

Agostino, Johnson, & Pascual-Leone (2010)

155 121 One-step multiplication, multiple-step multiplication

Antisaccade task, colour stroop, number stroop

Contingency naming task, trail making test

Letter memory Visual n-back task

Alloway (2007) 55 104 WOND Composite listening digit counting recall

Word recall, digit recall, nonword recall

Mazes, block recall, dotmatrix

Alloway & Alloway (2010)

98 60 WOND Composite verbal digit listening recall

Word recall, digit recall

Alloway & Archibald (2008)

34 105 WOND Odd one out, Mr X, Spatial span

Word recall, digit recall, nonword recall

Mazes, block recall, dotmatrix

Alloway et al. (2005) 192 61 Tees Baseline Scheme

Composite backwards digit counting recall listening recall

Alloway & Temple (2007)

40 116 WOND Composite digit listening counting recall

Odd one out, Mr X, Spatial span

Word recall, digit recall, nonword recall

Mazes, block recall, dotmatrix

Andersson (2007) 69 119 Written arithmetical multi-digit calculation, word problems

Trail making test

Verbal fluency task

Digit recall Dotmatrix

Andersson (2008a) 182 125 written arithmetical multi-digit calculation task

Colour stroop Trail making test

Verbal fluency task

Corsi blocks

Andersson (2008b) 124 141 written arithmetical multi-digit calculation task

Trail making test

Digit recall Visual matrix span

Andersson & Lyxell (2007)

165 121 mathematics screening task, arithmetic facts retrieval

Colour stroop Trail making test

Verbal fluency task

Digit recall Corsi blocks

Barrouillet & Lépine (2005)

91 113 Arithmetic task Reading and letter span

Counting span

Barrouillet, Mignon, & Thevenot (2008)

48 109 Subtraction task Reading and letter span

Counting span

Baylisse, Jarrold, Baddeley & Gunn (2005)

56 96 NFER Nelson Mathematics task

Verbal search task

Visuospatial search task

Digit recall Corsi blocks

Berg (2008) 90 122 WRAT3 Composite Semantic Categorisation and Auditory Digit Sequencing

Word recalldigit recall

Dotmatrix, corsi blocks

Blair & Razza (2007) 170 61 Maths battery adopted from Early Childhood Longitudinal Study

Peg tapping Item Selection

Bowey (1995) 99 65 Arithmetic subtest of WISC-R

Nonword repetition Test

Digit recall

Brock, Rimm-Kaufman, Nathanson & Grimm (2009)

173 65 Woodcock-Johnson III test of achievement

Toy Sort task, gift wrap task

Bull, Espy, & Wiebe (2008)

287 54 PIPS Shape school inhibition, tower of London

Shape school switching aspect

Backward digit recall

Corsi blocks backwards

Corsi blocks

Bull & Johnston (1997)

68 89 Group mathematics test, single digit addition

Composite word recall, digit recall and counting span

Digit recall

Camos (2008) 71 95 Transcoding task

Counting span

Chan & Ho (2010) 168 110 Hong Kong Backward digit Visual memory

attainment test for mathematics

recall subtest of Gardner Test of Visual Perceptual Skills

Cirino (2011) 286 73 Nonsymbolic and symbolic comparison, symbolic labeling, counting

Spatial working memory test

Clark, Pritchard & Woodward (2010)

104 48 Two subtests of the Woodcock-Johnson tests of achievement, Teachers report

Shape school inhibition, tower of Hanoi, BRIEF inhibition scale

Shape school switching aspect, flexible item selection task, BRIEF shifting scale

Cormier & Dea (1997)

103 94 WRAT-R arithmetic subtest

Backward digit recall

Corsi blocks backwards

Digit recall Corsi blocks

Costa et al. (2011) 98 122 Brazilian arithmetic test, symbolic and nonsymbolic comparison, word problems, basic arithmetic

Backward digit recall

Corsi blocks backwards

Digit recall Corsi blocks

Cowan (2005) 167 89 Addition retrieval, basic arithmetic, counting, word problems, transcoding, comparison

Backward digit recall

Digit recall Corsi blocks

Cowan et al. (2011) 259 95 WIAT II, basic calculation, calculation principles, number knowledge

Backward digit and listening recall composite

Word recall, digit recall

Block recall, mazes

De Jong & Van der Leij (1999)

166 73 Speeded calculation test

Word recall, nonword recall

De Smedt et al. (2009) 106 76 Standardized achievement tests for mathematics from the Flemish Student Monitoring System

Backward digit recall

Counting span Digit recall, nonword recall

Block recall, visual pattern test

De Smedt, Taylor, Archibald, & Ansari (2010)

37 120 Woodcock-Johnson III calculation, arithmetic verification

Nonword recall

Durand, Hulme, Larkin, & Snowling (2005)

162 107 WOND arithmetic, digit comparison, speeded addition and subtraction

Word recall, nonword recall

Fazio (1999) 32 112 KABC arithmetic, arithmetic, fact retrieval

Digit recall

Fuchs et al. (2010a) 280 79 Maths facts fluency; word problems

Composite listening recall counting recall backward digit recall

Word recall, digit recall, nonword recall

Fuchs et al. (2010b) 205 75 Number sets, number line estimation, double digit addition and subtraction, word problems

Composite listening recall counting recall backward digit recall

Digit recall, nonword recall

Block recall, mazes

Gathercole, Alloway, Willis & Adams (2006)

46 108 WOND Composite backwards digit counting recall listening recall

Word recall, digit recall

Gathercole & Pickering (2000)

111 94 Group Arithmetic Test, basic Number Skills Test

Composite listening recall counting recall backward digit recall

Nonword recall, serial recall recognition

Gathercole, Pickering, Knight & Stegmann (2004)

40 94 Part of key stage assessments

Backward digit recall, listening recall

Digit recall

Gathercole, Tiffany, Briscoe, Thorn, & the ALSPAC team (2005)

39 60 WOND Composite backwards digit and listening recall

Digit recall, nonword recall

Hecht, Close & Santisi (2003)

105 126 Arithmetic addition and multiplication test, fraction computation and estimation

Counting span

Hecht, Torgesen, Wagner, & Rashotte (2001)

201 92 General computation

Composite digit span, memory for sentence, sentence span

Hecht & Vagi (2010) 181 114 Arithmetic addition and multiplication test, fraction computation and estimation

Counting span

Henry & Winfield (2010)

67 91 Number skills from BASII

Listening recall Odd one out Word recall, digit recall

Spatial span, pattern span

Hillman et al. (2005) 105 106 WRAT Go-no go taskHolmes & Adams (2006)

148 107 Key stage assessment number & algebra, shape, space & measures, handling data, mental arithmetic

Listening recall Nonword recall Mazes

Holmes, Adams & Hamilton (2008)

107 103 Key stage assessment number & algebra, shape, space & measures, handling data, mental arithmetic

Pattern span, block recall

Hutton & Towse (2001)

58 110 Number skills from BASII

Maths recall, maths recall backwards

Digit recall Number recall, number recall backwards

Iglesias-Sarmiento & Deaño (2011)

38 129 Neuropsychological Battery of Assessment of Mathematical Skills

Backward digit recall

Digit recall

Imbo & Vandierendonck (2006)

63 123 Arithmetic Tempo Test

Digit recall

Jenks, De Moor & Van Lieshout (2009)

73 84 Simple, complex and arithmetic addition, simple and arithmetic subtraction

Inhibition naming

Shifting naming Backward digit recall

Word recall, digit recall

Block recall

Jenks, De Moor, Van Lieshout, Maathuis, Keus & Gorter (2007)

73 84 ENT Backward digit recall

Word recall, digit recall

Block recall

Kail & Hall (1999) 275 123 Word problems Listening recall, reading span

Word recall, digit recall

Keeler & Swanson (2001)

111 127 WRAT-R arithmetic subtest

Digit recall, sentence recall

Mapping and directions task

Kleemans, Segers, & Verhoeven (2011)

172 73 ENT Backward digit recall

Word recall, sentence recall

Memory span

Kleemans, Segers, & Verhoeven (2012)

160 73 Addition and subtraction tests

Word recall, sentence recall

Memory span

Koponen, Mononen, Räsänen, & Ahonen

29 123 Addition, subtraction,

Digit recall

(2006) counting, number lines, comparison, mapping

Koumoula et al. (2004)

240 107 NUCALC Composite forward and backward digit recall

Krajewski & Schneider (2009a)

147 75 DEMAT Backward digit recall

Digit recall

Krajewski & Schneider (2009b)

91 67 DEMAT Digit recall Dotmatrix, corsi blocks

Kroesbergen, Van Luit, Van Lieshout, Van Loosbroek, & Van de Rijt (2009)

115 72 ENT Expressive attention task, tower of London

Backward digit recall

Kyttälä, Aunio, & Hautamäki (2010)

232 71 ENT Backward word recall

Odd one out Nonword recall Dotmatrix, corsi blocks

Leather & Henry (1994)

71 89 WISC-R Arithmetic ability Task

Listening recall Counting span Word recall

Lee, Ng, Bull, Pe, & Ho (2011)

151 121 WIAT-I-III Listening recall Pictorial updating, Mr X

Lee, Ng, & Ng (2009) 255 134 Arithmetic computation, arithmetic word problems, relational task

Number stroop, stop signal task

Plus-minus task, number-letter switching

Counting recall, letter memory, keep track

Lee, Ng, Ng, & Lim (2004)

151 128 Word problems Composite listening recall counting recall backward digit recall

Word recall, digit recall, nonword recall

Block recall, mazes

Lee, Ng, Pe, Ang, Hasshim, & Bull (2010)

163 83 WIAT-II, number problems, geometry problems, shape problems

Flanker task, simon task

Simon task, flanker task, picture-symbol switching task

Listening recall Pictorial updating, Mr X

LeFevre et al. (2010) 182 69 Subitising, Block recall

number naming, arithmetic, Keymath R, number lines, comparison

Lemaire & Lecacheur (2011)

106 126 Computational estimation task

Stroop task Trail making test

Excluded letter fluency task

Lundberg & Sterner (2006)

60 106 Mental calculation and algorithm test from the Swedish National Assessment Program

Backward digit recall

Mabbott & Bisanz (2003)

120 132 Arithmetic subtest of WRAT-III

Operation span, backward digit recall

Mabbott & Bisanz (2008)

92 122 Computational computer task

Operation span, backward digit recall

Mahone et al. (2002) 76 122 WIAT maths composite

BRIEF inhibition scale

Mannamaa, Kikas, Peets, & Palu (2012)

723 107 Number facts, arithmetic, word problems, problem solving

Word recognition test, phonological analysis test

Figure recognition test

Mazzocco, Bhatia, & Lesniak-Karpiak (2006)

65 105 TEMA-2, Woodcock-Johnson-R, counting

Shape recall, location recall

Mazzocco & Kover (2007)

178 102 TEMA-2 Two attribute CNT

McLean & Hitch (1999)

36 105 Graded Arithmetic–Mathematics Test

Crossing out task

Trail making written, verbal, & colour

Digit recall, nonword recall

Visual matrix span, corsi blocks

Moeller, Pixner, Zuber, Kaufmann, & Nuerk (2011)

94 88 Addition test Word recall Corsi blocks

Monette, Bigras, & Guay (2011)

85 70 Arithmetic subtest of WIAT-II

Day-night test, fruit stroop test, knock and tap test

Card sort test, trials-P

Backward word recall

Corsi blocks backwards

Navarro et al. (2011) 219 85 ENT Stroop task Backward digit recall

Digit recall

Noel (2009) 80 59 Counting, numerical decisions, addition

Composite backward word recall and category span task

Word recall Corsi blocks

Nunes, Bryant, Barros, & Sylva (2012)

2413 102 Mathematical reasoning, WISC arithmetics subtest, key stage 2 maths

Backward digit recall

Nunes et al. (2007) 59 72 British ability scales II

Dotmatrix

Nyroos & Wiklund-Hornqvist (2012)

40 102 Written and mental arithmetic, number understanding, area and volume, division and fractions

Listening recall Digit recall Block recall

Passolunghi & Lanfranchi (2012)

70 62 Counting, ENT, standardised mathematics test

Verbal double task, backward digit span, word fluency task

Visual double task

Word recall, digit recall

Mazes, block recall

Passolunghi, Mammarella, & Altoe (2008)

72 78 Standardised maths task

Backward word recall, backward digit recall, listening recall

Word recall, digit recall

Passolunghi & Siegel (2004)

49 125 Number comparison

Listening recall Counting span Word recall, digit recall

Passolunghi, Vercelloni, & Schadee

170 76 Standardised maths task

Backward word recall, backward

Word recall, digit recall

(2007) digit recall, listening recall

Ransdell & Hecht (2003)

65 95 Florida Comprehension Assessment task

Counting span

Rasmussen & Bisanz (2005)

63 72 Verbal and nonverbal addition

Sun-Moon Stroop task

Backward digit recall

Counting span Digit recall Corsi blocks

Rasmussen & Bisanz (2011)

41 65 Woodcock-Johnson III test of achievement

Backward digit recall, word list matching

Word recall, digit recall, nonword recall

Corsi blocks

Rasmussen, Ho, & Bisanz (2003)

24 55 Addition, subtraction, three-term problems

Digit recall Corsi blocks

Robinson, Abbott, Berninger, & Busse (1996)

310 70 Key math, Woodcock-Johnson

Counting span Visuospatial span test

Rose, Feldman, & Jankowski (2011)

124 134 Woodcock-Johnson III test of achievement

CANTAB rapid visual info processing, go-no go task

CANTAB intra/extradimensional test, trail making test

Listening recall, counting recall

CANTAB spatial working memory

Simmons, Singleton, & Horne (2008)

42 63 British ability scales number

Corsi blocks

Simmons, Wilis, & Adams (2012)

90 82 British ability scales number

Word recall nonword recall,

Block recall, mazes

St.Clair-Thompson & Gathercole (2006)

51 141 National curriculum test

Stop signal task, stroop task

Plus-minus task, local-global task

Letter memory, backward digit recall, listening recall

Keep track, odd one out

Spatial span

St.Clair-Thompson & Sykes (2010)

81 89 Various national curriculum tests

Backward digit recall, listening recall, counting recall

Counting span Word recall Block recall

Swanson (2006a) 127 88 WIAT-M, WRAT-M

Random number and letter generation, categorical and letter fluency

Listening recall, digit sentence recall, backward digit recall, updating task

Word recall, digit recall, nonword recall

Dotmatrix, mapping and directions test

Swanson (2006b) 320 75 WRAT-III arithmetic calculation, word problems

Random number and letter generation, categorical and letter fluency

Composite sentence span, semantic association task, digit sentence span, backward digit span

Word recall, digit recall, nonword recall

Visual matrix span, mapping and directions test

Swanson (2011) 104 80 WISC–III, word problems, WRAT–III, WIAT, test of computational fluency

Random number and letter generation, categorical and letter fluency

Composite listening sentence span, conceptual span, updating

Word recall, digit recall, nonword recall

Visual matrix span, mapping and directions test

Swanson, Cooney & Brock (1993)

110 110 WRAT-M Reading span

Swanson & Sachs-Lee (2001)

73 138 Word problems Composite sentence span auditory digit sequencing story retelling

Dotmatrix, mapping and directions test

Thorell (2007) 145 76 Learning problems screening battery

Stroop task, go/no-go task

Digit recall Pig house memory test

Van der Sluis, De Jong, & Van der Leij (2007)

172 128 Arithmetic Tempo Test

Quantity and object inhibition, stroop task, numerical size inhibition

Object shifting, symbol shifting, place shifting, trail making test

Letter and digit memory

Keep track

Van der Ven, Kroesbergen, Boom, & Leseman (2011)

211 77 Cito Animal stroop, local-global task, simon task

Trail making test, animal shifting, sorting test

Backward digit span, keep track

Odd one out

Van Rooijen, Verhoeven, Smits. Ketelaar, Becher, & Steenbergen (2012)

116 87 Student Monitoring System for Arithmetic Performance (CITO)

Backward digit span

Digit recall

Waber, Gerber, Turcios, Wagner, & Forbes (2006)

93 132 MCAS - mathemetics

D-KEFS, Nepsy tower

Letter number sequencing

Wanless, McClelland, Acock, Chen, & Chen (2011)

91 49 TEMA-2 Head-to-toes task

Whang & Hancock (1997)

158 125 CTBS mathematics achievement, arithmetic production and verification

Composite word recall, digit recall and add a digit

Wu et al. (2008) 59 97 WIAT-II Backward digit recall

Counting span Digit recall Block recall

Zheng, Swanson, & Marcoulides (2011)

310 104 WIAT, WRAT, WISC-R Arithmetic ability Task, word problems

Listening recall, digit span, sentence span

Word recall, digit recall, nonword recall

Dotmatrix, mapping and directions test

Zuber, Pixner, Moeller, & Nuerk (2009)

130 88 Transcoding task

Backward letter recall

Corsi blocks backwards

Word recall Corsi blocks

Note. VSSP = visuospatial sketchpad. PL = phonological loop. WOND: Wechsler Objective Numerical Dimensions. NFER: National Foundation for Educational Research. WRAT: Wide Range Achievement Test. WISC-R: Wechsler Intelligence Scale for Children Revised. PIPS: Performance Indicators in Primary Schools. WIAT: Wechsler Individual Achievement Test. KABC: Kaufman Assessment Battery for Children. BAS: British Ability Scales. NUCALC: Number Processing and Calculation in Children. DEMAT: Deutscher Mathematiktest (German Test for Mathematics). ENT: Early Numeracy Test. TEMA: Test of Early Mathematics Ability. CITO: Centraal Instituut voor Toetsontwikkeling (Central Instritute for Test Development). MCAS: Massachusetts Comprehensive Assessment System. CANTAB: Cambridge Neuropsychological Test Automated Battery. BRIEF: Behavior Rating Inventory of Executive Function. CNT: Contingency Naming Test. D-KEFS: Delis–Kaplan Executive Function System. Age is reported at the earliest time point for each study, and averaged between groups, if applicable.

References

Agostino A., Johnson J. and Pascual-Leone J., Executive functions underlying multiplicative reasoning: Problem type matters, Journal of Experimental Child Psychology 105, 2010, 286–305, DOI: 10.1016/j.jecp.2009.09.006.

Alloway T.P., Working memory, reading, and mathematical skills in children with developmental coordination disorder, Journal of Experimental Child Psychology 96, 2007, 20–36, DOI: 10.1016/j.jecp.2006.07.002.

Alloway T.P. and Alloway R.G., Investigating the predictive roles of working memory and IQ in academic attainment, Journal of Experimental Child Psychology 106, 2010, 20–29, DOI: 10.1016/j.jecp.2009.11.003.

Alloway T.P. and Archibald L., Working memory and learning in children with developmental coordination disorder and specific language impairment, Journal of Learning Disabilities 41, 2008, 251–262, DOI: 10.1177/0022219408315815.

Alloway T.P., Gathercole S.E., Adams A.-M., Willis C., Eaglen R. and Lamont E., Working memory and phonological awareness as predictors of progress towards early learning goals at school entry, British Journal of Developmental Psychology 23, 2005, 417–426, DOI: 10.1348/026151005X26804.

Alloway T.P., Gathercole S.E., Kirkwood H. and Elliott J., The cognitive and behavioural characteristics of children with low working memory, Child Development 80, 2009, 606–621, DOI: 10.1111/j.1467-8624.2009.01282.x.

Alloway T.P. and Temple K.J., A comparison of working memory skills and learning in children with developmental coordination disorder and moderate learning difficulties, Applied Cognitive Psychology 21, 2007, 473–487, DOI: 10.1002/acp.1284.

Andersson U., The contribution of working memory to children’s mathematical word problem solving, Applied Cognitive Psychology 21, 2007, 1201–1216, DOI: 10.1002/acp.1317.

Andersson U., Working memory as a predictor of written arithmetic skills in children: The importance of executive functions, British Journal of Educational Psychology 78, 2008, 181–203, DOI: 10.1348/000709907X209854.

Andersson U., Mathematical competencies in children with different types of learning difficulties, Journal of Educational Psychology 100, 2008, 48–66, DOI: 10.1037/0022-0663.100.1.48.

Andersson U. and Lyxell B., Working memory deficit in children with mathematical problems: A general or specific deficit?, Journal of Experimental Child Psychology 96, 2007, 197–228, DOI: 10.1016/j.jecp.2006.10.001.

Barrouillet P. and Lépine R., Working memory and children’s use of retrieval to solve addition problems, Journal of Experimental Child Psychology 91, 2005, 183–204, DOI: 10.1016/j.jecp.2005.03.002.

Barrouillet P., Mignon M. and Thevenot C., Strategies in subtraction problem solving in children, Journal of Experimental Child Psychology 99, 2008, 233–251, DOI: 10.1016/j.jecp.2007.12.001.

Baylisse D.M., Jarrold C., Baddeley A.D. and Gunn D.M., The relationship between short-term memory and working memory: Complex span made simple?, Memory 13, 2005, 414–421, DOI: 10.1080/09658210344000332.

Berg D.H., Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory and reading, Journal of Experimental Child Psychology 99, 2008, 288–308, DOI: 10.1016/j.jecp.2007.12.002.

Blair C. and Razza R.P., Relating effortful control, executive functioning, and false belief understanding to emerging math and literacy ability in kindergarten, Child Development 87, 2007, 647–663, DOI: 10.1111/j.1467-8624.2007.01019.x.

Bowey J.A., Socioeconomic status differences in preschool phonological sensitivity and first grade reading achievement, Journal of Educational Psychology 87, 1995, 476–487, DOI: 10.1037/0022-0663.87.3.476.

Brock L.L., Rimm-Kaufman S.E., Nathanson L. and Grimm K.J., The contributions of “hot” and “cool” executive function to children’s academic achievement, learning related behaviors, and engagement in kindergarten, Early Childhood Research Quarterly 24, 2009, 337–349, DOI: 10.1016/j.ecresq.2009.06.001.

Bull R., Espy K.A. and Wiebe S.A., Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years, Developmental Neuropsychology 33, 2008, 205–228, DOI: 10.1080/87565640801982312.

Bull R. and Johnston R.S., Children’s arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory, Journal of Experimental Child Psychology 65, 1997, 1–24, DOI: 10.1006/jecp.1996.2358.

Camos V., Low working memory capacity impedes both efficiency and learning of number transcoding in children, Journal of Experimental Child Psychology 99, 2008, 37–57, DOI: 10.1016/j.jecp.2007.06.006.

Chan B.M. and Ho C.S., The cognitive profile of Chinese children with mathematics difficulties, Journal of Experimental Child Psychology 107, 2010, 260–279, DOI: 10.1016/j.jecp.2010.04.016.

Cirino P.T., The interrelationships of mathematical precursors in kindergarten, Journal of Experimental Child Psychology 108, 2011, 713–733, DOI: 10.1016/j.jecp.2010.11.004.

Clark C.A.C., Pritchard V.E. and Woodward L.J., Preschool executive functioning abilities predict early mathematics achievement, Developmental Psychology 46, 2010, 1176–1191, DOI: 10.1037/a0019672.

Cormier P. and Dea S., Distinctive pattern of relationship of phonological awareness and working memory with reading development, Reading and Writing: An Interdisciplinary Journal 9, 1997, 193–206, DOI: 10.1023/A:1007932721290.

Costa A.J., Lopes Silva B.J., Chagas P.P., Krinziger H., Lonneman J., Wilmes K., et al., A hand full of numbers: A role for offloading in arithmetics learning?, Frontiers in Psychology 2 (2011), 2011, DOI: 10.3389/fpsyg.2011.00368, [article 368].

Cowan R., Donlan C., Newton E.J. and Lloyd D., Number skills and knowledge in children with specific language impairment, Journal of Educational Psychology 97, 2005, 732–744, DOI: 10.1037/0022-0663.97.4.732.

Cowan R., Donlan C., Shepherd D.L., Cole-Fletcher R., Saxton M. and Hurry J., Basic calculation proficiency and mathematics achievement in elementary school children, Journal of Educational Psychology 103, 2011, 786–803, DOI: 10.1037/a0024556.

De Jong P.F. and Van der Leij A., Specific contributions of phonological abilities to early reading acquisition: Results from a Dutch latent variable longitudinal study, Journal of Educational Psychology 91, 1999, 450–476, DOI: 10.1037/0022-0663.91.3.450.

De Smedt B., Janssen R., Bouwens K., Verschaffel L., Boets B. and Ghesquière P., Working memory and individual differences in mathematics achievement: A longitudinal study from first to second grade, Journal of Experimental Child Psychology 103, 2009, 186–201, DOI: 10.1016/j.jecp.2009.01.004.

De Smedt B., Taylor J., Archibald L. and Ansari D., How is phonological processing related to individual differences in children’s arithmetic skills?, Developmental Science 13, 2010, 508–520, DOI: 10.1111/j.1467-7687.2009.00897.x.

Durand M., Hulme C., Larkin R. and Snowling M., The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds, Journal of Experimental Child Psychology 91, 2005, 113–136, DOI: 10.1016/j.jecp.2005.01.003.

Fazio B.B., Arithmetic calculation, short-term memory, and language performance in children with specific language impairment: A 5-year follow-up, Journal of Speech, Language, and Hearing Research 42, 1999, 420–431.

Fuchs L.S., Geary D.C., Compton D.L., Fuchs D., Hamlett C.L. and Bryant J.D., The contributions of numerosity and domain-general abilities to school readiness, Child Development 81, 2010, 1520–1533, DOI: 10.1111/j.1467-8624.2010.01489.x.

Fuchs L.S., Geary D.C., Compton D.L., Fuchs D., Hamlett C.L., Seethaler P.M., et al., Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?, Developmental Psychology 46, 2010, 1731–1746, DOI: 10.1037/a0020662.

Gathercole S.E., Alloway T.P., Willis C. and Adams A.-M., Working memory in children with reading disabilities, Journal of Experimental Child Psychology 93, 2006, 265–281, DOI: 10.1016/j.jecp.2005.08.003.

Gathercole S.E. and Pickering S.J., Assessment of working memory in six- and seven-year-old children, Journal of Educational Psychology 92, 2000, 377–390.

Gathercole S.E., Pickering S.J., Knight C. and Stegmann Z., Working memory skills and educational attainment: Evidence from national curriculum assessments at 7 and 14 years of age, Applied Cognitive Psychology 18, 2004, 1–16, DOI: 10.1002/acp.934.

Gathercole S.E., Tiffany C., Briscoe J. and Thorn A., The ALSPAC team, Developmental consequences of poor phonological short-term memory function in childhood: A longitudinal study, Journal of Child Psychology and Psychiatry 46, 2005, 598–611, DOI: 10.1111/j.1469-7610.2004.00379.x.

Hecht S.A., Close L. and Santisi M., Sources of individual differences in fraction skills, Journal of Experimental Child Psychology 86, 2003, 277–302, DOI: 10.1016/j.jecp.2003.08.003.

Hecht S.A., Torgesen J.K., Wagner R.K. and Rashotte C.A., The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades, Journal of Experimental Child Psychology 79, 2001, 192–227, DOI: 10.1006/jecp.2000.2586.

Hecht S.A. and Vagi K.J., Sources of group and individual differences in emerging fraction skills, Journal of Educational Psychology 102, 2010, 843–859, DOI: 10.1037/a0019824.

Henry L. and Winfield J., Working memory and educational achievement in children with intellectual disabilities, Journal of Intellectual Disability Research 54, 2010, 354–365, DOI: 10.1111/j.1365-2788.2010.01264.x.

Hillman C.H., Pontifex M.B., Motl R.W., O’Leary K.C., Johnson C.R., Scudder M.R., et al., From ERPs to academics, Developmental Cognitive Neuroscience 2S, 2005, S90–S98, DOI: 10.1016/j.dcn.2011.07.004.

Holmes J. and Adams J.W., Working memory and children’s mathematical skills: Implications for mathematical development and mathematics curriculum, Educational Psychology 26, 2006, 339–366, DOI: 10.1080/01443410500341056.

Holmes J., Adams J.W. and Hamilton C.J., The relationship between visiospatial sketchpad capacity and children’s mathematical skills, European Journal of Cognitive Psychology 20, 2008, 272–289, DOI: 10.1080/09541440701612702.

Hutton U.M.Z. and Towse J.N., Short-term memory and working memory as indices of children’s cognitive skills, Memory 9, 2001, 383–394, DOI: 10.1080/09658210042000058.

Iglesias-Sarmiento V. and Deaño M., Cognitive processing and mathematical achievement: A study with schoolchildren between fourth and sixth grade of primary education, Journal of Learning Disabilities 44, 2011, 570–583, DOI: 10.1177/0022219411400749.

Imbo I. and Vandierendonck A., The development of strategy use in elementary school children: Working memory and individual differences, Journal of Experimental Child Psychology 96, 2007, 284–309, DOI: 10.1016/j.jecp.2006.09.001.

Jenks K.M., De Moor J. and Van Lieshout E.C.D.M., Arithmetic difficulties in children with cerebral palsy are related to executive functioning and working memory, Journal of Child Psychology and Psychiatry 50, 2009, 824–833, DOI: 10.1111/j.1469-7610.2008.02031.x.

Jenks K.M., De Moor J., Van Lieshout E.C.D.M., Maathuis K.G.B., Keus I. and Gorter G.W., The effect of cerebral palsy on arithmetic accuracy is mediated by working memory, intelligence, early numeracy and instruction time, Developmental Neuropsychology 32, 2007, 861–879, DOI: 10.1080/87565640701539758.

Kail R. and Hall R.K., Sources of developmental change in children’s word-problem performance, Journal of Educational Psychology 91, 1999, 660–668, DOI: 10.1037/0022-0663.91.4.660.

Keeler M.L. and Swanson H.L., Does strategy knowledge influence working memory in children with mathematical disabilities?, Journal of Learning Disabilities 34, 2001, 418–434, DOI: 10.1177/002221940103400504.

Kleemans T., Segers E. and Verhoeven L., Precursors to numeracy in kindergartners with specific language impairment, Research in Developmental Disabilities 32, 2011, 2901–2908, DOI: 10.1016/j.ridd.2011.05.013.

Kleemans T., Segers E. and Verhoeven L., Naming speed as a clinical marker in predicting basic calculation skills in children with specific language impairment, Research in Developmental Disabilities 33, 2012, 882–889, DOI: 10.1016/j.ridd.2011.12.007.

Koponen T., Mononen R., Räsänen P. and Ahonen T., Basic numeracy in children with specific language impairment: Heterogeneity and connections to language, Journal of Speech, Language, and Hearing Research 49, 2006, 58–73, DOI: 10.1044/1092-4388(2006/005.

Koumoula A., Tsironi V., Stamouli V., Bardani I., Siapati S., Graham A., et al., An epidemiological study of number processing and mental calculation in Greek schoolchildren, Journal of Learning Disabilities 37, 2004, 377–388, DOI: 10.1177/00222194040370050201.

Krajewski K. and Schneider W., Exploring the impact of phonological awareness, visio-spatial working memory, and pre-school quantity number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study, Journal of Experimental Child Psychology 103, 2009, 516–531, DOI: 10.1016/j.jecp.2009.03.009.

Krajewski K. and Schneider W., Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study, Learning and Instruction 19, 2009, 513–526, DOI: 10.1016/j.learninstruc.2008.10.002.

Kroesbergen E.H., Van Luit J.E.H., Van Lieshout E.C.D.M., Van Loosbroek E. and Van de Rijt B.M., Individual differences in early numeracy: The role of executive functions and subitizing, Journal of Psychoeducational Assessment 27, 2009, 226–236, DOI: 10.1177/0734282908330586.

Kyttälä M., Aunio P. and Hautamäki J., Working memory resources in young children with mathematical difficulties, Scandinavian Journal of Psychology 51, 2010, 1–15, DOI: 10.1111/j.1467-9450.2009.00736.x.

Leather C.V. and Henry L.A., Working memory span and phonological awareness tasks as predictors of early reading ability, Journal of Experimental Child Psychology 58, 1994, 88–111, DOI: 10.1006/jecp.1994.1027.

Lee K., Ng S.F., Bull R., Pe M.L. and Ho R.H.M., Are patterns important? An investigation of the relationships between proficiencies in patterns, computation, executive functioning, and algebraic word problems, Journal of Educational Psychology 103, 2011, 269–281, DOI: 10.1037/a0023068.

Lee K., Ng E.L. and Ng S.F., The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problems, Journal of Educational Psychology 101, 2009, 373–387, DOI: 10.1037/a0013843.

Lee K., Ng S.F., Ng E.L. and Lim Z.Y., Working memory and literacy as predictors of performance on algebraic word problems, Journal of Experimental Child Psychology 89, 2004, 140–158, DOI: 10.1016/j.jecp.2004.07.001.

Lee K., Ng S.F., Pe M.L., Ang S.Y., Hasshim M.N.A.M. and Bull R., The cognitive underpinnings of emerging mathematical skills: Executive functioning, patterns, numeracy, and arithmetic, British Journal of Educational Psychology 82, 2010, 82–99, DOI: 10.1111/j.2044-8279.2010.02016.x.

Lefevre J.-A., Fast L., Skwarchuk S.-L., Smith-Chant B.L., Bisanz J., Kamawar D., et al., Pathways to mathematics: longitudinal predictors of performance, Child Development 81, 2010, 1753–1767, DOI: 10.1111/j.1467-8624.2010.01508.x.

Lemaire P. and Lecacheur M., Age-related changes in children’s executive functions and strategy selection: A study in computational estimation, Cognitive Development 26, 2011, 282–294, DOI: 10.1016/j.cogdev.2011.01.002.

Lundberg I. and Sterner G., Reading, arithmetic, and task orientation. How are they related?, Annals of Dyslexia 56, 2006, 361–377, DOI: 10.1007/s11881-006-0016-0.

Mabbott D.J. and Bisanz J., Developmental change and individual differences in children’s multiplication, Child Development 74, 2003, 1091–1107, DOI: 10.1111/1467-8624.00594.

Mabbott D.J. and Bisanz J., Computational skills, working memory, and conceptual knowledge in older children with mathematical learning disabilities, Journal of Learning Disabilities 41, 2008, 15–28, DOI: 10.1177/0022219407311003.

Mahone E.M., Cirino P.T., Cutting L.E., Cerrone P.M., Hagelthorn K.M., Hiemenz J.R., et al., Validity of the behavior rating inventory of executive function in children with ADHD and/or tourette syndrome, Archives of Clinical Neuropsychology 17, 2002, 643–662, DOI: 10.1016/S0887-6177(01)00168-8.

Mannamaa M., Kikas E., Peets K. and Palu A., Cognitive correlates of math skills in third-grade students, Educational Psychology 32, 2012, 21–44, DOI: 10.1080/01443410.2011.621713.

Mazzocco M.M.M., Bhatia S.N. and Lesniak-Karpiak K., Visuospatial skills and their association with math performance in girls with fragile X or Turner syndrome, Child Neuropsychology 12, 2006, 87–110, DOI: 10.1080/09297040500266951.

Mazzocco M.M.M. and Kover S.T., A longitudinal assessment of executive functioning skills and their association with math performance, Child Neuropsychology: A Journal on Normal and Abnormal Development in Childhood and Adolescence 13, 2007, 18–45, DOI: 10.1080/09297040600611346.

McLean J.F. and Hitch G.J., Working memory impairments in children with specific arithmetic learning difficulties, Journal of Experimental Child Psychology 74, 1999, 240–260, DOI: 10.1006/jecp.1999.2516.

Moeller K., Pixner S., Zuber J., Kaufmann L. and Nuerk H.-C., Early place-value understanding as a precursor for later arithmetic performance – A longitudinal study on numerical development, Research in Developmental Disabilities 32, 2011, 1837–1851, DOI: 10.1016/j.ridd.2011.03.012.

Monette S., Bigras M. and Guay M.C., The role of executive functions in school achievement at the end of grade 1, Journal of Experimental Child Psychology 109, 2011, 158–173, DOI: 10.1016/j.jecp.2011.01.008.

Navarro J.I., Aguilar M., Alcalde C., Ruiz G., Marchena E. and Menacho I., Inhibitory processes, working memory, phonological awareness, naming speed, and early arithmetic achievement, Spanish Journal of Psychology 14, 2011, 580–588, DOI: 10.5209/rev_SJOP.2011.v14.n2.6.

Noel M.-P., Counting on working memory when learning to count and add: A preschool study, Developmental Psychology 45, 2009, 1630–1643, DOI: 10.1037/a0016224.

Nunes T., Bryant P., Barros R. and Sylva K., The relative importance of two different mathematical abilities to mathematical achievement, British Journal of Educational Psychology 82, 2012, 136–156, DOI: 10.1111/j.2044-8279.2011.02033.x.

Nyroos M. and Wiklund-Hornqvist C., The association between working memory and educational attainment as measured in different mathematical subtopics in the Swedish national assessment: Primary education, Educational Psychology 32, 2012, 239–256, DOI: 10.1080/01443410.2011.643578.

Passolunghi M.-C. and Lanfranchi S., Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade, British Journal of Educational Psychology 82, 2012, 42–63, DOI: 10.1111/j.2044-8279.2011.02039.x.

Passolunghi M.-C., Mammarella I.C. and Altoè G., Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades, Developmental Neuropsychology 33, 2008, 229–250, DOI: 10.1080/87565640801982320.

Passolunghi M.-C. and Siegel L.S., Working memory and access to numerical information in children with disability in mathematics, Journal of Experimental Child Psychology 88, 2004, 348–367, DOI: 10.1016/j.jecp.2004.04.002.

Passolunghi M.-C., Verelloni B. and Schadee H., The precursors of mathematics learning: Working memory, phonological ability and numerical competence, Cognitive Development 22, 2007, 165–184, DOI: 10.1016/j.cogdev.2006.09.001.

Ransdell S. and Hecht S., Time and resource limits on working memory: Cross-age consistency in counting span performance, Journal of Experimental Child Psychology 86, 2003, 303–313, DOI: 10.1016/j.jecp.2003.08.002.

Rasmussen C. and Bisanz J., Representation and working memory in early arithmetic, Journal of Experimental Child Psychology 91, 2005, 137–157, DOI: 10.1016/j.jecp.2005.01.004.

Rasmussen C. and Bisanz J., The relation between mathematics and working memory in young children with fetal alcohol spectrum disorders, Journal of Special Education 45, 2011, 184–191, DOI: 10.1177/0022466909356110.

Rasmussen C., Ho E. and Bisanz J., Use of the mathematical principle of inversion in young children, Journal of Experimental Child Psychology 85, 2003, 89–102, DOI: 10.1016/S0022-0965(03)00031-6.

Robinson N.M., Abbott R.D., Berninger V.W. and Busse J., The structure of abilities in math-precocious young children: Gender similarities and differences, Journal of Educational Psychology 88, 1996, 341–352, DOI: 10.1037//0022-0663.88.2.341.

Rose S.A., Feldman J.F. and Jankowski J.J., Modeling a cascade of effects: The role of speed and executive functioning in preterm/full-term differences in academic achievement, Developmental Science 14, 2011, 1161–1175, DOI: 10.1111/j.1467-7687.2011.01068.x.

Simmons F., Singleton C. and Horne J., Brief report – Phonological awareness and visual–spatial sketchpad functioning predict early arithmetic attainment: Evidence from a longitudinal study, European Journal of Cognitive Psychology 20, 2008, 711–722, DOI: 10.1080/09541440701614922.

Simmons F.R., Willis C. and Adams A.-M., Different components of working memory have different relationships with different mathematical skills, Journal of Experimental Child Psychology 111, 2012, 139–155, DOI: 10.1016/j.jecp.2011.08.011.

St Clair-Thompson H.L. and Gathercole S.E., Executive functions and achievements in school: Shifting, updating, inhibition, and working memory, The Quarterly Journal of Experimental Psychology 59, 2006, 745–759, DOI: 10.1080/17470210500162854.

St Clair-Thompson H.L. and Sykes S., Scoring methods and the predictive ability of working memory tasks, Behavior Research Methods 42, 2010, 969–975, DOI: 10.3758/BRM.42.4.969.

Swanson H.L., Cognitive processes that underlie mathematical precociousness in young children, Journal of Experimental Child Psychology 93, 2006, 239–264, DOI: 10.1016/j.jecp.2005.09.006.

Swanson H.L., Cross-sectional and incremental changes in working memory and mathematical problem solving, Journal of Educational Psychology 98, 2006, 265–281, DOI: 10.1037/0022-0663.98.2.265.

Swanson H.L., Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children, Journal of Educational Psychology 103, 2011, 821–837, DOI: 10.1037/a0025114.

Swanson H.L., Cooney J.B. and Brock S., The influence of working memory and classification ability on children’s word problem solution, Journal of Experimental Child Psychology 55, 1993, 374–395, DOI: 10.1006/jecp.1993.1021.

Swanson H.L. and Sachs-Lee C., Mathematical problem solving and working memory in children with learning disabilities: Both executive functioning and phonological processes are important, Journal of Experimental Child Psychology 79, 2001, 294–321, DOI: 10.1006/jecp.2000.2587.

Thorell L.B., Do delay aversion and executive function deficits make distinct contributions to the functional impact of ADHD symptoms? A study of early academic skill deficits, Journal of Child Psychology and Psychiatry 48, 2007, 1061–1070, DOI: 10.1111/j.1469-7610.2007.01777.x.

Van der Sluis S., De Jong P.F. and Van der Leij A., Executive functioning in children, and its relations with reasoning, reading, and arithmetic, Intelligence 35, 2007, 427–449, DOI: 10.1016/j.intell.2006.09.001.

Van der Ven S.H.G., Boom J., Kroesbergen E.H. and Leseman P.P.M., Microgenetic patterns of children’s multiplication learning: Confirming the overlapping waves model by latent growth modeling, Journal of Experimental Child Psychology 113, 2012, 1–19, DOI: 10.1016/j.jecp.2012.02.001.

Van Rooijen M., Verhoeven L., Smits D.-W., Ketelaar M., Becher J.G. and Steenbergen B., Arithmetic performance of children with cerebral palsy: The influence of cognitive and motor factors, Research in Developmental Disabilities 33, 2012, 530–537, DOI: 10.1016/j.ridd.2011.10.020.

Waber D.P., Gerber E.B., Turcios V.Y., Wagner E.R. and Forbes P.W., Executive functions and performance on high-stakes testing in children from urban schools, Developmental Neuropsychology 29, 2006, 459–477, DOI: 10.1207/s15326942dn2903_5.

Wanless S.B., McClelland M.M., Acock A.C., Chen F.-M. and Chen J.-L., Behavioral regulation and early academic achievement in Taiwan, Early Education and Development 22, 2011, 1–28, DOI: 10.1080/10409280903493306.

Whang P.A. and Hancock G.R., Modeling the mathematics achievement of Asian-American elementary students, Learning and Individual Differences 9, 1997, 63–88, DOI: 10.1016/S1041-6080(97)90020-0.

Wu S.S., Meyer M.L., Maeda U., Salimpoor V., Tomiyama S., Geary D.C., et al., Standardized assessment of strategy use and working memory in early mental arithmetic performance, Developmental Neuropsychology 33, 2008, 365–393, DOI: 10.1080/87565640801982445.

Zheng X., Swanson H.L. and Marcoulides G.A., Working memory components as predictors of children’s mathematical word problem solving, Journal of Experimental Child Psychology 110, 2011, 482–498, DOI: 10.1016/j.jecp.2011.06.001.

Zuber J., Pixner S., Moeller K. and Nuerk H.-C., On the language specificity of basic number processing: Transcoding in a language with inversion and its relation to working memory capacity, Journal of Experimental Child Psychology 102, 2009, 60–77, DOI: 10.1016/j.jecp.2008.04.003.