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Okul Öncesi Çocukların Uzunluk Modelleri Kullanılarak Sorulan Sorulara Verdikleri Cevapların İncelenmesi

Year 2025, Volume: 14 Issue: 2, 358 - 369

Özlem Doğan Temur , Nurdan Korkmaz , Serap Akbaba Dağ

Abstract

Bu çalışmanın amacı okul öncesi çocukların uzunluk modelleri kullanılarak yapılan etkinliklerde sorulan sorulara verdikleri cevapları incelemektir. Araştırma nitel araştırma yöntemlerinden temel nitel araştırma olarak desenlenmiştir. Bu amaçla araştırmacılardan birinin çalıştığı okul öncesi sınıfında 18 çocuk ile çalışma yapılmıştır. Araştırmada uzunluk modeli temelli sayılarda sıra, büyüklük, mesafe ve referans noktası gibi bileşenlere dair literatür taranarak ve alan uzmanlarının desteği ile etkinlik temelli on üç sorudan oluşan görüşme formu hazırlanmıştır. Formun son hâli her çocuğa etkinlik şeklinde bireysel olarak uygulanmıştır. Bunun için ahşap malzemeden oluşan bir uzunluk modeli aracı kullanılmıştır. Her görüşme ortalama on beş dakika kadar sürmüştür. Görüşmeler için araştırmacı kamera kaydı almış, sonrasında her kayıt metne dökülmüş ve analiz için hazır hâle getirilmiştir. Hazır veriler içerik analizi ile analiz edilmiştir. Sorulan sorular çerçevesinde sayı hissi bağlamında her birinde mesafe kavramının etkisi ile “yakın-uzak”, “arasında”, “ileri-geri” ana kavramlarıyla sayının büyüklüğü, anlamı, konumu bağlamında cevaplar incelendiğinde genel olarak bu yaş çocukların verilen sayıya yakın ve uzak sayıları belirleyebildikleri, cevaplarında başlangıç noktasını ve sıradaki sayıyı dikkate aldıkları, model üzerinde sayının konumunu belirlerken, sayılar arasındaki ilişkiye dikkat ettikleri; zorlandıkları durumlarda ise kullanılan araçların etkisiyle doğru cevaba ulaşabildikleri gözlemlenmiştir.Sayı çizgisi modelinde verilen bir noktadan “ileri-geri” mesafeyi tahmin etme sürecinde hatalı cevap veren bazı çocukların sonraki soruda mesafe artmasına rağmen uzunluk modelinin kullanımıyla doğru cevaba yöneldikleri dikkati çekmiştir.

Keywords

Okul öncesi matematik eğitimi sayı-mesafe ilişkisi

References

  • Balcı, A. (2009). Sosyal bilimlerde araştırma. Pegem Akademi.
  • 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
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş. & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Pegem Akademi.
  • Chan, J. Y. C., & Scalise, N. R. (2022). Numeracy skills mediate the relation between executive function and mathematics achievement in early childhood. Cognitive Development, 62, 101154. https://doi.org/10.1016/j.cogdev.2022.101154
  • Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches (1st ed.). London: SAGE Publications.
  • 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
  • Feldman, A., & Berger, A. (2022). Development of the mental number line representation of numbers 0–10 and its relationship to mental arithmetic. Brain sciences, 12(3), 335. https://doi.org/10.3390/brainsci12030335
  • Fisher, A. V., Hirsh-Pasek, K., Newcombe, N. S., & Golinkoff, R. M. (2013). Taking shape: Supporting preschoolers’ acquisition of geometric knowledge through guided play. Child Development, 84(6), 1872–1878. https://doi.org/10.1111/cdev.12091
  • Friso-van den Bos, I., Kroesbergen, E. H., Van Luit, J. E., Xenidou-Dervou, I., Jonkman, L. M., Van der Schoot, M., & Van Lieshout, E. C. D. M. (2015). Longitudinal development of number line estimation and mathematics performance in primary school children. Journal of Experimental Child Psychology, 134, 12–29. https://doi.org/10.1016/j.jecp.2015.02.002
  • Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all children. Phi Delta Kappan, 97(3), 63-68. https://doi.org/10.1177/0031721715614831
  • Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child development, 78(4), 1343-1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x
  • 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
  • Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The roles of representation in school mathematics, 2001, 1-23.4
  • Gunderson, E. A., & Hildebrand, L. (2021). Relations among spatial skills, number line estimation, and exact and approximate calculation in young children. Journal of Experimental Child Psychology, 212, 105251. https://doi.org/10.1016/j. jecp.2021.105251
  • 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
  • Hartmann, M., Mast, F. W., & Fischer, M. H. (2016). Counting is a spatial process: Evidence from eye movements. Psychological Research, 80, 399-409. https://doi.org/10.1007/s00426-015-0722-5
  • Hoffmann, D., Hornung, C., Martin, R., & Schiltz, C. (2013). Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds. Journal of experimental child psychology, 116(4), 775-791. https://doi.org/10.1016/j.jecp.2013.07.013
  • Hollingworth, A. (2006). Scene and position specificity in visual memory for objects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32(1), 58–69. https://doi:10.1037/0278-7393.32.1.58
  • Holyoak, K. J. (1978). Comparative judgments with numerical reference points. Cognitive Psychology, 10(2), 203-243. https://doi.org/10.1016/0010-0285(78)90014-2
  • Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). San Francisco, CA, USA: Jossey-Bass.
  • Mix, K. S. (2019). Why are spatial skill and mathematics related? Child Development Perspectives, 13(2), 121-126. https://doi.org/10.1111/cdep.12323
  • Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197-243. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
  • Mix, K. S., Levine, S. C., & Huttenlocher, J. (2002). Quantitative development in infancy and early childhood. New York: Oxford UniversityPress. https://global.oup.com/academic/product/quantitative-development-in-infancy-and-early-childhood 9780195123005
  • Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215 (5109), 1519-1520. https://doi.org/10.1038/2151519a0
  • Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29–43. https://www.aft.org/sites/default/files/periodicals/Newcombe.pdf
  • Pesenti, M., Thioux, M., Seron, X., & De Volder, A. (2000). Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: A PET study. Journal of Cognitive Neuroscience, 12, 461–479. https://doi.org/10.1162/089892900562273
  • 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
  • Saxe, G. B., Gearhart, M., Shaughnessy, M., Earnest, D., Cremer, S., Sitabkhan, Y., Platas, L., & Young, A. (2009). A methodological framework and empirical techniques for studying the travel of ideas in classroom communities. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge in classroom interaction (pp. 203–222). Routledge.
  • Saxe, G. B., Shaughnessy, M. M., Gearhart, M., & Haldar, L. C. (2013). Coordinating numeric and linear units: Elementary students’ strategies for locating whole numbers on the number line. Mathematical Thinking and Learning, 15(4), 235–258. https://doi.org/10.1080/10986065.2013.835579
  • Schreier, M. (2012). Qualitative content analysis in practice. Qualitative content analysis in practice, 1-280. 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., & 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
  • Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., Arthur M. Jacobs & Stern, E. (2008). A validation of eye movements as a measure of elementary school children's developing number sense. Cognitive Development, 23(3), 409-422. https://doi.org/10.1016/j.cogdev.2008.07.002
  • 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., Thompson, C. A., & Opfer, J. E. (2009). The logarithmic‐to‐linear shift: One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3(3), 143-150. https://doi.org/10.1111/j.1751-228X.2009.01064.x
  • Sprenger, P., & Benz, C. (2020). Children’s perception of structures when determining cardinality of sets—results of an eye-tracking study with 5-year-old children. ZDM, 52(4), 753-765. https://doi.org/10.1007/s11858-020-01137-x
  • Thompson, C. A., & Opfer, J. E. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development, 81(6), 1768-1786. https://doi.org/10.1111/j.1467-8624.2010.01509.x
  • Turconi, E., Jemel, B., Rossion, B., & Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research, 21(1), 22-38. https://doi.org/10.1016/j.cogbrainres.2004.05.003
  • Van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of learning disabilities, 39(6), 496-506. https://doi.org/10.1177/00222194060390060201
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık.

Examining Preschool Children's Answers to Number Questions on Length Models

Year 2025, Volume: 14 Issue: 2, 358 - 369

Özlem Doğan Temur , Nurdan Korkmaz , Serap Akbaba Dağ

Abstract

The aim of this study is to examine preschool children's answers to questions asked in activities using length models. The study was designed as basic qualitative research from qualitative research methods. For this purpose, the study was conducted with 18 students in the preschool class where one of the researchers worked. In the study, an interview form consisting of thirteen activity-based questions was prepared by reviewing the literature on components such as order, magnitude, distance and reference point in length model-based numbers and with the support of field experts. The final version of the form was applied to each student individually as an activity. For this purpose, a length modeling tool made of wood was used. Each interview lasted approximately fifteen minutes. The researcher took camera recordings for the interviews, then each recording was transcribed and made ready for analysis. The ready data were analyzed by content analysis. When the answers were analyzed in the context of number sense—based on the concepts of size, meaning, and location of numbers, as well as the ideas of near–far, between, forward, and backward—it was found that most children at this age could generally identify numbers that were close to or far from a given number. In their responses, they often considered the starting point and the next number. They also used the model to determine the position of numbers and noticed the distance and relationships between them. When they faced difficulties, the tools provided helped guide them toward the correct answer. It was noteworthy that some of the children who gave incorrect answers in the process of estimating the "forward and backward" distance from a point given in the number line model were directed to the correct answer with the use of the length model, although the distance increased in the next question.

Keywords

Preschool mathematics education number-distance relationship

References

  • Balcı, A. (2009). Sosyal bilimlerde araştırma. Pegem Akademi.
  • 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
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş. & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Pegem Akademi.
  • Chan, J. Y. C., & Scalise, N. R. (2022). Numeracy skills mediate the relation between executive function and mathematics achievement in early childhood. Cognitive Development, 62, 101154. https://doi.org/10.1016/j.cogdev.2022.101154
  • Creswell, J. W., & Poth, C. N. (2016). Qualitative inquiry and research design: Choosing among five approaches (1st ed.). London: SAGE Publications.
  • 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
  • Feldman, A., & Berger, A. (2022). Development of the mental number line representation of numbers 0–10 and its relationship to mental arithmetic. Brain sciences, 12(3), 335. https://doi.org/10.3390/brainsci12030335
  • Fisher, A. V., Hirsh-Pasek, K., Newcombe, N. S., & Golinkoff, R. M. (2013). Taking shape: Supporting preschoolers’ acquisition of geometric knowledge through guided play. Child Development, 84(6), 1872–1878. https://doi.org/10.1111/cdev.12091
  • Friso-van den Bos, I., Kroesbergen, E. H., Van Luit, J. E., Xenidou-Dervou, I., Jonkman, L. M., Van der Schoot, M., & Van Lieshout, E. C. D. M. (2015). Longitudinal development of number line estimation and mathematics performance in primary school children. Journal of Experimental Child Psychology, 134, 12–29. https://doi.org/10.1016/j.jecp.2015.02.002
  • Fuson, K. C., Clements, D. H., & Sarama, J. (2015). Making early math education work for all children. Phi Delta Kappan, 97(3), 63-68. https://doi.org/10.1177/0031721715614831
  • Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child development, 78(4), 1343-1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x
  • 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
  • Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The roles of representation in school mathematics, 2001, 1-23.4
  • Gunderson, E. A., & Hildebrand, L. (2021). Relations among spatial skills, number line estimation, and exact and approximate calculation in young children. Journal of Experimental Child Psychology, 212, 105251. https://doi.org/10.1016/j. jecp.2021.105251
  • 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
  • Hartmann, M., Mast, F. W., & Fischer, M. H. (2016). Counting is a spatial process: Evidence from eye movements. Psychological Research, 80, 399-409. https://doi.org/10.1007/s00426-015-0722-5
  • Hoffmann, D., Hornung, C., Martin, R., & Schiltz, C. (2013). Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds. Journal of experimental child psychology, 116(4), 775-791. https://doi.org/10.1016/j.jecp.2013.07.013
  • Hollingworth, A. (2006). Scene and position specificity in visual memory for objects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32(1), 58–69. https://doi:10.1037/0278-7393.32.1.58
  • Holyoak, K. J. (1978). Comparative judgments with numerical reference points. Cognitive Psychology, 10(2), 203-243. https://doi.org/10.1016/0010-0285(78)90014-2
  • Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). San Francisco, CA, USA: Jossey-Bass.
  • Mix, K. S. (2019). Why are spatial skill and mathematics related? Child Development Perspectives, 13(2), 121-126. https://doi.org/10.1111/cdep.12323
  • Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197-243. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
  • Mix, K. S., Levine, S. C., & Huttenlocher, J. (2002). Quantitative development in infancy and early childhood. New York: Oxford UniversityPress. https://global.oup.com/academic/product/quantitative-development-in-infancy-and-early-childhood 9780195123005
  • Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215 (5109), 1519-1520. https://doi.org/10.1038/2151519a0
  • Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29–43. https://www.aft.org/sites/default/files/periodicals/Newcombe.pdf
  • Pesenti, M., Thioux, M., Seron, X., & De Volder, A. (2000). Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: A PET study. Journal of Cognitive Neuroscience, 12, 461–479. https://doi.org/10.1162/089892900562273
  • 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
  • Saxe, G. B., Gearhart, M., Shaughnessy, M., Earnest, D., Cremer, S., Sitabkhan, Y., Platas, L., & Young, A. (2009). A methodological framework and empirical techniques for studying the travel of ideas in classroom communities. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge in classroom interaction (pp. 203–222). Routledge.
  • Saxe, G. B., Shaughnessy, M. M., Gearhart, M., & Haldar, L. C. (2013). Coordinating numeric and linear units: Elementary students’ strategies for locating whole numbers on the number line. Mathematical Thinking and Learning, 15(4), 235–258. https://doi.org/10.1080/10986065.2013.835579
  • Schreier, M. (2012). Qualitative content analysis in practice. Qualitative content analysis in practice, 1-280. 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., & 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
  • Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., Arthur M. Jacobs & Stern, E. (2008). A validation of eye movements as a measure of elementary school children's developing number sense. Cognitive Development, 23(3), 409-422. https://doi.org/10.1016/j.cogdev.2008.07.002
  • 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., Thompson, C. A., & Opfer, J. E. (2009). The logarithmic‐to‐linear shift: One learning sequence, many tasks, many time scales. Mind, Brain, and Education, 3(3), 143-150. https://doi.org/10.1111/j.1751-228X.2009.01064.x
  • Sprenger, P., & Benz, C. (2020). Children’s perception of structures when determining cardinality of sets—results of an eye-tracking study with 5-year-old children. ZDM, 52(4), 753-765. https://doi.org/10.1007/s11858-020-01137-x
  • Thompson, C. A., & Opfer, J. E. (2010). How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development, 81(6), 1768-1786. https://doi.org/10.1111/j.1467-8624.2010.01509.x
  • Turconi, E., Jemel, B., Rossion, B., & Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research, 21(1), 22-38. https://doi.org/10.1016/j.cogbrainres.2004.05.003
  • Van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of learning disabilities, 39(6), 496-506. https://doi.org/10.1177/00222194060390060201
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık.
There are 39 citations in total.

Details

Primary Language Turkish
Subjects Early Childhood Education, Mathematics Education
Journal Section Research Article
Authors

Özlem Doğan Temur 0000-0002-1877-0973

Nurdan Korkmaz 0000-0001-9501-6942

Serap Akbaba Dağ 0000-0003-2188-563X

Early Pub Date June 19, 2025
Publication Date
Submission Date March 20, 2024
Acceptance Date May 23, 2025
Published in Issue Year 2025Volume: 14 Issue: 2

Cite

APA Temur, Ö. D., Korkmaz, N., & Akbaba Dağ, S. (2025). Okul Öncesi Çocukların Uzunluk Modelleri Kullanılarak Sorulan Sorulara Verdikleri Cevapların İncelenmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 14(2), 358-369. https://doi.org/10.30703/cije.1456289

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