Improving Low Mathematics Achievers’ Number Sense via Number Line Training with Board Games

Year 2024, , 41 - 56, 29.07.2024

Mehmet Hayri Sarı , Sinan Olkun

https://doi.org/10.30786/jef.1371037

Abstract

This study investigated the effect of a number line training via lineer board games with specific contents, namely numerical and figural, on students’ number line estimation skills, arithmetic performance, and mathematics achievement. A total of 30 first graders (15 in experimental and 15 in control group) participated in the study. There were 2 speech and language disorder (SLD) students, one in each, in the control and experimental groups. Number line training with a board game, Sahibingo® was implemented in the experimental group, while a non-numerical board game, Animalbingo, was used in the control group. Training lasted for 30 minutes a day, one day a week, and 4 weeks (2 hours in total). Results indicated that students, including the SLD, in the experimental group improved their number line estimation skills in 0-10 and 0-20 number range, but not in the 0-100 range. Improvements did not reflect in arithmetic performance and mathematics achievement scores. Although there are some improvements in small range number line estimations possibly because of the familiarity there is no improvement in the larger range and in terms of mathematics achievement scores, possibly because of the shorter period of training. It can be concluded that low mathematics achievers’ number sense can be improved via lineer board games with numerical content. Future research may investigate the effect of longer periods and may include other students with special needs.

Keywords

Number sense, Number line training, board games, mathematics achievement, low mathematics achievers

Ethical Statement

There is no economic, commercial, legal or professional conflict of interest with any institution, organization or person in this study.

Supporting Institution

yok

Project Number

yok

Thanks

yok

References

• Aragón-Mendizábal, E., Aguilar-Villagrán, M., Navarro-Guzmán, J. I., & Howell, R. (2017). Improving number sense in kindergarten children with low achievement in mathematics. Anales de Psicología/Annals of Psychology, 33(2), 311-318. https://doi.org/10.6018/analesps.33.2.239391
• Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3-18. https://doi.org/10.1111/j.1469-7610.2004.00374.x
• Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education (8th ed.). Routledge.
• Cohen, L., & Dehaene, S. (2000). Calculating without reading: Unsuspected residual abilities in pure alexia. Cognitive Neuropsychology, 17, 563–583.
• Coolen, I. E. J. I., Riggs, K. J., Bugler, M., & Castronovo, J. (2022). The approximate number system and mathematics achievement: it's complicated. A thorough investigation of different ANS measures and executive functions in mathematics achievement in children. Journal of Cognitive Psychology, 34(6), 796-818. https://doi.org/10.1080/20445911.2022.2044338
• Decarli, G., Zingaro, D., Surian, L., & Piazza, M. (2023). Number sense at 12 months predicts 4-year-olds’ maths skills. Developmental Science, 26(6), e13386. https://doi.org/https://doi.org/10.1111/desc.13386
• Dehaene, S. (1997). Number sense how the mind creates mathematics. London: Macmillan.
• Dehaene, S. (2009). Origins of mathematical intuitions. Annals of the New York Academy of Sciences, 1156(1), 232-259. https://doi.org/10.1111/j.1749-6632.2009.04469.x
• Ebersbach, M., Luwel, K., Frick, A., Onghena, P., & Verschaffel, L. (2008). The relationship between the shape of the mental number line and familiarity with numbers in 5-to 9-year old children: Evidence for a segmented linear model. Journal of Experimental Child Psychology, 99(1), 1-17. https://doi.org/10.1016/j.jecp.2007.08.006
• Ebersbach, M., Luwel, K., & Verschaffel, L. (2015). The relationship between children’s familiarity with numbers and their performance in bounded and unbounded number line estimations. Mathematical Thinking and Learning, 17(2-3), 136-154.
• Elofsson, J., Gustafson, S., Samuelsson, J., & Träff, U. (2016). Playing number board games supports 5-year-old children’s early mathematical development. The Journal of Mathematical Behavior, 43, 134-147. https://doi.org/https://doi.org/10.1016/j.jmathb.2016.07.003
• 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
• Fidan, E. (2013). İlkokul öğrencileri için matematik dersi sayılar öğrenme alanında başarı testi geliştirilmesi [Developing an achievement test for primary school students in the field of learning numbers in mathematics course] [Yayınlanmamış Yüksek Lisans Tezi], [Unpublished Master's Thesis], Ankara University, Institute of Educational Sciences, Ankara.
• Fischer, U., Moeller, K., Bientzle, M., Cress, U., & Nuerk, H.-C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177-183. https://doi.org/10.3758/s13423-010-0031-3
• Fischer, U., Moeller, K., Huber, S., Cress, U., & Nuerk, H.-C. (2015). Full-body movement in numerical trainings: A pilot study with an interactive whiteboard. International Journal of Serious Games, 2(4), 23-35. https://doi.org/10.17083/ijsg.v2i4.93
• Friso-Van Den Bos, I., Kroesbergen, E. H., & Van Luit, J. E. (2018). Counting and number line trainings in kindergarten: Effects on arithmetic performance and number sense. Frontiers in Psychology, 9, 975. https://doi.org/10.3389/fpsyg.2018.00975
• Gallagher-Mitchell, T., Simms, V., & Litchfield, D. (2018). Learning from where ‘eye’ remotely look or point: Impact on number line estimation error in adults. Quarterly Journal of Experimental Psychology, 71(7), 1526-1534. https://doi.org/10.1080/17470218.2017.1335335
• Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive internet-based sample. Proc. Natl Acad. Sci. USA, 109. https://doi.org/10.1073/pnas.1200196109
• Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement [Research Support, N.I.H., Extramural]. Nature, 455(7213), 665-668. https://doi.org/10.1038/nature07246
• Hellstrand, H., Korhonen, J., Linnanmäki, K., & Aunio, P. (2020). The Number Race–computer-assisted intervention for mathematically low-performing first graders. European Journal of Special Needs Education, 35(1), 85-99. https://doi.org/10.1080/13488678.2019.1615792
• Käser, T., Baschera, G.-M., Kohn, J., Kucian, K., Richtmann, V., Grond, U., Gross, M., & von Aster, M. (2013). Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition. Frontiers in Psychology, 4, 489. https://doi.org/10.3389/fpsyg.2013.00489
• Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Goebel, S., Grabner, R., Henik, A., Jordan, N. C., Karmiloff-Smith, A. D., Kucian, K., Rubinsten, O., Szucs, D., Shalev, R., & Nuerk, H.-C. (2013). Dyscalculia from a developmental and differential perspective [Opinion]. Frontiers in Psychology, 4. https://doi.org/10.3389/fpsyg.2013.00516
• Kohn, J., Rauscher, L., Kucian, K., Käser, T., Wyschkon, A., Esser, G., & von Aster, M. (2020). Efficacy of a computer-based learning program in children with developmental dyscalculia. What influences individual responsiveness? Frontiers in Psychology, 11, 1115. https://doi.org/10.3389/fpsyg.2020.01115
• Kucian, K., & von Aster, M. (2015). Developmental dyscalculia. European Journal of Pediatrics, 174(1), 1–13. https://doi.org/10.1007/s00431-014-2455-7
• Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schonmann, C., Plangger, F., Galli, M., Martin, E., & von Aster, M. (2011). Mental number line training in children with developmental dyscalculia [Research Support, Non-U.S. Gov't]. Neuroimage, 57(3), 782-795. https://doi.org/10.1016/j.neuroimage.2011.01.070
• Kullik, U. (2004). Computer-unterstützte rechen trainings programme. In G. W. Lauth, M. Grünke, & J. C. Brunstein (Eds.), Interventionen bei Lernstörungen (pp. 329-337). Hogrefe. https://doi.org/https://doi.org/10.1016/B978-0-12-801871-2.00009-5
• Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students [Research Support, Non-U.S. Gov't]. Cognition, 93(2), 99-125. https://doi.org/10.1016/j.cognition.2003.11.004
• 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.
• Laski, E. V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50(3), 853-864. https://doi.org/10.1037/a0034321
• 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, 641. https://doi.org/10.3389/fpsyg.2013.00641
• Libertus, M. E. (2019). Understanding the link between the approximate number system and math abilities. In D. C. Geary, D. B. Berch, & K. Mann Koepke (Eds.), Cognitive foundations for improving mathematical learning (Vol. 5, pp. 91-106). Academic Press. https://doi.org/https://doi.org/10.1016/B978-0-12-815952-1.00004-9
• Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292-1300.
• Link, T., Huber, S., Nuerk, H.-C., & Moeller, K. (2014). Unbounding the mental number line—new evidence on children's spatial representation of numbers [Original Research]. Frontiers in Psychology, 4, 1021. https://doi.org/10.3389/fpsyg.2013.01021
• Link, T., Moeller, K., Huber, S., Fischer, U., & Nuerk, H.-C. (2013). Walk the number line – An embodied training of numerical concepts. Trends in Neuroscience and Education, 2(2), 74-84. https://doi.org/10.1016/j.tine.2013.06.005
• Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia) [Research Support, N.I.H., Extramural]. Child Dev, 82(4), 1224-1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x
• Mera, C., Delgado, C., Aragón, E., Menacho, I., Canto, M. D. C., & Navarro, J. I. (2022). Contributions of the psychology of mathematical cognition in early childhood education using apps. Frontiers in Psychology, 13, 913970. https://doi.org/10.3389/fpsyg.2022.913970
• Moeller, K., Fischer, U., Nuerk, H.-C., & Cress, U. (2015). Computers in mathematics education – Training the mental number line. Computers in Human Behavior, 48, 597-607. https://doi.org/10.1016/j.chb.2015.01.048
• Muldoon, K., Towse, J., Simms, V., Perra, O., & Menzies, V. (2013). A longitudinal analysis of estimation, counting skills, and mathematical ability across the first school year. Developmental Psychology, 49(2), 250-257. https://doi.org/10.1037/a0028240
• Nelwan, M., Friso-van den Bos, I., Vissers, C., & Kroesbergen, E. (2022). The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties. Child Neuropsychology, 28(2), 143-170. https://doi.org/10.1080/09297049.2021.1959905
• Obersteiner, A., Reiss, K., & Ufer, S. (2013). How training on exact or approximate mental representations of number can enhance first-grade students’ basic number processing and arithmetic skills. Learning and Instruction, 23, 125-135. https://doi.org/10.1016/j.learninstruc.2012.08.004
• Obersteiner, A., & Tumpek, C. (2016). Measuring fraction comparison strategies with eye-tracking. ZDM Mathematics Education, 48, 255-266.
• Olkun, S., Can, D., & Yeşilpınar, M. (2013). Hesaplama performansı testi: Geçerlilik ve güvenilirlik çalışması [Computational performance testing: Validity and reliability study.], USOS 2013 Ulusal Sınıf Öğretmenliği Sempozyumu [USOS 2013 National Classroom Teaching Symposium], Aydın, Türkiye.
• Olkun, S., & Sarı, M. H. (2016, 24-31 July). Geometric aspect of number line estimations 13th International Congress on Mathematical Education, Hamburg, Germany.
• Passolunghi, M. C., Cargnelutti, E., & Pastore, M. (2014). The contribution of general cognitive abilities and approximate number system to early mathematics. Br. J. Educ. Psychol., 84. https://doi.org/10.1111/bjep.12054
• Ramani, G. B., Jaeggi, S. M., Daubert, E. N., & Buschkuehl, M. (2017). Domain-specific and domain-general training to improve kindergarten children’s mathematics. Journal of Numerical Cognition, 3(2), 468-495. https://doi.org/10.5964/jnc.v3i2.31
• Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low‐income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375-394. https://doi.org/10.1111/j.1467-8624.2007.01131.x
• Räsänen, P., Salminen, J., Wilson, A. J., Aunio, P., & Dehaene, S. (2009). Computer-assisted intervention for children with low numeracy skills. Cognitive Development, 24(4), 450-472. https://doi.org/10.1016/j.cogdev.2009.09.003
• Rousselle, L., & Noel, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing [Comparative Study Controlled Clinical Trial Research Support, Non-U.S. Gov't]. Cognition, 102(3), 361-395. https://doi.org/10.1016/j.cognition.2006.01.005
• Rubinsten, O., & Henik, A. (2005). Automatic activation of internal magnitudes: A study of developmental dyscalculia [Comparative Study]. Neuropsychology, 19(5), 641-648. https://doi.org/10.1037/0894-4105.19.5.641
• Sarı, M. H., & Olkun, S. (2020). Developing number sense in students with mathematics learning disability risk. International Online Journal of Primary Education, 9(2), 228-243.
• Sarı, M.H. & Olkun, S. (2023). Sayı hissini geliştirmek için tasarlanan oyunların çocukların sayı hissi performansı üzerindeki etkisi [The effect of games designed to develop number sense on children's number sense performance]. 1st International Congress on Math Learning Difficulties, 13-15 Ekim, Online, Türkiye.
• 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.
• Schindler, M., Schovenberg, V., & Schabmann, A. (2020). Enumeration processes of children with mathematical difficulties: An explorative eye-tracking study on subitizing, groupitizing, counting, and pattern recognition. Learning Disabilities: A Contemporary Journal, 18(2), 193-211.
• Shalev, R. S., Manor, O., & Gross-Tsur, V. (2005). Developmental dyscalculia: a prospective six-year follow up. Developmental Medicine & Child Neurology, (47), 121-125.
• Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children [Clinical Trial, Randomized Controlled Trial, Research Support, U.S. Gov't, Non-P.H.S. Research Support, U.S. Gov't, P.H.S.]. Child Dev, 75(2), 428-444. https://doi.org/10.1111/j.1467-8624.2004.00684.x
• Siegler, R. S., & Booth, L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). Psychology Press.
• Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low‐income children's numerical development. Developmental Science, 11(5), 655-661. https://doi.org/10.1111/j.1467-7687.2008.00714.x
• Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—but not circular ones—ımproves low-ıncome preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545-560. https://doi.org/10.1037/a0014239
• Skagerlund, K. & Träff, U. (2016). Number processing and heterogeneity of developmental dyscalculia: subtypes with different cognitive profiles and deficits. Journal of Learning Disa¬bilities, 46(1), 36–50. http://dx.doi.org/10.1177/0022219414522707
• Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10(1), 89-96. https://doi.org/10.1111/j.1467-7687.2007.00569.x
• Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences, 110(45), 18116-18120.
• Sullivan, J., & Barner, D. (2014). The development of structural analogy in number-line estimation. Journal of Experimental Child Psychology, 128, 171-189. https://doi.org/10.1016/j.jecp.2014.07.004
• Whyte, J. C., & Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Developmental Psychology, 44(2), 588.
• Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson, & K. Fischer (Eds.), Human behavior, learning, and the developing brain: Atypical development (pp. 212-237). Guilford Press.
• Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006). Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1), 19. https://doi.org/10.1186/1744-9081-2-19
• Wilson, A. J., Dehaene, S., Dubois, O. e., & Fayol, M. (2009). Effects of an adaptive game intervention on accessing number sense in low-socioeconomic-status kindergarten children. International Mind, Brain, and Education, 3(4), 224-234.
• Wynn, K. (1992a). Addition and subtraction by human infants. Nature, 358(27), 749-750.
• Wynn, K. (1992b). Children's acquisition of the number words and the counting system. Cognitive Psychology, 24, 220-251.
• Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88-101.
• Xue, F., & Spelke, E. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1-B11.
• Zax, A., Slusser, E., & Barth, H. (2019). Spontaneous partitioning and proportion estimation in children’s numerical judgments. Journal of Experimental Child Psychology, 185, 71-94.