LukiMat ja Mavalka: Matemaattisten taitojen tuen tarpeen tunnistaminen esiopetuksessa
DOI:
https://doi.org/10.58955/jecer.130937Keywords:
assessment, LukiMat, mathematical skills, MavalkaAbstract
In Finland, there are only a few mathematical assessment tools suitable for pre-primary education. There is still very little research on their effectiveness and reliability. This study examined two of the most common pre-primary school mathematics assessment tools in Finland: the LukiMat pre-primary school mathematics - Identifying need of support and the Mathematical Skills Inventory (Mavalka) 2. The aim of the study was to find out what kind of mathematical skills children have at the beginning of the pre-primary school year, whether these assessment tools find the children whose mathematical skills are weak, that is below the 25th percentile, and what kind of math performance profiles low-performing children have. In addition, the study looked at the self-concept and interest in mathematics of pre-primary school children and their relationship with mathematical performance. Seventy-two pre-primary school-age children participated in the study. They were given the LukiMat and Mavalka assessments and a questionnaire measuring their self-concept and interest in mathematics at the beginning of the pre-primary school year. The correlation between LukiMat and Mavalka was found to be strong, with 15 (65.2%) of the same children found to have weak skills. The performance profile of each child in need of support was individual, highlighting the importance of assessing mathematical subskills to guide teaching and support. Regression analysis showed that self-concept and interest were not related to mathematical skills. The study showed that LukiMat and Mavalka are reliable assessment tools for assessing pre-primary school children's mathematical skills.
References
Ainley, M. & Hidi, S. (2014). Interest and enjoyment. Teoksessa R. Pekrun & L. Linnenbrink-Garcia (toim.), International handbook of emotions in education (s. 205–227). Routledge/Taylor & Francis Group.
Aunio, P. (2019). Early numeracy skills learning and learning difficulties—Evidence-based assessment and interventions. Teoksessa D. C. Geary, D. B. Berch & K. Mann Koepke (toim.), Cognitive foundations for improving mathematical learning (s. 195–214). Elsevier. https://doi.org/10.1016/B978-0-12-815952-1.00008-6
Aunio, P., Hautamäki, J. & Mononen, R. (2018). Matematiikan oppimisen ja oppimisvaikeuksien pedagoginen arviointi. Teoksessa J. Joutsenlahti, H. Silfverberg & P. Räsänen (toim.) Matematiikan opetus ja opettaminen (s. 240–256). Bookwell Oy.
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. & Nurmi, J.-E. (2006). Developmental dynamics between mathematical performance, task motivation, and teachers’ goals during the transition to primary school. British Journal of Educational Psychology, 76(1), 21–40. https://doi.org/10.1348/000709905X51608
Berner, V.-B., Seitz-Stein, K., Segerer, R., Oesterlen, E. & Niklas, F. (2022). ‘Good’ or ‘well calculated’? Effects of feedback on performance and self-concept of 5- to 7-year-old children in math. Educational Psychology, 42(3), 296–315. https://doi.org/10.1080/01443410.2021.2001790
Björn, P., Aro, M. & Koponen, T. (2015). Interventiovastemallien tarjoamat mahdollisuudet kolmiportaisen tuen kehittämiseen: esimerkkinä matematiikan oppimisen tuki. Oppimisen ja oppimisvaikeuksien erityislehti, 25(3), 10–25.
Brankaer, C., Ghesquière, P., & De Smedt, B. (2017). Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP test). Behavior Research Methods, 49(4), 1361–1373. https://doi.org/https://doi.org/10.3758/s13428-016-0792-3
Clements, D. H. & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach (3. painos). Routledge.
Dehaene, S. (1997/2011). Number sense. How the mind creates mathematics. Oxford University Press.
DePascale, M., Jaeggi, S. M. & Ramani, G. B. (2023). The influence of home environmental factors on kindergarten children’s addition strategy use. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.1027431
De Smedt, B. (2022). Individual differences in mathematical cognition: A Bert’s eye view. Current Opinion in Behavioral Sciences, 46, 101175. https://doi.org/10.1016/j.cobeha.2022.101175
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
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? Findings from a longitudinal study. British Journal of Educational Psychology, 82, 64–81. https://doi.org/10.1348/2044-8279.002002
Devine, A., Hill, F., Carey, E. & Szűcs, D. (2018). Cognitive and emotional math problems largely dissociate: Prevalence of developmental dyscalculia and mathematics anxiety. Journal of Educational Psychology, 110(3), 431–444. https://doi.org/10.1037/edu0000222
Doctoroff, G. L., Fisher, P. H., Burrows, B. M. & Edman, M. T. (2016). Preschool children’s interest, social–emotional skills, and emergent mathematics skills. Psychology in the Schools, 53(4), 390–403. https://doi.org/10.1002/pits.21912
Eccles, J. S. & Wang, M.-T. (2016). What motivates females and males to pursue careers in mathematics and science? International Journal of Behavioral Development, 40(2), 100–106. https://doi.org/10.1177/0165025415616201
Fisher, P. H., Dobbs-Oates, J., Doctoroff, G. L. & Arnold, D. H. (2012). Early math interest and the development of math skills. Journal of Educational Psychology, 104(3), 673–681. https://doi.org/10.1037/a0027756
Fuchs, D. & Fuchs, L. S. (2005). Responsiveness-to-intervention: A blueprint for practitioners, policymakers, and parents. Teaching Exceptional Children, 38(1), 57–61. https://doi.org/10.1177/004005990503800112
Geary, D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental and Behavioral Pediatrics, 32(3), 250–263. https://doi.org/10.1097/DBP.0b013e318209edef
Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science: A Journal of the American Psychological Society, 22(1), 23–27. https://doi.org/10.1177/0963721412469398
Gelman, R. & Gallistel, C. R. (1978). The child’s understanding of number. Harvard University Press.
Gunderson, E. A., Park, D., Maloney, E. A., Beilock, S. L. & Levine, S. C. (2018). Reciprocal relations among motivational frameworks, math anxiety, and math achievement in early elementary school. Journal of Cognition and Development, 19(1), 21–46. https://doi.org/https://doi.org/10.1080/15248372.2017.1421538
Hall, L., Lyme, C. & Tazzyman, S. (2016). Five degrees of happiness: Effective smiley face Likert scales for evaluating with children. IDC '16: Proceedings of the The 15th International Conference on Interaction Design and Children, 311–321, https://doi.org/10.1145/2930674.2930719
Hannula, M. S. & Holm, M. E. (2018). Oppilaan matematiikkakuva oppimistuloksena ja oppimisen taustatekijänä. Teoksessa J. Joutsenlahti, H. Silfverberg & P. Räsänen (toim.), Matematiikan opetus ja oppiminen (s. 132–154). Niilo Mäki Instituutti.
Hellstrand, H., Korhonen, J., Räsänen, P., Linnanmäki, K. & Aunio, P. (2020). Reliability and validity evidence of the early numeracy test for identifying children at risk for mathematical learning difficulties. International Journal of Educational Research, 102. https://doi.org/10.1016/j.ijer.2020.101580
Koponen, T., Aunola, K. & Nurmi, J.-E. (2019). Verbal counting skill predicts later math performance and difficulties in middle school. Contemporary Educational Psychology, 59, 101803. https://doi.org/10.1016/j.cedpsych.2019.101803
Koponen, T., Salminen, J., Aunio, P. & Polet, J. (2011). LukiMat—Oppimisen arviointi: Matematiikan tuen tarpeen tunnistamisen välineet esikouluun. Käyttäjän opas. LukiMat. http://www.lukimat.fi/lukimat-oppimisen-arviointi/materiaalit/tuen-tarpeen-tunnistaminen/esiopetus/matematiikka/kayttajan-opas/E-mat-kasikirja
Krajewski, K. & Schneider, W. (2009). 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(6), 513–526. https://doi.org/10.1016/j.learninstruc.2008.10.002
Lampinen, A., Ikäheimo, H. & Dräger, M. (2014). Mavalka: Matematiikan valmiuksien kartoitus. Opettajan ohje (2. painos). Opperi.
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
Latvala, J.-M., Koponen, T., Salmi, P. & Heikkilä, R. (2012). LukiMat-palvelu tukemassa lukemisen ja matematiikan taitojen oppimista ja oppimisen arviointia. NMI-Bulletin, 2, 36–53.
Lerkkanen, M.-K., Kiuru, N., Pakarinen, E., Viljaranta, J., Poikkeus, A.-M., Rasku-Puttonen, H., Siekkinen, M. & Nurmi, J.-E. (2012). The role of teaching practices in the development of children’s interest in reading and mathematics in kindergarten. Contemporary Educational Psychology, 37(4), 266–279. https://doi.org/10.1016/j.cedpsych.2011.03.004
Lopez-Pedersen, A., Mononen, R., Korhonen, J., Aunio, P. & Melby-Lervåg, M. (2021). Validation of an early numeracy screener for first graders. Scandinavian Journal of Educational Research, 65(3), 404–424. https://doi.org/10.1080/00313831.2019.1705901
Lê, M.-L. & Noël, M.-P. (2021). Preschoolers’ mastery of advanced counting: The best predictor of addition skills 2 years later. Journal of Experimental Child Psychology, 212, 105252. https://doi.org/10.1016/j.jecp.2021.105252
Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O. & Baumert, J. (2005). Academic self-concept, interest, grades and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76(2), 397–416. https://doi.org/10.1111/j.1467-8624.2005.00853.x
Mononen, R., Aunio, P., Hotulainen, R. & Ketonen, R. (2013). Matematiikan osaaminen ensimmäisen luokan alussa. NMI-bulletin, 23(4), 12–25.
Mononen, R., Aunio, P. & Leijo, S. (2021). Esiopetusikäisten lasten matemaattisten taitojen tukeminen ThinkMath -interventiolla. Oppimisen ja oppimisvaikeuksien erityislehti NMI-bulletin, 31(3), 43–63.
Niemivirta, M., Tapola, A., Tuominen, H., Korhonen, J. & Mononen, R. (2019). Competence perceptions, interest and value in mathematics (CIVM). Julkaisematon. Oslon yliopisto, Itä-Suomen yliopisto, Helsingin yliopisto ja Åbo Akademi.
Opetushallitus [OPH] (2014). Esiopetuksen opetussuunnitelman perusteet. https://www.oph.fi/sites/default/files/documents/esiopetuksen_opetussuunnitelman_perusteet_2014.pdf
Pekrun, R. & Linnenbrink-Garcia, L. (toim.) (2014). International handbook of emotions in education. Routledge, Taylor & Francis Group.
Perusopetuslaki (1998/628). Oikeusministeriö. https://www.finlex.fi/fi/laki/ajantasa/1998/19980628
Pollack, C., Wilmot, D., Centanni, T. M., Halverson, K., Frosch, I., D’Mello, A. M., Romeo, R. R., Imhof, A., Capella, J., Wade, K., Al Dahhan, N. Z., Gabrieli, J. D. E. & Christodoulou, J. A. (2021). Anxiety, motivation, and competence in mathematics and reading for children with and without learning difficulties. Frontiers in Psychology, 12. https://www.frontiersin.org/articles/10.3389/fpsyg.2021.704821
Primi, C., Donati, M. A., Izzo, V. A., Guardabassi, V., O’Connor, P. A., Tomasetto, C. & Morsanyi, K. (2020). The Early Elementary School Abbreviated Math Anxiety Scale (the EES-AMAS): A new adapted version of the AMAS to measure math anxiety in young children. Frontiers in Psychology, 11, 14. https://doi.org/https://doi.org/10.3389/fpsyg.2020.01014
Rawlings, A. M., Niemivirta, M., Korhonen, J., Lindskog, M., Tuominen, H. & Mononen, R. (2023). Achievement emotions and arithmetic fluency – Development and parallel processes during the early school years. Learning and Instruction, 86, 101776. https://doi.org/10.1016/j.learninstruc.2023.101776
Rusanen, E. & Räsänen, P. (2012). Matematiikassa heikosti suoriutuvien lasten laskustrategioiden kehitys. NMI bulletin, 22(3), 28–41.
Salminen, J., Khanolainen, D., Koponen, T., Torppa, M. & Lerkkanen, M.-K. (2021). Development of numeracy and literacy skills in early childhood—A longitudinal study on the roles of home environment and familial risk for reading and math difficulties. Frontiers in Education, 6. https://doi.org/10.3389/feduc.2021.725337
Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York, NY: Routledge.
Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J. & De Smedt, B. (2017). Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: A meta‐analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372
Sorvo, R., Koponen, T., Viholainen, H., Aro, T., Räikkönen, E., Peura, P., Tolvanen, A. & Aro, M. (2019). Development of math anxiety and its longitudinal relationships with arithmetic achievement among primary school children. Learning and Individual Differences, 69, 173–181. https://doi.org/10.1016/j.lindif.2018.12.005
Stensen, K. & Lydersen, S. (2022). Indre konsistens: fra alfa til omega? [Internal consistency: From alpha to omega?]. Tidsskrift for Den Norske Legeforening. https://doi.org/10.4045/tidsskr.22.0112
Terveyden ja hyvinvoinnin laitos (2011). ICD-10 tautiluokitus. Suomalainen 3. uudistettu painos Maailman terveysjärjestön (WHO) luokituksesta ICD-10. https://urn.fi/URN:NBN:fi-fe201205085423
Terveyden ja hyvinvoinnin laitos (2023). Kansallinen koodistopalvelin, v8.4.0. Haettu 11.30osoitteesta: https://koodistopalvelu.kanta.fi/codeserver/pages/classification-list-page.xhtml
The jamovi project (2022). Jamovi (Version 2.3). https://www.jamovi.org.
Träff, U., Skagerlund, K., Östergren, R. & Skagenholt, M. (2023). The importance of domain-specific number abilities and domain-general cognitive abilities for early arithmetic achievement and development. British Journal of Educational Psychology, 93(3), 825–841. https://doi.org/10.1111/bjep.12599
Tuominen, H., Niemivirta, M., Korhonen, J., Tapola, A. & Mononen, R. (2021). Matemaattisten taitojen ja motivaation profiilit ensimmäisen luokan oppilailla. Psykologia, 56(6), 548–566.
Vanbinst, K., Ceulemans, E., Ghesquière, P. & De Smedt, B. (2015). Profiles of children’s arithmetic fact development: A model-based clustering approach. Journal of Experimental Child Psychology, 133, 29–46. https://doi.org/10.1016/j.jecp.2015.01.003
Vanbinst, K., Ghesquière, P. & De Smedt, B. (2014). Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: A longitudinal study in children with persistent mathematical learning difficulties. Research in Developmental Disabilities, 35(11), 3001–3013. https://doi.org/10.1016/j.ridd.2014.06.023
Väisänen, E. (2017). Laskemisen sujuvuus osana matemaattisia taitoja: Sujuvuuden seuranta ja matemaattisten taitojen tukeminen alakoulussa [väitöskirja, Helsingin yliopisto]. HELDA, Helsingin yliopiston julkaisuarkisto. http://urn.fi/URN:ISBN:978-951-51-3814-9
Xu, C., LeFevre, J.-A., Skwarchuk, S.-L., Di Lonardo Burr, S., Lafay, A., Wylie, J., Osana, H. P., Douglas, H., Maloney, E. A. & Simms, V. (2021). Individual differences in the development of children’s arithmetic fluency from grades 2 to 3. Developmental Psychology, 57(7), 1067–1079. https://doi.org/10.1037/dev0001220