Prvi koraki v razvoju presejalnega testa za merjenje občutka za števila pri mlajših osnovnošolcih
DOI:
https://doi.org/10.20419/2024.33.600Ključne besede:
občutek za števila, numerično procesiranje, simbolna in nesimbolna količina, merjenje, osnovnošolciPovzetek
Občutek za števila se nanaša na niz veščin numeričnega procesiranja, ki se razvije še pred vstopom v osnovno šolo in se nadalje razvija s starostjo in izkušnjami. Raziskave so potrdile pomembnost teh veščin za matematične dosežke učencev. Zgodnje odkrivanje učencev, ki imajo težave z numeričnim procesiranjem, omogoča zgodnje intervencije in je zato ključnega pomena za zmanjševanje primanjkljajev učencev na tem področju. Namen naše raziskave je bil razviti pripomoček tipa papir-svinčnik za merjenje veščine ocenjevanja in primerjave količin, zasnovan za skupinsko izvedbo v razredu, ki ga lahko uporabimo v prvih treh razredih osnovne šole kot hiter presejalni test za odkrivanje primanjkljajev v občutku za števila. Razvili smo tri naloge za merjenje nesimbolnega in simbolnega občutka za števila (test ocenjevanja na številskih daljicah, test primerjave površin, test primerjave števil); uporaba teh nalog je hitra in enostavna. Teste smo preizkusili na skupini 316 učencev prvih treh razredov slovenske osnovne šole. Rezultati so pokazali, da razviti testi predstavljajo dobro izhodišče za nadaljnji razvoj presejalnega testa.
Prenosi
Literatura
Andersson, U., & Östergren, R. (2012). Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities. Learning and Individual Differences, 22, 701–714. https://doi.org/10.1016/j.lindif.2012.05.004
Andrews, P., & Sayers, J. (2015). Foundational number sense: A framework for analysing early number-related teaching. In O. Helenius, A. Engström, T. Meaney, P. Nilsson, E. Norén, J. Sayers, & M. Österhom (Eds.), Developments of mathematics teaching: Design, scale, effects (pp. 17–26). SMDF.
Aunio, P., & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual differences, 20(5), 427–435. https://doi.org/10.1016/j.lindif.2010.06.003
Aunio, P., & Räsänen, P. (2016). Core numerical skills for learning mathematics in children aged five to eight years – A working model for educators. European Early Childhood Education Research Journal, 24(5), 684–704. https://doi.org/10.1080/1350293X.2014.996424
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(4), 699–713. https://doi.org/10.1037/0022-0663.96.4.699
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031. https://doi.org/10.1111/j.1467-8624.2008.01173.x
Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5, 400–405.
Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148. https://doi.org/10.1007/s10857-011-9173-0
Dehaene, S. (2011). The number sense: How the mind creates mathematics. Oxford University Press.
De Smedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278– 292. https://doi.org/10.1016/j.jecp.2010.09.003
De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48–55. https://doi.org/10.1016/j.tine.2013.06.001
De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103(4), 469– 479. https://doi.org/10.1016/j.jecp.2009.01.010
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(6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Fletcher, J. M., & Vaughn, S. (2009). Response to intervention: Preventing and remediating academic difficulties. Child Development Perspectives, 3(1), 30–37. https://doi.org/10.1111/j.1750-8606.2008.00072.x
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
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(3), 277–299. https://doi.org/10.1080/87565640801982361
Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. https://doi.org/10.1037/a0026218
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293–304. https://doi.org/10.1177/00222194050380040301
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433
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(5), 1457–1465. https://doi.org/10.1037/a0012682
Japelj Pavešić, B., & Cankar, G. (2018). Linking mathematics TIMSS achievement to national examination scores and school marks: Unexpected gender differences in Slovenia. Orbis Scholae, 12(2), 77–100. https://doi.org/10.14712/23363177.2018.294
Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39(2), 181–195. https://doi.org/10.1080/02796015.2010.12087772
Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867. https://doi.org/10.1037/a0014939
Kavkler, M. (2002). Kako otroci rešujejo osnovne matematične probleme [How children solve mathematical problems]. In N. Končnik Goršič & M. Kavkler (Eds.), Specifične učne težave otrok in mladostnikov (pp. 157–172). Svetovalni center za otroke, mladostnike in starše Ljubljana.
Kolkman, M. E., Kroesbergen, E. H., & Leseman, P. P. M. (2013). Early numerical development and the role of nonsymbolic and symbolic skills. Learning and Instruction, 25, 95–103. https://doi.org/10.1016/j.learninstruc.2012.12.001
Landerl, K. (2013). Development of numerical processing in children with typical and dyscalculic arithmetic skills—A longitudinal study. Frontiers in Psychology, 4, Article 459. https://doi.org/10.3389/fpsyg.2013.00459
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8–9-year-old students. Cognition, 93(2), 99– 125. https://doi.org/10.1016/j.cognition.2003.11.004
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. https://doi.org/10.1016/j.jecp.2009.03.006
Landerl, K., & Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology, 103(4), 546–565. https://doi.org/10.1016/j.jecp.2008.12.006
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(6), 1723– 1743. https://doi.org/10.1111/j.1467-8624.2007.01087.x
LeFevre, J.-A., Jimenez Lira, C., Sowinski, C., Cankaya, O., Kamawar, D., & Skwarchuk, S.-L. (2013). Charting the role of the number line in mathematical development. Frontiers in Psychology, 4, Article 641. https://doi.org/10.3389/fpsyg.2013.00641
Lourenco, S. F., & Bonny, J. W. (2017). Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children. Developmental Science, 20(4), Article e12418, 1–16. https://doi.org/10.1111/desc.12418
Lourenco, S. F., Bonny, J. W., Fernandez, E. P., & Rao, S. (2012). Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences, 109(46), 18737–18742. https://doi.org/10.1073/pnas.1207212109
Magajna, L., Kavkler, M., Čačinovič Vogrinčič, G., Pečjak, S., & Bregar Golobič, K. (2008). Učne težave v osnovni šoli: Koncept dela [Learning difficulties in primary school: Work concept]. Zavod republike Slovenije za šolstvo.
Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6(9), Article e23749. https://doi.org/10.1371/journal.pone.0023749
McGraw-Hill Education (n.d.). The Number Knowledge Test.
Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019. https://doi.org/10.1177/0956797613482944
Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Science, 14(12), 542–551. https://doi.org/10.1016/j.tics.2010.09.008
Praet, M., & Desoete, A. (2014). Number line estimation from kindergarten to grade 2: A longitudinal study. Learning and Instruction, 33, 19–28. https://doi.org/10.1016/j.learninstruc.2014.02.003
Rousselle, L., & Noël, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102, 361–395. https://doi.org/10.1016/j.cognition.2006.01.005
Sasanguie, D., De Smedt, B., Defever, E., & Reynvoet, B. (2012). Association between basic numerical abilities and mathematics achievement. British Journal of Developmental Psychology, 30(2), 344–357. https://doi.org/10.1111/j.2044-835X.2011.02048.x
Sasanguie, D., Göbel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number–space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418–431. https://doi.org/10.1016/j.jecp.2012.10.012
Schleepen, T. M. J., Van Mier, H. I., & De Smedt, B. (2016). The contribution of numerical magnitude comparison and phonological processing to individual differences in fourth graders’ multiplication fact ability. PloS ONE, 11(6), Article e0158335. https://doi.org/10.1371/journal.pone.0158335
Schneider, M., Merz, S., Stricker, J., De Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89(5), 1467–1484. https://doi.org/10.1111/cdev.13068
Siegler, R. S. (2016). Magnitude knowledge: The common core of numerical development. Developmental Science, 19(3), 341–361. https://doi.org/10.1111/desc.12395
Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444. https://doi.org/10.1111/j.1467-8624.2004.00684.x
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. https://doi.org/10.1111/1467-9280.02438
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1), Article 20. https://doi.org/10.1186/1744-9081-2-20
Xenidou-Dervou, I., Molenaar, D., Ansari, D., van der Schoot, M., & van Lieshout, E. C. D. M. (2017). Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement. Learning and Instruction, 50, 1–13. https://doi.org/10.1016/j.learninstruc.2016.11.001
Yang, D.-C., & Li, M. F. (2008). An investigation of 3rd-grade Taiwanese students’ performance in number sense. Educational Studies, 34(5), 443–455. https://doi.org/10.1080/03055690802288494
Yang, D.-C., & Lin, Y.-C. (2015). Assessing 10- to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test. Educational Research, 57(4), 368–388. https://doi.org/10.1080/00131881.2015.1085235
Prenosi
Objavljeno
Številka
Rubrika
Licenca
Avtorske pravice (c) 2024 Katja Depolli Steiner, Cirila Peklaj, Anja Podlesek

To delo je licencirano pod Creative Commons Priznanje avtorstva-Deljenje pod enakimi pogoji 4.0 mednarodno licenco.