Detecting Children With Arithmetic Disabilities From Kindergarten: Evidence From a 3-Year Longitudinal Study on the Role of Preparatory Arithmetic Abilities
Restricted accessResearch articleFirst published online May, 2010
Detecting Children With Arithmetic Disabilities From Kindergarten: Evidence From a 3-Year Longitudinal Study on the Role of Preparatory Arithmetic Abilities
In a 3-year longitudinal study, 471 children were classified, based on their performances on arithmetic tests in first and second grade, as having persistent arithmetic disabilities (AD), persistent low achieving (LA), persistent typical achieving, inconsistent arithmetic disabilities (DF1), or inconsistent low achieving in arithmetic. Significant differences in the performances on the magnitude comparison in kindergarten (at age 5—6) were found between the AD and LA and between the AD and DF1 groups. Furthermore, the percentage of true-positive AD children (at age 7—8) correctly diagnosed in kindergarten by combination of procedural counting, conceptual counting, and magnitude comparison tasks was 87.50%. When composing clinical samples, researchers should pay attention when stipulating restrictive or lenient cutoffs for arithmetic disabilities and select children based on their scores in 2 consecutive years, because the results of studies on persistent low achievers or children with inconsistent disabilities cannot be generalized to children with persistent arithmetic disabilities.
American Psychiatric Association. (2000). Diagnostic and statistical manual of mental disorders (4th ed., text rev.). Washington, DC: Author.
2.
Aunola, K., Leskinen, E., Lerkkanen, M.-K., & Nurmi, J.-E. ( 2004). Developmental dynamics of math performance from preschool to Grade 2. Journal of Educational Psychology, 96, 699-713.
3.
Baroody, A.J. ( 1992). Remedying common counting difficulties. In J. Bideaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children’s developing numerical abilities (pp. 307-324). Hillsdale, NJ: Lawrence Erlbaum.
4.
Barrouillet, P., & Lepine, R. ( 2005). Working memory and children’s use of retrieval to solve addition problems. Journal of Experimental Child Psychology, 91, 183-204.
5.
Baudonck, M., Debusschere, A., Dewulf, B., Samyn, F., Vercaemst, V., & Desoete, A. ( 2006). De Kortrijkse Rekentest Revision KRT-R [The Kortrijk Arithmetic Test Revised, KRT-R]. Kortrijk, Belgium: CAR Overleie.
6.
Berch, D.B. ( 2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities , 38, 333-339.
7.
Blöte, A.W., Lieffering, L.M., & Ouwehand, K. ( 2006). The development of many-to-one counting in 4-year-old children. Cognitive Development, 21, 332-348.
8.
Bull, R., Espy, K.A., & Wiebe, S.A. ( 2008). Short-term memory, working memory and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33, 205-228.
9.
Butterworth, B. ( 2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46, 3-18.
10.
Chard, D.J., Clarke, B., Baker, S., Otterstedt, J., Braun, D., & Katz, R. ( 2005). Using measures of number sense to screen for difficulties in mathematics: Preliminary findings. Assessment for Effective Intervention, 30, 3-14.
11.
Coleman, M.R., Buysse, V., & Neitzel, J. ( 2006). Recognition and response. An Early intervening system for young children at-risk for learning disabilities. Research synthesis and recommendations. Chapel Hill: University of North Carolina FPG Child Development Institute.
12.
Dehaene, S. ( 1997). The number sense. Oxford, UK: Oxford University Press.
13.
Dehaene, S., Bossini, S., & Giraux, P. ( 1993). The mental representation of parity and number magnitude . Journal of Experimental Psychology: General, 122, 371-396.
14.
Desoete, A. ( 2006). Validiteitsonderzoek met de TEDI-MATH [Validity research on the TEDI-MATH]. Diagnostiek-wijzer, 9, 140-157.
15.
Desoete, A. ( 2007a). Students with mathematical disabilities in Belgium: From definition, classification and assessment to STI-CORDI devices. In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (Vol. 20, pp. 181-222). Amsterdam: Elsevier.
16.
Desoete, A. ( 2007b). De TEDI-MATH. De plaats van de TEDI-MATH in de diagnostiek van dyscalculie in Vlaanderen [The value of the TEDI-MATH in the assessment of mathematical learning disabilities in Flanders]. Caleidoscoop , 19(6), 6-19.
17.
Desoete, A. ( 2008). Co-morbidity in mathematical learning disabilities: Rule or exception? Open Rehabilitation Journal, 1, 15-26.
18.
Desoete, A., Ceulemans, A., Roeyers, H., & Huylebroeck, A. (2009). Subitizing or counting as possible screening variables for learning disabilities in mathematics education or learning?Educational Research Review, 4, 55-66.
19.
Desoete, A., & Grégoire, J. (2007). Numerical competence in young children and in children with mathematics learning disabilities. Learning and Individual Differences, 16, 351-367.
20.
Desoete, A., Roeyers, H., & De Clercq, A. ( 2004). Children with mathematics learning disabilities in Belgium . Journal of Learning Disabilities, 37, 50-61.
21.
Desoete, A., Roeyers, H., Schittekatte, M., & Grégoire, J. (2006). Dyscalculie-gevoelige kennis en vaardigheden in het basisonderwijs in Vlaanderen, Wallonië en Frankrijk [Dyscalculia-sensitive knowledge and skills in elementary education in the Flemish and French speaking part of Belgium and in France]. Pedagogische Studieën, 83, 105-121.
22.
Desoete, A., Stock, P., Schepens, A., Baeyens, D., & Roeyers, H. ( 2009). Classification, seriation and counting in grades 1, 2, and 3 as two-year longitudinal predictors for low achieving in numerical facility and arithmetical achievement?Journal of Psychoeducational Assessment, 27, 252-264.
23.
De Vos, T. ( 1992). TTR: Tempotest rekenen [Arithmetic number facts test] . Lisse, Netherlands: Swets & Zeitlinger.
24.
Dickerson Mayes, S., Calhoun, S.L., Bixler, E.O., & Zimmerman, D.N. (2009). IQ and neuropsychological predictors of academic achievement. Learning and Individual Differences, 19, 238-241.
25.
DiPerna, J.C., Lei, P.-W., & Reid, E.E. ( 2007). Kindergarten predictors of mathematical growth in the primary grades: An investigation using the Early Childhood Longitudinal Study-Kindergarten cohort. Journal of Educational Psychology, 99, 369-379.
26.
Dowker, A. ( 2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. New York: Psychology Press.
27.
Dumont, J.J. ( 1994). Leerstoornissen I. Theorie en model (nieuwe uitgave) [Learning disabilities I: Theory and model (new ed.)]. Rotterdam, Netherlands: Lemniscaat.
28.
Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P., et al. (2007). School readiness and later achievement . Developmental Psychology, 43, 1428-1446.
29.
Durand, M., Hulme, C., Larkin, R., & Snowling, M. ( 2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year olds. Journal of Experimental Child Psychology , 91, 113-136.
30.
Fischer, B., Gebhardt, C., & Hartnegg, K. ( 2008). Subitizing an visual counting in children with problems acquiring basic arithmetic skills. Optometry and Vision Development , 39, 24-29.
31.
Fletcher, J.M., Coulter, W.A., Reschly, D.J., & Vaughn, S. ( 2004). Alternative approaches to the definition and identification of learning disabilities: Some questions and answers. Annals of Dyslexia, 54, 304-331.
32.
Fletcher, J.M., Denton, C., & Francis, D.J. ( 2005). Validity of alternative approaches for the identification of learning disabilities: Operationalizing unexpected underachievement. Journal of Learning Disabilities, 38, 545-552.
33.
Frank, A.R. ( 1989). Counting skills: A foundation for early mathematics. Arithmetic Teacher, 37, 14-17.
34.
Fuchs, L.S., & Fuchs, D. ( 2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research and Practice , 16, 85-95.
35.
Fuchs, L.S., Fuchs, D., Compton, D.L., Bryant, J.D., Hamlett, C.L., & Seethaler, P.M. (2007). Mathematics screening and progress monitoring at first grade: Implications for responsiveness to intervention . Exceptional Children, 73, 311-330.
36.
Fuson, C.K. ( 1988). Children’s counting and concepts of number. New York: Springer-Verlag.
37.
Gallistel, C.R., & Gelman, R. ( 1990). The what and how of counting. Cognition , 34, 197-199.
38.
Geary, D.C. ( 1994). Children’s mathematical development. Washington, DC: American Psychological Association . Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.
39.
Geary, D.C., Bailey, D.H., & Hoard, M.K. (in press). Predicting mathematical achievement and mathematical learning disability with a simple screening tool: The Number Sets Test. Journal of Psychoeducational Assessment.
40.
Geary, D.C., Bow-Thomas, C.C., & Yao, Y. ( 1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372-391.
41.
Geary, D.C., & Hoard, M.K. ( 2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 253-268). New York: Psychology Press.
42.
Geary, D.C., Hoard, M.K., Byrd-Craven, J., Nugent, L., & Numtee, C. ( 2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development , 78, 1343-1359.
43.
Geary, D.C., & Widaman, K.F. ( 1992). Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16, 47-80.
44.
Gelman, R. ( 1990). First principles organize attention to and learning about relevant data: Number and animate-inanimate distinctions as examples. Cognitive Science, 14, 79-106.
45.
Gelman, R., & Gallistel, C.R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
46.
Gersten, R., & Chard, D. ( 1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education , 44, 18-28.
47.
Gersten, R., Jordan, N.C., & Flojo, J.R. ( 2005). Early identification and Intervention for students with mathematics difficulties. Journal of Learning Disabilities , 38, 293-304.
48.
Gevers, W., Lammertyn, J., Notebaert, W., Verguts, T. & Fias, W. ( 2006). Automatic response activation of implicit spatial information: Evidence from the SNARC effect. Acta Psychologica, 122, 221-233.
49.
Ghesquière, P., & Ruijssenaars, A. (1994). Vlaamse normen voor studietoetsen Rekenen en technisch lezen lager onderwijs. [Flemish norms for school tests on mathematics and technical reading in elementary school]. Leuven, Belgium: K.U.L.-C.S.B.O.
50.
Grégoire, J. ( 2001). L’evaluation clinique de l’intelligence de l’enfant: Théorie et pratique du WISC-III [The clinical evaluation of children’s intelligence: Theory and practice of the WISC-III] (2nd ed.). Sprimont, Belgium: Mardaga.
51.
Grégoire, J. ( 2005). Développement logique et compétences arithmétiques: Le modèle piagétien est-il toujours actuel? [Longitudinal development and arithmetical competences: Is the Piagetical model still actual?]. In M. Crahay, L. Verschaffel, E. De Corte, & J. Grégoire (Eds.), Enseignement et apprentissage des mathématiques [Teaching and learning mathematics] (pp. 57-77). Brussels, Belgium: De Boeck.
52.
Grégoire, J., Noel, M., & Van Nieuwenhoven ( 2004). TEDI-MATH. Amsterdam, the Netherlands: Pearson.
53.
Griffin, S. ( 2004). Building number sense with Number Worlds: A mathematics program for young children. Early Childhood Research Quarterly , 19, 173-180.
54.
Gross-Tsur, V., Manor, O., & Shalev, R.S. ( 1996). Developmental dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology, 38, 25-33.
55.
Hammill, D.D. ( 1990). On defining learning disabilities: An emerging consensus . Journal of Learning Disabilities, 23, 74-84.
56.
Hanley, T.V. ( 2005). Commentary on early identification and interventions for students with mathematical difficulties: Make sense-Do the math. Journal of Learning Disabilities, 38, 346-349.
57.
Hannula, M.M., & Lehtinen, E. ( 2005). Spontaneous focussing on numerosity and mathematical skills of young children. Learning and Instruction, 15, 237-256.
58.
Holloway, I.D., & Ansari, D. ( 2009). Mapping numerical magnitudes Onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103, 17-29.
59.
Johansson, B.S. ( 2005). Number-word sequence skill and arithmetic performance . Scandinavian Journal of Psychology, 46, 157-167.
60.
Jordan, N.C., Hanich, L.B., & Kaplan, B. ( 2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74, 834-850.
61.
Jordan, N.C., Kaplan, D., Olah, L.N., & Locuniak, M.N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153-175.
62.
Jordan, N.C., Levine, S.C., & Huttenlocher, J. (1995). Calculation abilities of young children with different patterns of cognitive functioning. Journal of Learning Disabilities, 28, 53-67.
63.
Kaufman, E.L., Lord, M.W., Reese, T.W., & Volkmann, J. ( 1949). The discrimination of visual number. American Journal of Psychology, 62, 498-525.
64.
Kavale, K.A., & Spaulding, L.S. (2008). Is response to intervention good policy for specific learning disability? Learning Disabilities Research and Practice, 23, 169-179.
65.
Kingma, J. ( 1984). Traditional intelligence, Piagetian tasks, and initial arithmetic in kindergarten and primary school grade one. Journal of Genetic Psychology, 145, 49-60.
66.
Klauer, K.J. ( 1992). In Mathematik mehr leistungsschwache Madchen, im Lesen und Rechschreiben mehr leistungsschwache Junden? [In mathematics more poor-performing girls, in reading and spelling more poor-performing boys?]Zeitschift fur Entwicklungspsychologie und Padagogische Psychologie, 26, 48-65.
Kosc, L. ( 1974). Developmental dyscalculia. Journal of Learning Disabilities, 7, 46-59.
69.
Kort, W., Schittekatte, M., Compaan, E.L., Bosmans, M., Bleichrodt, N., Vermeir, G., et al. (2002). Handleiding WISC-IIINL [Manual of the WISC-IIINL]. LondonPsychological Corporation and Amsterdam: NIP Dienstencentrum.
70.
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8-9 year old students. Cognition, 93, 99-125.
71.
Laski, E.V., & Siegler, R.S. ( 2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation and numerical magnitude comparison. Child Development, 78, 1723-1743.
72.
Le Corre, M., Van de Walle, G., Brannon, E.M., & Carey, S. ( 2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology , 52, 130-169.
73.
Le Fevre, J.-A., Smith-Chant, B.L., Fast, L., Skwarchuk, S.-L., Sargla, E., Arnup, J.S., et al. (2006). What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2. Journal of Experimental Child Psychology, 93, 285-303.
74.
Lourenço, O., & Machado, A. ( 1996). In defense of Piaget’s theory: A reply to 10 common criticisms. Psychological Review, 103, 143-164.
75.
Marzocchi, G.M., Lucangeli, D., De Meo, T., Fini, F., & Cornoldi, C. ( 2002). The disturbing effect of irrelevant information on arithmetic problem solving in inattentive children. Developmental Neuropsychology , 21, 73-92.
76.
Mazzocco, M.M.M. ( 2001). Math learning disability and math LD subtypes: Evidence from studies of Turner syndrome, Fragile X syndrome and Neurofibromatosis Type 1. Journal of Learning Disabilities, 34, 520-533.
77.
Mazzocco, M.M.M. ( 2005). Challenges in identifying target skills for math disability screening and intervention. Journal of Learning Disabilities , 38, 318-323.
78.
Mazzocco, M.M.M., Devlin, K.T., & McKenney, S.J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology , 33, 318-344.
79.
Mazzocco, M.M.M., & Kover, S.T. ( 2007). A longitudinal assessment of executive function skills and their association with math performance. Child Neuropsychology , 13, 18-45.
80.
Mazzocco, M.M.M., & Myers, G.F. ( 2003). Complexities in identifying and defining mathematics learning disability in the primary school-age years. Annals of Dyslexia, 53, 218-253.
81.
Mazzocco, M.M.M., & Thompson, R.E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research and Practice, 20, 142-155.
82.
Muldoon, K.P., Lewis, C., & Francis, B. ( 2007). Using cardinality to compare quantities: The role of social-cognitive conflict in early numeracy. Developmental Science, 10, 694-711.
83.
Murphy, M.M., Mazzocco, M.M.M., Hanich, L.B., & Early, M.C. ( 2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40, 458-478.
84.
Nan, Y., Knösche, T.R., & Luo, Y.-J. (2006). Counting in everyday life: Discrimination and enumeration. Neuropsychologica, 44, 1103-113.
85.
Nunes, T., & Bryant, P. ( 1996). Children doing mathematics. Oxford , UK: Blackwell.
86.
Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, A., Gardner, A., et al. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25, 147-166.
87.
Pasnak, R., Cooke, W.D., & Hendricks, C. ( 2006). Enhancing academic performance by strengthening class-inclusion reasoning. Journal of Psychology, 140, 603-613.
88.
Passolunghi, M.C., Mammarella, I.C., & Altoe, G. ( 2008). Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades. Developmental Neuropsychology, 33, 229-250.
89.
Passolunghi, M.C., & Siegel, L.S. ( 2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88, 348-367.
90.
Piaget, J. ( 1965). The child’s conception of number. New York: Norton.
91.
Piaget, J., & Inhelder, B. ( 1959). La genèse des structures logiques éléméntaires: Classification et sériation [The development of basic logical structures: Classification and seriation]. Neuchâtel, France: Delachaux and Niestlé.
92.
Piaget, J., & Szeminska, A. ( 1941). La genèse du nombre chez l’enfant [The development of numbers in children]. Neuchâtel, France: Delanchaux et Niestlé.
93.
Porter, J. ( 1998). The understanding of counting in children with severe learning difficulties and nursery children. British Journal of Educational Psychology, 68, 331-345.
94.
Reeve, R.A., & Reynolds, F.J. (2004, July). The nature of young children’s mathematical (dis)abilities. Poster presented at the International Society of the Study of Behavioral Development , Ghent, Belgium.
95.
Reusser, K. ( 2000). Success and failure in school mathematics: effects of instruction and school environment. European Child and Adolescent Psychiatry, 9, II/7-II/26.
96.
Ricken, G., & Fritz, A. ( 2006). Working memory functions in children with different arithmetical performance at kindergarten. Psychologie in Erziehung Und Unterricht, 53, 263-274.
97.
Rousselle, L., & Noël, M.P. (2007). Basic numeric skills in children with mathematics learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition, 102, 361-395.
98.
Ruijssenaars, A. J. J. M., Van Luit, H., & Van Lieshout, E. C. D. M. (Eds.). (2004). Rekenproblemen en dyscalculie [Arithmetic problems and dyscalculia]. Rotterdam, Netherlands: Lemniscaat.
Shalev, R.S., Manor, O., & Gross-Tsur, V. (2005). Developmental dyscalculia: A prospective six-year follow-up. Developmental Medicine and Child Neurology, 47, 121-125.
101.
Sophian, C. ( 1992). Learning about numbers: Lessons for mathematics education from preschool number development. In J. Bideaud , C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children’s developing numerical abilities (pp. 19-40). Hillsdale, NJ: Lawrence Erlbaum.
102.
Stock, P., Desoete, A., & Roeyers, H. ( 2006). Focussing on mathematical disabilities: A search for definition, classification and assessment. In S. V. Randall (Ed.), Learning disabilities: New research (pp. 29-62): Hauppage, NY: Nova Science.
103.
Stock, P., Desoete, A., & Roeyers, H. ( 2007). Early markers for arithmetic difficulties. Educational and Child Psychology, 24, 28-39.
104.
Stock, P., Desoete, A., & Roeyers, H. (in press). Predicting arithmetic abilities: The role of preparatory arithmetic markers and intelligence. Journal of Psychoeducational Assessment .
105.
Teisl, J.T., Mazzocco, M.M.M., & Myers, G.F. ( 2001). The utility of kindergarten teacher ratings for predicting low academic achievement in first grade. Journal of Learning Disabilities, 34, 286-293.
106.
Van de Rijt, B.A.M., & Van Luit, J.E.H. (1999). Milestones in the development of infant numeracy. Scandinavian Journal of Psychology, 40, 65-71.
107.
Van der Sluis, S., de Jong, P.F., & van der Leij, A. (2007). Executive functioning in children and its relations with reasoning, reading, and arithmetic. Intelligence, 35, 427-449
108.
Vaughn, S., & Fuchs, L.S. ( 2003). Redefining learning disabilities as inadequate response to instruction: The promise and potential problems. Learning Disabilities Research and Practice, 18, 137-143.
109.
Von Aster, M.G. & Shalev, R.S. ( 2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49, 868-873.
110.
Wechsler, D. ( 1991). Wechsler Intelligence Scale for Children (3rd ed.). San Antonio, TX: Psychological Corporation.
111.
Wynn, K. ( 1990). Children’s understanding of counting. Cognition, 36, 155-193.
112.
Wynn, K. ( 1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220-251.
113.
Xu, F. ( 2003). Numerosity discrimination in infants: Evidence for two systems of representations. Cognition, 89, B15-B25.
114.
Xu, F., & Spelke, E.S. ( 2000). Large number discrimination in 6-month-old infants. Cognition, 74, 1-11.
115.
Zhou, X., Chen, C., Chen, C., & Dong, Q. ( 2008). Holistic or compositional representation of two-digit numbers? Evidence from distance, magnitude, and SNARC-effects in a number-matching task. Cognition, 106, 1525-1536.
