Number Line Estimations, Place Value Understanding and Mathematics Achievement

Year 2021, Issue: 19, 37 - 47, 25.01.2021

Mehmet Hayri Sarı , Sinan Olkun

https://doi.org/10.30786/jef.729843

Cited By: 7

Abstract

Current study investigated the relationships among mathematics achievement, place value understanding and number line estimations. We used a curriculum-based math achievement test (MAT, Mathematics Achievement Test), a place value test (PVT), and a mental number line estimation test (MNL) as the data collection tools. A total of 355 fourth graders participated in the study. They were recruited from schools located in middle-low socioeconomic areas of central Anatolia. Correlations were statistically significant among all these tests scores (MAT, PVT, MNL). The highest correlation was obtained between PVT and MAT scores. PVT have also stronger correlations with MNL (0-1000). The average scores of MAT and MNL tests were correlated inversely as expected. The correlations between mathematics achievement scores and MNL (0-1000) was highest. The three MNL tests alltogether have explained 40% of the variance in MAT. Similar to PVT, MNL (0-1000) alone accounted for 36% of the variance in MAT. Meanwhile, MNL (0-1000) (large numbers) contributed MAT more. PVT explained 70% of the variance in MAT. In all tests, PVT contributed more to MAT. Generally, boys did better in all MNL tests but only the result of MNL (0-1000) was significant favoring boys. We can conclude, based on these results that both approximate number acuity and place value understanding contribute to the general math achievement as well as each other. While the place value concept seems to be a representational tool that enhence the acuity of approximate numbers, the relative magnitudes of numbers support place value understanding conceptually.

Keywords

Number sense, mental number line, math achievement, place value

References

• Bicknell, B., & Young-Loveridge, J. (2015). Young children's number line placements and place-value understanding. Paper presented at the Annual Meeting of the Mathematics Education Research Group of Australasia (MERGA), Australia.
• Brannon, E. M., Jordan, K. E., & Jones, S. M. (2010). Behavioral signatures of numerical cognition. In M. L. Platt & A. A. Ghazanfar (Eds.), Primate neuroethology (pp. 144-159). Oxford: Oxford University Press.
• Burns, M., & Tank, B. (1988). A collection of math lessons from grades one through three. White Plains, NY: Math Solutions Publications.
• Büyüköztürk, Ş., Çakmak, E., Akgün, Ö., Karadeniz, Ş., & Demirel, F. (2008). Bilimsel araştırma yöntemleri (4. bs.) [Scientific research methods]. (4th ed.). Ankara: Pegem Akademi.
• Chu, F. W., vanMarle, K., & Geary, D. C. (2015). Early numerical foundations of young children's mathematical development. J Exp Child Psychol, 132, 205-212. doi:10.1016/j.jecp.2015.01.006
• Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42.
• Dehaene, S. (2008). Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation. In P. Haggard & Y. Rossetti (Eds.), Sensorimotor foundations of higher cognition (attention and performance) (Vol. 22, pp. 527-574). New York: Oxford UP.
• Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 320(5880), 1217-1220.
• Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72.
• Fidan, E. (2013). İlkokul öğrencileri için matematik dersi sayılar öğrenme alanında başarı testi geliştirilmesi. [Development of achievement tests in the number domain of mathematics course for elementary school students]. (Unpublished Master Thesis), Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü,
• Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1-2), 43-74.
• Gallistel, C. R., & Gelman, R. (2005). Mathematical cognition. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning. (pp. 559-588). New York, NY, US: Cambridge University Press.
• Huntley-Fenner, G., & Cannon, E. (2000). Preschoolers' magnitude comparisons are mediated by a preverbal analog mechanism. Psychological Science, 11(2), 147-152.
• Lambert, K., & Moeller, K. (2019). Place-value computation in children with mathematics difficulties. Journal of Experimental Child Psychology, 178, 214-225.
• Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256-261. doi:https://doi.org/10.1016/j.cognition.2011.07.009
• MacDonald, B. L., Westenskow, A., Moyer-Packenham, P. S., & Child, B. (2018). Components of place value understanding: Targeting mathematical difficulties when providing interventions. School Science and Mathematics, 118(1-2), 17-29. doi:10.1111/ssm.12258
• Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2009). Children’s early mental number line: Logarithmic or decomposed linear? Journal of Experimental Child Psychology, 103(4), 503-515. doi:https://doi.org/10.1016/j.jecp.2009.02.006
• Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. C. (2011). Early place-value understanding as a precursor for later arithmetic performance—A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837-1851. doi:https://doi.org/10.1016/j.ridd.2011.03.012
• Namkung, J. M., & Fuchs, L. S. (2016). Cognitive predictors of calculations and number line estimation with whole numbers and fractions among at-risk students. Journal of Educational Psychology, 108(2), 214-228. doi:10.1037/edu0000055
• Nataraj, M. S., & Thomas, M. O. (2007). Developing the concept of place value. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th Aannual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 523-532): MERGA Inc.
• Olkun, S., & Sarı, M. H. (2016). Geometric aspect of number line estimations. Paper presented at the 13th International Congress on Mathematical Education.
• Olkun, S., Mutlu, Y., & Sarı, M.H. (2017). The relationships between number sense and mathematics achievement. International Conference on Education and New Developments 2017, June 24-26, Lisbon, Portugal.
• Olkun, S., Sarı, M.H., & Smith G.G. (2019). Geometric aspects of number line estimations. Journal of Education and Future, 15, 37-46. Retrieved from http://dergipark.gov.tr/jef/issue/44124/460279
• Rouder, J. N., & Geary, D. C. (2014). Children's cognitive representation of the mathematical number line. Developmental Science, 17(4), 525-536.
• Sarı, M.H., & Olkun, S. (2018). The relationships among number line estimations, mathematics achievement and place value concept. An International Conference on Education, Technology and Science 2018, May 6-9, Belgrade, Serbia.
• Sarı, M.H., & Olkun, S. (2019). Relationship between place value understanding, arithmetic performance and mathematics achievement in general. Elementary Education Online, 18(2), 953-958, [Online]: http://ilkogretim-online.org.tr
• Sarı, M.H., & Aydoğdu, Ş. (2020). The effect of concrete and technology-assisted learning tools on place value concept, achievement in mathematics and arithmetic performance. International Journal of Curriculum and Instruction 12(1), 197–224
• Siegler, R. S., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444.
• Skagerlund, K. (2016). Magnitude processing in developmental dyscalculia: A heterogeneous learning disability with different cognitive profiles. LiU-Tryck, Linköping: Linköping Studies in Arts and Science No. 669.
• Spelke, E. & Kinzler, K. (2007). Core knowledge. Developmental Science 10(1), 89–96.
• van Marle, K., Chu, F. W., Li, Y., & Geary, D. C. (2014). Acuity of the approximate number system and preschoolers’ quantitative development. Developmental Science, 17(4), 492-505. doi:10.1111/desc.12143