Strategie szacowania miejsca liczb na osi u dzieci z dyskalkulią i typowo rozwijających się

American Psychiatric Association (2013). Diagnostic and Statistical Manual of Mental Disorders (5th edition). Washington, DC: American Psychiatric Association.
Crossref   Google Scholar

Ashcraft, M. H., Moore, A. M (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111(2), 246–267. DOI: 10.1016/j.jecp.2011.08.005
Crossref   Google Scholar

Barth, H. C., Paladino, A. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14, 545–551. DOI: 10.1037/a0028560
Crossref   Google Scholar

Benjamini, Y., Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B, 57(1) (Methodological), 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x
Crossref   Google Scholar

Berteletti, I., Lucangeli, D., Piazza, M., Dehaene, P., Zorzi, M. (2010). Numerical Estimation in Preschoolers. Developmental Psychology, 46(2), 545–551. DOI: 10.1037/a0017887
Crossref   Google Scholar

Boland, P. J., Hutchinson, K. (2000). Student selection of random digits. Journal of the Royal Statistical Society: Series D (The Statistician), 49, 519–529. DOI: 10.1111/1467-9884.00250
Crossref   Google Scholar

Bonato, M., Fabbri, S., Umiltà, C., Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33, 1410–1419. DOI: 10.1037/0096-1523.33.6.1410
Crossref   Google Scholar

Booth, J.L., Siegler R.S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41, 189–201. DOI: 10.1037/0012-1649.41.6.189
Crossref   Google Scholar

Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14, 534–541. DOI: 10.1016/j.tics.2010.09.007
Crossref   Google Scholar

Butterworth, B. (2003). Dyscalculia Screener by Brian Butterworth. Highlighting pupils with specific learning difficulties in maths. nferNelson Publishing Company Limited, London.   Google Scholar

Butterworth, B., Varma S., Laurillard, D. (2011). Dyscalculia: From Brain to Education. Science, 332, 1049–1053. DOI: 10.1126/science.1201536
Crossref   Google Scholar

Cai, Y.C., Li, S.X. (2015). Small number preference in guiding attention. Experimental Brain Research, 233, 539–550. DOI: 10.1007/s00221-014-4134-3
Crossref   Google Scholar

Cangöz, B., Altun, A., Olkun, S. Kacar, F. (2013). Computer Based Screening Dyscalculia: Cognitive and Neuropsychological Correlates. Turkish Online Journal of Educational Technology, 12(3).   Google Scholar

Cappeletti, M., Muggleton, N., Walsh, V. (2009). Quantity without numbers and numbers without quantity in the parietal cortex. Neuroimage, 46, 522–529. DOI: 10.1016/j.neuroimage.2009.02.016
Crossref   Google Scholar

Cipora, K., Nuerk, H.C. (2013). Is the SNARC effect related to the level of mathematics? No systematic relationship observed despitemore power,more repetitions, andmore direct assessment of arithmetic skill. The Quarterly Journal of Experimental Psychology, 66, 1974–1991. DOI: 10.1080/17470218.2013.772215
Crossref   Google Scholar

Cipora, K., Patro, K., Nuerk, H.-C. (2015). Are spatial-numerical associations a cornerstone for arithmetic learning? The lack of genuine correlations suggests no. Mind, Brain, and Education, 9, 190–206. DOI: 10.1111/mbe.12093
Crossref   Google Scholar

Cohen, D. J., Blanc-Goldhammer, D. (2011). Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin & Review, 18, 331–338. DOI: 10.3758/s13423-011-0059-z
Crossref   Google Scholar

Cohen, D. J. Quinlan, P.T. (2018). The log–linear response function of the bounded number-line task is unrelated to the psychological representation of quantity. Psychonomic Bulletin & Review, 25, 447–454. DOI: 10.3758/s13423-017-1290-z
Crossref   Google Scholar

Dehaene, S. (2011). Number sense. How the mind creates mathematics. Oxford University Press.   Google Scholar

Dehaene, S., Molko, N., Cohen, L., Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14, 218–224. DOI: 10.1016/j.conb.2004.03.008
Crossref   Google Scholar

Dehaene, S., Piazza, M., Pinel, P., Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. DOI: 10.1080/02643290244000239
Crossref   Google Scholar

Ebersbach, M., Luwel, K. Verschaffel, L. (2013). Comparing apples and pears in studies on magnitude estimations. Frontiers in Psychology, 4, 332. DOI: 10.3389/fpsyg.2013.00332
Crossref   Google Scholar

Feigenson, L., Dehaene, S., Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. DOI: 10.1016/j.tics.2004.05.002
Crossref   Google Scholar

Field, A., Miles, J. Field, Z. (2012). Discovering statistics using R, London: Sage.   Google Scholar

Field, A., Wilcox, R. R. (2017). Robust statistical methods: a primer for clinical psychology and experimental psychopathology researchers. Behaviour Research and Therapy, 98, 19–38. DOI: 10.1016/j.brat.2017.05.013
Crossref   Google Scholar

Fischer, M. H., Shaki, S. (2014). Spatial associations in numerical cognition—From single digits to arithmetic. The Quarterly Journal of Experimental Psychology, 67(8), 1461–1483. DOI: 10.1080/17470218.2014.927515
Crossref   Google Scholar

Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345–362. DOI: 10.1037/0033-2909.114.2.345
Crossref   Google Scholar

Geary, D. C. (2011). Cognitive predictors of individual differences in achievement growth in mathematics: a five year longitudinal study. Developmental Psychology, 47, 1539–1552. DOI: 10.1037/a0025510
Crossref   Google Scholar

Geary, D. C., Hoard, M. K., Byrd-Craven, J., De Soto, C. M. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121. DOI: 10.1016/j.jecp.2004.03.002
Crossref   Google Scholar

Geary, D. C., Hoard, M. K, Nugent, L., Bailey, D. H. (2012). Mathematical Cognition Deficits in Children With Learning Disabilities and Persistent Low Achievement: A Five-Year Prospective Study, Journal of Educational Psychology, 104, 206–223. DOI: 10.1037/a0025398
Crossref   Google Scholar

Geary, D. C., Hoard, M.K., Nugent, L., Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33, 277–299. DOI: 10.1080/87565640801982361
Crossref   Google Scholar

Georges, C., Hoffmann, D., Schiltz, C. (2017). Mathematical abilities in elementary school: Do they relate to number–space associations? Journal of Experimental Child Psychology, 161, 126–147. DOI: 10.1016/j.jecp.2017.04.011
Crossref   Google Scholar

Göbel, S. M., Calabria, M., Farnè, A., Rossetti, Y. (2006). Parietal rTMS distorts the mental number line: simulating 'spatial' neglect in healthy subjects. Neuropsychologia, 44, 860–868. DOI: 10.1016/j.neuropsychologia.2005.09.007
Crossref   Google Scholar

Gut M., Matulewski, J., Goraczewski, Ł. Prokalkulia 6–9: Test oceny behawioralnych wskaźników umysłowych reprezentacji liczb i ryzyka dyskalkulii. Pomorskie Centrum Diagnozy, Terapii i Edukacji Matematycznej Promathematica, Gdańsk 2016.   Google Scholar

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
Crossref   Google Scholar

Halberda, J., Mazzocco, M. M., Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668. DOI: 10.1038/nature07246
Crossref   Google Scholar

de Hevia, M.D., Vallar, G., Girelli, L. (2008). Visualizing numbers in the mind's eye: the role of visuo-spatial processes in numerical abilities. Neuroscience & Biobehavioral Reviews, 32, 1361–1372. DOI: 10.1016/j.neubiorev.2008.05.015
Crossref   Google Scholar

Hoffmann, D., Mussolin, C., Martin R., Schiltz, C. (2014). The impact of mathematical proficiency on the number-space association. PLoS ONE, 9(1), e85048. DOI: 10.1371/journal.pone.0085048
Crossref   Google Scholar

Hollands, J. G., Dyre, B. P. (2000). Bias in proportion judgments: The cyclical power model. Psychological Review, 107, 500–524. DOI: 10.1037/0033-295X.107.3.500
Crossref   Google Scholar

Hubbard, E. M., Piazza, M., Pinel, P., Dehaene S. (2005). Interactions between number and space in parietal cortex. Nature Review of Neuroscience, 6, 435–448. DOI: 10.1038/nrn1684
Crossref   Google Scholar

Isaacs, E. B., Edmonds, C. J., Lucas, A., Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: a neural correlate. Brain, 124, 1701–1707. DOI: 10.1093/brain/124.9.1701
Crossref   Google Scholar

Kaufmann, L., von Aster, M. (2012). The Diagnosis and Management of Dyscalculia. Deutsches Arzteblatt International, 109(45), 767–778. DOI: 10.3238/arztebl.2012.0767
Crossref   Google Scholar

Koontz, K. L., Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2, 1–23. DOI: 10.1080/135467996387525
Crossref   Google Scholar

Krajcsi, A., Kojouharova, P., Lengyel, G. (2017). Development of Understanding Zero. Preprints.
Crossref   Google Scholar

Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., Gälli, M., Martin E., von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. Neuroimage 57, 782–795. DOI: 10.1016/j.neuroimage.2011.01.070
Crossref   Google Scholar

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. DOI: 10.1016/j.cognition.2003.11.004
Crossref   Google Scholar

Landerl, K., Fussenegger, B., Moll, K., Willburger, E. (2009). Dyslexia and dyscalculia: two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology, 103(3), 309–324. DOI: 10.1016/j.jecp.2009.03.006
Crossref   Google Scholar

LeFevre, J-A, Lira,C. J., Sowinski, C., Cankaya, O., Kamawar, D., Skwarchuk, S-L. (2013). Charting the role of the number line in mathematical development. Frontiers in Psychology, 4, 641. DOI: 10.3389/fpsyg.2013.00641
Crossref   Google Scholar

Link, T., Huber, S., Nuerk, H-Ch., Moeller, K. (2014). Unbounding the mental number line – new evidence on children’s spatial representation of numbers. Frontiers in Psychology, 4, 1021. DOI: 10.3389/fpsyg.2013.01021
Crossref   Google Scholar

Longo, M.R., Lourenco, S.F. (2007). Spatial attention and the mental number line: Evidence for characteristic biases and compression. Neuropsychologia, 37, 843–855. DOI: 10.1016/j.neuropsychologia.2006.11.002
Crossref   Google Scholar

Longo, M. R., Lourenco, S.F., Francisco, A. (2012). Approaching stimuli bias attention in numerical space. Acta Psychologica, 140, 129–132. DOI: 10.1016/j.actpsy.2012.04.001
Crossref   Google Scholar

Luwel, K., Peeters, D, Dierckx, G., Elke Sekeris E., Verschaffel, L. (2018). Benchmark-based Strategy Use in Atypical Number Lines. Canadian Journal of Experimental Psychology, 72(4), 253–263. DOI: 10.1037/cep0000153
Crossref   Google Scholar

Mair, P., Wilcox, R. (2016). Robust statistical methods in r using the wrs2 package. Unpublished technical report.   Google Scholar

McCaskey, U., von Aster, M., Maurer, U., Martin, E., O’Gorman Tuura, R., Kucian, K. (2018). Longitudinal brain development of numerical skills in typically developing children and children with developmental dyscalculia. Frontiers in Human Neuroscience, 11, 629. DOI: 10.3389/fnhum.2017.00629
Crossref   Google Scholar

Merrit, D. J., Brannon, E. M. (2013). Nothing to it: Precursors to a zero concept in preschoolers. Behavioural Processes, 93, 91–97. DOI: 10.1016/j.beproc.2012.11.001
Crossref   Google Scholar

Michels, L., O’Gorman, R., Kucian, K (2018). Functional hyperconnectivity vanishes in children with developmental dyscalculia after numerical intervention. Developmental Cognitive Neuroscience, 30, 291–303. DOI: 10.1016/j.dcn.2017.03.005
Crossref   Google Scholar

Mix, K. S., Cheng, Y. L. (2012). The relation between space and math: developmental and educational implications. Advances in Child Development and Behavior, 42, 197–243. DOI: 10.1016/b978-0-12-394388-0.00006-x
Crossref   Google Scholar

Molko, N., Cachia, A., Riviere, D., Mangin, J. F., Bruandet, M., Le Bihan, D., Cohen, L., Dehaene, S. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40, 847–858. DOI: 10.1016/s0896-6273(03)00670-6
Crossref   Google Scholar

Mussolin, C., Mejias, S., Noël, M.P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115, 10–25. DOI: 10.1016/j.cognition.2009.10.006
Crossref   Google Scholar

Mussolin, C., De Volder, A., Grandin, C., Schlögel, X., Nassogne, M. C., Noël, M. P. (2009). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22, 860–874. DOI: 10.1162/jocn.2009.21237
Crossref   Google Scholar

Nuerk, H. C., Moeller, K., Klein, E., Willmes, K., Fischer, M. (2011). Extending the mental number line. A review of multi-digit number processing. Journal of Psychology, 219, 3–22. DOI: 10.1027/2151-2604/a000041
Crossref   Google Scholar

Patro, K., Nuerk, H.-Ch., Cress, U., Haman, M. (2014). How number-space relationships are assessed before formal schooling: A taxonomy proposal. Frontiers in Psychology, 5, 419. doi.org/10.3389/fpsyg.2014.00419
Crossref   Google Scholar

Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S., Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116, 33–41. DOI: 10.1016/j.cognition.2010.03.012
Crossref   Google Scholar

Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274–278. DOI: 10.1037/h0028573
Crossref   Google Scholar

Rinaldi, L., Girelli, L. (2016). A place for zero in the brain. Trends in Cognitive Sciences, 20(8), 563–564. DOI: 10.1016/j.tics.2016.06.006
Crossref   Google Scholar

Rotzer, S., Kucian, K., Martin, E., von Aster, M., Klaver, P., Loenneker T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage, 39, 417–422. DOI: 10.1016/j.neuroimage.2007.08.045
Crossref   Google Scholar

Rouder, J. N, Geary, D. C. (2014). Children's cognitive representation of the mathematical number line. Developmental Science, 17(4), 525–536. DOI: 10.1111/desc.12166
Crossref   Google Scholar

Rykhlevskaia, E., Uddin, L. Q., Kondos, L., Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3, 51. DOI: 10.3389/neuro.09.051.2009
Crossref   Google Scholar

Sandrini M., Rusconi E. (2009). A brain for numbers. Cortex, 45, 796–803. DOI: 10.1016/j.cortex.2008.09.002
Crossref   Google Scholar

Sasanguie, D., Verschaffel, L., Reynvoet, B. Luwel, K. (2016). The Development of Symbolic and Non-Symbolic Number Line Estimations: Three Developmental Accounts Contrasted Within Cross-Sectional and Longitudinal Data. Psychologica Belgica, 56(4), 382–405. DOI: 10.5334/pb.276
Crossref   Google Scholar

Schwarz, W., Eiselt, A. K. (2009). The perception of temporal order along the mental number line. Journal of Experimental Psychology: Human Perception and Performance, 35, 989–1004. DOI: 10.1037/a0013703
Crossref   Google Scholar

Sella, F., Sasanguie, D., Reynvoet, B. (2020). Judging the order of numbers relies on familiarity rather than activating the mental number line. Acta Psychologica, 204, 1–7. DOI: 10.1016/j.actpsy.2020.103014
Crossref   Google Scholar

Siegler, R. S., Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243. DOI: 10.1111/1467-9280.02438
Crossref   Google Scholar

Wai, J., Lubinski, D., Benbow, C. P. (2009). Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835. DOI: 10.1037/a0016127
Crossref   Google Scholar

Wechsler, D. (1974). Wechsler intelligence scale for children—revised. New York: Psychological Corporation.   Google Scholar

Wellman, H. M., Miller, K. (1986). Thinking about nothing: Development of concepts of zero. British Journal of Developmental Psychology, 4, 31–42. DOI: 10.1111/j.2044-835X.1986.tb00995.x
Crossref   Google Scholar

Wilcox, R. R. (2012). Introduction to Robust Estimation & Hypothesis Testing. 3rd edition. Amsterdam, The Netherlands: Elsevier.
Crossref   Google Scholar