Language in the prediction of mathematical (dis)abilities ? Evidence from a longitudinal study following-up children from kindergarten till grade 2.

Volume 1, Issue 1, December 2016     |     PP. 37-64      |     PDF (491 K)    |     Pub. Date: December 23, 2016
DOI:    356 Downloads     7542 Views  

Author(s)

Magda Praet, PhD, scientific collaborator at Ghent University, Ghent, Belgium
Annemie Desoete, professor at Ghent University (Experimental Clinical and Health Psychology Developmental Disorders) and Artevelde University college, Ghent, Belgium

Abstract
Previous studies suggested that early numeracy predict mathematical abilities and disabilities. Although there is evidence for a significant relationship between language and numeracy, it remains an open question to what extent mathematics is truly dependent on language. In addition the question on how different language components relate to children's mathematical performance remains unresolved. This longitudinal study examined how receptive language, expressive language, the understanding of grammatical rules and the structure of language assessed in kindergarten were differentially related to children's early arithmetic skills in kindergarten and to their number knowledge, mental arithmetic skills and fact retrieval abilities in grade 1 and 2. A group of 132 children was followed-up from kindergarten till grade 2. The relationship between counting and arithmetic and the value of number estimation was confirmed in this study. In addition, our data revealed that expressive language had a unique contribution of 30.1% in explaining the variance of early arithmetic skills in kindergarten. Moreover, there was a unique longitudinal prediction for expressive kindergarten language of 28.3% for number knowledge and of 22.1% for mental arithmetic in grade 1. Expressive language assessed in kindergarten still added 5% to the prediction of number knowledge in grade 2. Receptive language in kindergarten added 10.8% to the explained variance of fact retrieval proficiency assessed in grade 2.

Keywords
expressive language, arithmetic, number knowledge, fact retrieval, receptive language

Cite this paper
Magda Praet, Annemie Desoete, Language in the prediction of mathematical (dis)abilities ? Evidence from a longitudinal study following-up children from kindergarten till grade 2. , SCIREA Journal of Education. Volume 1, Issue 1, December 2016 | PP. 37-64.

References

[ 1 ] Ansari, D., Donlan, C., Thomas, M. S. C., Ewing, S. A., Peen, T., & Karmiloff-Smith, A. (2003). What makes counting count? Verbal and visuo-spatial contributions to typical and atypical counting development. Journal of Experimental Child Psychology, 85, 50-62. doi:10.1016/S0022-0965(03)00026-2
[ 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. doi: 10.1037/0022-0663.96.4.699
[ 3 ] Ashcraft, M. H., & Moore, A. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111, 246-267. doi: 10.1016/j.jecp.2011.08.005
[ 4 ] Barner, D., Chow, K., & Yang, S. (2009). Finding one’s meaning: A test of the relation between quantifiers and integers in language development. Cognitive Psychology, 58, 195-219. doi: 10.1016/j.cogpsych.2008.07.001
[ 5 ] Baudonck, M., Debusschere, A., Dewulf, B., Samyn, F., Vercaemst, V., & Desoete, A. (2006). Kortrijkse Rekentest Revisie (KRT-R) [Kortrijk Arithmetic Test Revision]. Kortrijk: Revalidatiecentrum Overleie.
[ 6 ] Berteletti, I., Lucangeli, D., Piazza, M., Dehaene, S., & Zorzi, M. (2010). Numerical estimation in preschoolers. Developmental Psychology, 46, 545-551. doi: 10.1037/a0017887
[ 7 ] Boonen, A. J. H., Kolkman, M. E., & Kroesbergen, E. H. (2011). The relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms. Journal of School Psychology, 49, 281-299. doi: 10.1016/j.jsp.2011.03.002
[ 8 ] Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189-201. doi: 10.1037/0012-1649.41.6.189
[ 9 ] Brannon, E. M. (2005). What animals know about number. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 85-108). New York: Psychology Press.
[ 10 ] Bull, R., & Johnston, R. (1997). Children’s arithmetical difficulties: Contributions from processing speed, item identification and short term memory. Journal of Experimental Child Psychology, 65, 1-24. doi.: 10.1006/jecp.1996.2358
[ 11 ] Cohen, D.J., & Blanc-Goldammer, D. (2011). Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin Reviews, 18, 331-338. doi: 10.3758/sI3423-011-0059-z
[ 12 ] Cohen Kadosh, R., Muggleton, N., Silvanto, J., & Walsh, V. (2010). Double dissociation of format-dependent and number-specific neurons in human parietal cortex. Cerebral Cortex, 20, 2166-2171. doi: 10.1093/cercor/bhp273
[ 13 ] Cowan, R., & Renton, M. (1996). Do they know what they are doing? Children’s use of economical addition strategies and knowledge of commutativity. Educational Psychology, 16, 407–420.
[ 14 ] Defever, E., Sasanguie, D., Gebuis, T., & Reynvoet, B. (2011). Children’s representation of symbolic and non-symbolic magnitude examined with the priming paradigm. Journal of Experimental Child Psychology, 109, 174-186. doi: 10.1016/j.jecp.2011.01.002
[ 15 ] Dehaene, S., Izard, V., & Piazza, M. (2005). Control over non-numerical parameters in numerosity experiments. Unpublished manuscript (available at http://www.unicog.org/…/DocumentationDotsGeneration.doc).
[ 16 ] Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999) Sources of mathematical thinking: behavioral and brain-imaging evidence Science, 284,970-974. doi:10.1126/science.284.5416.970
[ 17 ] Desoete, A., & Grégoire, J. (2006). Numerical competence in young children and in children with mathematics learning disabilities. Learning and Individual Differences, 16, 351-367. doi: 10.1016/j.lindif.2006.12.006
[ 18 ] Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? British Journal of Educational Psychology,, 82, 64–81. doi: 10.1348/2044-8279.002002
[ 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. doi: 10.1016/j.lindif.2006.12.006
[ 20 ] De Vos, T. (1992). TempoTest Rekenen (TTR)(Arithmetic Number fact Test). Nijmegen : Berkhout
[ 21 ] Dowker, A.D. (2005). Individual differences in arithmetic. Implications for psychology, neuroscience and education. New York: Psychology Press.
[ 22 ] Dowker, A.D. (2008). Individual differences in numerical abilities in preschoolers. Developmental Science, 11, 50-654. doi: 10.1111/j.1467-7687.2008.00713.x
[ 23 ] Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani,L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446. doi:10.1037/0012-1649.43.6.1428
[ 24 ] Fischer, B., Gebhardt, C., & Hartnegg, K. (2008). Subitizing and visual counting in children with problems acquiring basic arithmetic skills. Optometry and Vision Development, 39, 24-29.
[ 25 ] Geary, D. C. (1993). Mathematical Disabilities - Cognitive, neuropsychological and genetic components. Psychological Bulletin, 114, 345-362. doi: 10.1037//0033-2909.114.2.345
[ 26 ] Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47, 1539-1552. doi: 10.1037/a0025510
[ 27 ] Ghesquière, P., & Ruyssenaers, A. 1994.Vlaamse normen voor studietoetsen rekenen en technisch lezen lager onderwijs (Flemish standards for study evaluation of mathematics and technical reading in primary schools) . Leuven Belgium: Catholic University of Leuven. Center for Educational and Professional Guidance.
[ 28 ] Grégoire, J. (2005). Développement logique et compétences arithmétiques. Le modèle piagétien est-il toujours actuel ? [Logical development and arithmetical skills. Is the Piagetian model still correct ?]. In M. Crahay, L. Verschaffel, E. De Corte & J. Grégoire. Enseignement et apprentissage des mathématiques. (pp.57-77). Bruxelles : De Boeck.
[ 29 ] Grégoire, J., Noël, M., & Van Nieuwenhoven (2004). Tedi-Math. Antwerpen: Harcourt.
[ 30 ] Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465. doi:10.1037/a0012682
[ 31 ] Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-U662. doi: 10.1038/nature07246
[ 32 ] Hannula, M. M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: Role on numerosity and subitizing-based enumeration. Mathematical Thinking, 9, 51-57. doi:10.1080/10986060709336605
[ 33 ] Hendriksen ,J., & Hurks, P. (2009) WPPSI-III-NL | Wechsler Preschool and Primary Scale of Intelligence.
[ 34 ] 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. doi: 10.1016/j.jecp.2008.04.001
[ 35 ] Hooper, S., Roberts, J., Sideris, J. Burchinal, M., & Zeisel, S. (2010). Longitudinal predictors of reading and math trajectories through middle school from African American versus Caucasian students across two samples. Development Psychology, 46, 1018-1029. doi:10.1037/a0018877
[ 36 ] Inglis, M., Attridge, N., Batchelor, S, & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychon Bull Rev , 18, 1222–1229. doi: 10.3758/s13423-011-0154-1
[ 37 ] Jordan, N., Kaplan, D., Olah, L., & Locuniak, M. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153-175. doi: 10.1111/j.1467-8624.2006.00862.x
[ 38 ] Jordan, J., Wylie, J., & Mulhern, G. (2010). Phonological awareness and mathematical difficulty: A longitudinal perspective. Britisch Journal of Developmental Psychology, 28, 89-107. doi: 10.1348/026151010X485197
[ 39 ] Kort, W., Schittecatte, M., Dekker, P.H., Verhaeghe, P., Compaan, E.L., Bosmans, M.,& Vermeir,; G. (2005). WISC-III-NL Wechsler Intelligent scale for Children. David Wechsler. 3th Ed NL (pp 1-48). Amsterdam: Harcourt test Publishers/NIP Dienstencentrum
[ 40 ] Kort, W., Schittekatte, M., & Compaan,E.,(2008) CELF-4-NL Test voor diagnose en evaluatie van taalproblemen. Handleiding [Test for the evaluation of language problems. Manual]. Amsterdam: Pearson.
[ 41 ] 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. doi: 10.1016/j.cogpsych.2005.07.002
[ 42 ] Le Fevre, J.-A., Smith-Chant, B. L., Fast, L., Skwarchuk, S.-L., Sargla, E., Arnup, J. S., Penner-Wilger, M., Bisanz, J., & Kamawar, D. (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. doi: 10.1016/j.cognition.2003.11.004
[ 43 ] Lourenço, O., & Machado, A. (1996). In Defense of Piaget’s Theory: A Reply to 10 Common Criticisms. Psychological Review, 103, 143-164.
[ 44 ] Maloney, E.A., Risko, E.F, Ansari, D., & Fugelsang, J. (2010). Mathematics anxiety affects counting but not subitizing during visual enumeration. Cognition, 114, 293-297. doi: 10.1016/j.cognition.2009.09.013
[ 45 ] Negen, J., & Sarnecka, B.W. (2012). Number-Concept Acquisition and General Vocabulary Development, Child Development doi: 10.1111/j.1467-8624.2012.01815.x
[ 46 ] Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, A., Gardner, A., & Carraher, J. (2006). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental psychology, 00, 1-21. doi: 10.1348/026151006X153127
[ 47 ] Passolunghi, M.C., Vercelloni, B., & Schadeee H. (2007). The precursors of mathematics learning:working memory, Phonological Ability and numerical competence. Cognitive development 22, 165-184 doi: 10.1016/j.cogdev.2006.09.001
[ 48 ] Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison : Reliability and validity of different task variants and outcome measures, and their relationship to arthmetic achievement in adults. Acta Psychologica, 140, 50-57. doi :10.1016/j.actpsy.2012.02.008
[ 49 ] Purpura, D.J., Hume, L.E., Sims, D,C., & Lonigan, C.J. (2011). Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy development. Journal of Experimental Child Psychology, 110, 647-658. doi: 10.1016/j.jecp.2011.07.004.
[ 50 ] Romano, E., Babchishin, L. Pagani, L.S., & Kohen, D. (2010). School readiness and later achievement: Replication and extension using a nationwide Canadian survey. Developmental Psychology, 46, 995-1007. doi: 10.1037/a0018880
[ 51 ] Sarnecka, B.W., & Carrey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108, 662-674. doi:10.1016/j.jecp.2009.02.007
[ 52 ] Sarnecka, B.W., Kamenskaya, V.G., Yamana, Y., Ogura, T., & Ydovina, Y.B. (2007). From grammatical number to exact numbers: early meanings of one, two and three in English, Russian and Japanese, Cognitive Psychology, 55, 136-168. doi: 10.1016/j.cogpsych.2006.09.001.
[ 53 ] Semel, E., Wiig, E. H., & Secord W.A.,(2008). CELF 4 Nl Clinical Evaluation of language Fundamentals. Amsterdam :Pearson.
[ 54 ] Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444. doi: 10.1111/j.1467-8624.2004.00684.x .
[ 55 ] Stock, P., & Desoete, A. (2009). Screening for mathematical disabilities in kindergarten. Developmental Neurohabilitation, 12, 389-397 doi: 10.3109/17518420903046752
[ 56 ] Stock, P., Desoete, A., & Roeyers, H. (2009). Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities? Learning and Individual Differences, 19, 419-422. doi: 10.1016/j.lindif.2009.03.002.
[ 57 ] Stock, P., Desoete, A., & Roeyers, H. (2010). Detecting children with arithmetic disabilities from kindergarten: Evidence from a three year longitudinal study on the role of preparatory arithmetic abilities. Journal of Learning Disabilities, 43, 250-268. doi: 10.1177/0022219409345011.
[ 58 ] Storch, S.A., & Whitehurst, G.J. (2002). Oral language and code-related precursors to reading: Evidence from a longitudinal structural model. Developmental Psychology, 38, 934-947. doi: 10.1037//0012-1649.38.6.934
[ 59 ] Van Opstal, F., Gevers, W., De Moor, W., & Verguts, T. (2008). Dissecting the symbolic distance effect: priming and comparison distance effects in numerical and non-numerical orders. Psychometric Bulletin & Review, 15, 419-425. doi: 10.3758/PBR.15.2.419
[ 60 ] Wechsler, D., Kort, W., Schittekatte, M., Bosmans, M., Compaan, E.L., Dekker, P.H., & Verhaeghe, P. (2002). Wechsler Intelligence Scale for Children-III-Nl. Amsterdam, The Netherlands: Harcourt.
[ 61 ] Wiese, H. (2003). Iconic and non-iconic stages in number development: the role of language. Trends in Cognitive Science, 7, 385-390. doi: 10.1016/S1364-6613(03)00192-X.