Geometric Aspects of Number Line Estimations

Yıl 2019, , 37 - 46, 25.01.2019

Sinan Olkun Mehmet Hayri Sarı , Glenn Gordon Smith

https://doi.org/10.30786/jef.460279

Cited By: 2

Öz

Number lines are implicitly embedded in nature. Yet researchers
use them for measuring number sense as if they are processed purely through
numerical reasoning. We argue that number line estimation tasks are done both
by numerical and geometric reasoning. The purpose of this research was to
investigate the relationships among mathematics achievement, geometry
achievement, spatial skills, and number line estimations. A total of 142 fourth
graders were administered 5 different tests: 2 curriculum-based math
achievement tests, a spatial visualization test, a number line estimation test,
and the Raven Standard Progresive Matrices test. Results showed; estimation
accuracy of the relative magnitude of numbers on an empty number line has more
to do with geometry achievement and diagrammatic reasoning rather than with numerical
or arithmetic reasoning. It seems that number line estimation tasks may
constitute an interplay between number and shape. Therefore, we conclude that using
multiple external representations of numbers, such as spatial, symbolic, and
verbal could be useful in developing a more robust number sense.

Anahtar Kelimeler

Number line estimations, numerical reasoning, geometric reasoning, number sense

Kaynakça

• Ansari, D., Donlan, C., Thomas, M. S. C., Ewing, S. A., Peen, T., & Karmiloff-Smith, A. (2003). What makes counting count? Verbal and visuo-spatial contributions to typical and atypical number development. Journal of Experimental Child Psychology, 85(1), 50-62. doi:10.1016/s0022-0965(03)00026-2Antell, S. E., & Keating, D. P. (1983). Perceptions of numerical invariance in neonates. Child Development (54), 695-701. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Dev Psychol, 42(1), 189-201. doi:10.1037/0012-1649.41.6.189Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534-541. doi:10.1016/j.tics.2010.09.007Büyüköztürk, Ş., Çakmak, E.K., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F. (2008). Bilimsel araştırma yöntemleri. (4.Baskı) Ankara: Pegem A Yayıncılık.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(4), 190-206. Dehaene, S. (2009). Origins of mathematical intuitions. Annals of the New York Academy of Sciences, 1156(1), 232-259. doi:10.1111/j.1749-6632.2009.04469.xDehaene, S., Molko, N., Cohen, L., & Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14(2), 218-224. doi:10.1016/j.conb.2004.03.008Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314. doi:10.1016/j.tics.2004.05.002Fidan, E. (2013). İlkokul öğrencileri için matematik dersi sayılar öğrenme alanında başarı testi geliştirilmesi. (Yayımlanmamış Yüksek Lisans Tezi), Ankara Üniversitesi, Eğitim Bilimleri Enstitüsü. 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. doi:10.1080/87565640801982361Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. J Exp Child Psychol, 76(2), 104-122. doi:10.1006/jecp.2000.2564Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge. Developmental Psychology, 48(5), 1229-1241. Izard, V., Pica, P., Spelke, E., & Dehaene, S. (2008). Exact equality and successor function: two key concepts on the path towards understanding exact numbers. Philosophical Psychology, 21(4), 491-505. doi:10.1080/09515080802285354Laski, 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.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. Front Psychol, 4, 641. doi:10.3389/fpsyg.2013.00641Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: dissociable systems. Neuropsychologia, 41(14), 1942-1958. doi:10.1016/s0028-3932(03)00123-4Link, 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. doi:10.1016/j.tine.2013.06.005MEB. (2004). İlköğretim matematik dersi öğretim programı. Ankara: Milli Eğitim Basımevi.Olkun, S. (2003). Comparing computer versus concrete manipulatives. Jl. of Computers in Mathematics and Science Teaching, 22(1), 43-56. Olkun, S., Akkurt-Denizli, Z., Kozan, S., & Ayyıldız, N. (2013, 23-25 Mayıs 2013 ). İlkokul öğrencileri için matematik dersi geometri ve ölçme öğrenme alanlarında başarı testi geliştirilmesi. Paper presented at the XII. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumunda (USOS) Adnan Menderes Üniversitesi: Aydın.Olkun, S., Altun, A., & Göçer Şahin, S. (2015). Beyond subitizing: symbolic manipulations of numbers. International Journal of Learning, Teaching and Educational Research, 10(1), 93-103. Olkun, S., Altun, A., Göçer Şahin, S., & Akkurt Denizli, Z. (2015). Deficits in basic number competencies may cause low numeracy in primary school children. Education and Science, 40(177). doi:10.15390/eb.2015.3287Olkun, S., & Denizli, Z. A. (2015). Using basic number processing tasks in determining students with mathematics disorder risk. Dusunen Adam: The Journal of Psychiatry and Neurological Sciences, 47-57. doi:10.5350/dajpn2015280105Sasanguie, D., De Smedt, B., Defever, E., & Reynvoet, B. (2011). Association between basic numerical abilities and mathematics achievement. British Journal of Developmental Psychology, no-no. doi:10.1111/j.2044-835X.2011.02048.xSasanguie, D., Gobel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement? J Exp Child Psychol, 114(3), 418-431. doi:10.1016/j.jecp.2012.10.012Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372. doi:10.1037/a0013840Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Dev, 75(2), 428-444. doi:10.1111/j.1467-8624.2004.00684.xSiegler, R. S., & Booth, L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). New York: Psychology Press.Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10(1), 89-96. doi:10.1111/j.1467-7687.2007.00569.xVerdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education, 3(1), 7-13. doi:10.1016/j.tine.2014.02.005