Learning or doing mathematics involves approximate quantification. The purpose of this research was to improve approximate number system acuity in primary school students with low achievement in mathematics. A quasi-experimental, pre-test, post-test design with a control group was utilized. Mathematics Achievement Test (MAT), Arithmetic Performance Test (APT), Number Line Estimation Test (NLE), and Raven Standard Progressive Matrices Test (RSPMT) have been conducted to identify the study groups. Initially, 302 students were surveyed with these tests. A total of 26 students scoring the lowest (bottom 25%) in all these tests, except RSPMT, have been included in the study. Students were randomly assigned to the experimental (13 students) and control groups (13 students). Experimental group played with Tablet-PC games designed to develop approximate number system, one of the components of number sense, in their free times in school. Control group, did not have any of these games but played nonmathematical games. Experimental group played with three games designed to develop number sense for two hours a week for a total of 6 hours. Analysis showed there was an increase in both of the estimation precision and mathematics achievement of the experimental group. The games played during the experimental process not only helped in teaching the spatial representation of magnitude but they also led to an improved mathematics achievement. The approximate number system sensitivity of experimental group continued to develop in retention period as measured by the 0-100 number line test. Despite an indication that number line estimation tasks have an impact on number sense and mathematics achievement, none of these results provided any evidence on being reflected on timed arithmetic performance. Activities targeting exact number system may be required for arithmetic performance. This hypothesis can be tested in future studies.

Keywords: Approximate number system, mathematics achievement, low achievers, number games, number sense


Başbay, A. (2008). Öğrenenlerin bireysel öğrenme görevleri ile zihinsel becerileri ve bilişsel faaliyet hızları arasındaki ilişki [Relationship between learners' individual learning tasks and their mental skills and decision making pace]. Education and Science, 33(149), 3-17.

Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333-339.

Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189-201. doi: 10.1037/0012-1649.41.6.189

Butterworth, B. (2005). The development of arithmetical abilities. J Child Psychol Psychiatry, 46(1), 3-18. doi: 10.1111/j.1469-7610.2004.00374.x

Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534-541. doi: 10.1016/j.tics.2010.09.007

Butterworth, B., & Laurillard, D. (2010). Low numeracy and dyscalculia: Identification and intervention. ZDM Mathematics Education, 42(6), 527-539. doi: 10.1007/s11858-010-0267-4

Büyüköztürk, Ş. (2010). Sosyal bilimler için veri analizi el kitabı [Data analysis handbook for social sciences] (11. ed.). Ankara: Pegem Akademi.

Büyüköztürk, Ş. (2014). Deneysel desenler [Experimental designs] (4. ed.). Ankara: Pegem Akademi.

Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2009). Bilimsel araştırma yöntemleri [Scientific research methods]. (4.ed.). Ankara: Pegem Akademi.

Can, A. (2014). SPSS ile bilimsel araştırma sürecinde nicel veri analizi [Quantitative data analysis in scientific research process with SPSS]. (3. Ed.). Ankara: Pegem Akademi.

Cohen, L., & Dehaene, S. (2000). Calculating without reading: Unsuspected residual abilities in pure alexia. Cognitive Neuropsychology, 17,563–583.

Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16(1), 16-36.

De Vos, T. (1992). Tempo-test rekenen (Number fact retrieval test). Nijmegen: Berkhout.

Feigenson, L., Dehaene, S. & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314. doi: 10.1016/j.tics.2004.05.002

Fidan, E. (2013). İlkokul öğrencileri için matematik dersi sayılar öğrenme alanında başarı testi geliştirilmesi [Developing achievement test in the field of learning math lesson numbers for elementary school students]. Unpublished Master's Thesis, Ankara University

Fischer, U., Moeller, K., Huber, S., Cress, U., & Nuerk, H. (2015). Full-body movement in numerical trainings: A pilot study with an interactive whiteboard. International Journal of Serious Games, 2(4), 23-35. DOI:

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. doi:10.3758/s13423-010-0031-3

Girelli, 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.2000.2564

Griffin, S., Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25-49). Cambridge, MA: MIT Press.

Halberda, J., Mazzocco, M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity predict maths achievement. Nature, 455, 665-668.

Hellgren, K., Halberda, J., Forsman, L., Aden, U., & Libertus, M. E. (2013). Compromised approximate number system acuity in extremely preterm school-aged children. Developmental Medicine and Child Neurology, 55, 1109–1114.

Heppner, P. P., Kivlighan, D. M. J., & Wampold, B. E. (1999). Research design in counseling (2. ed.). Belmont, CA: Wadsworth.

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: 10.1080/09515080802285354

Karasar, N. (2012). Bilimsel araştırma yöntemi [Scientific research method]. (24. Ed.). Ankara: Nobel Publishing.

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. Front Dev Psychol 4,1–13.

Kiili, K., Devlin, K., Perttula, T., Tuomi, P., & Lindstedt, A. (2015). Using video games to combine learning and assessment in mathematics education. International Journal of Serious Games, 2(4), 37-55.

Kiriş, N., & Karakaş, S. (2004). Predicting Level of attention deficit hyperactivity disorder (adhd) from tests of ıntelligence and other related neuropsychological devices. Journal of Clinical Psychiatry, 7(3), 139-152.

Kucian, K., & von Aster, M. (2015). Developmental dyscalculia. European Journal of Pediatrics, 174(1), 1–13. doi:10.1007/s00431-014-2455-7

Kullik, U. (2004). Computer-unterstützte rechen trainings programme, in Interventionen bei Lernstörungen, eds G. W. Lauth, M. Grünke, and J. C. Brunstein (Göttingen: Hogrefe), 329–337.

Kurt, M., Bekçi, B., & Karakaş, S. (2004). Postmenopozal dönemdeki estrojen replasman tedavisinin bilişsel süreçlere etkisi [The effect of estrogen replacement therapy on cognitive processes in postmenopausal period]. Turkish Journal of Clinical Psychiatry, 7(1), 5-16.

Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93(2), 99-125. doi: 10.1016/j.cognition.2003.11.004

Laski, E.V., & Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50(3), 853-864.

Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14, 1292–1300.

Lipton, J., & Spelke, E. (2003). Origins of number sense: Large-Number discrimination in human infants. Psychological Science, 14(5), 396-401.

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. doi: 10.1016/j.tine.2013.06.005

Link, T., Schwarz, E. J., Huber, S., Fischer, U., Nuerk, H. C., Cress, U., & Moeller, K. (2014). Mathe mit der Matte- Verkörperlichtes Training basisnumerischer Kompetenzen. Zeitschrift für Erziehungswissenschaft, 17, 257-277.

Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Dev, 82(4), 1224-1237. doi: 10.1111/j.1467-8624.2011.01608.x

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.

National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

Olkun, S. (2012). Sayı hissi: Nedir? Neden önemlidir? Nasıl gelişir? [Number sense: what is it, why is it important? how we develop it?] Eğitimci Öğretmen Dergisi, 10, 6

Olkun, S., Can, D., & Yeşilpınar, M. (2013). Hesaplama performansı testi: Geçerlilik ve güvenilirlik çalışması [Calculation Performance Test: A validity and reliability study]. Proceedings of the XII. National Classroom Teacher Education Symposium. Aydın: Adnan Menderes University, pp.89-92.  

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

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. (2016). Geometric aspect of number line estımations. Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany.

Olkun, 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/dajpn2015280105

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.2015.3287

Olkun, S. & Özdem, Ş. (2015). Kavramsal şipşak sayılama uygulamalarının hesaplama performansına etkisi [The effect of conceptual subitizing training on calculation performance]. Baskent University Journal of Education, 2(1), 1-9. Available [Online]:

Praet, M., & Desoete, A. (2014). Number line estimation from kindergarten to grade 2: a longitudinal study. Learning and Instruction, 33, 19-28.

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.

Raven, J., Raven, J. C., & Court, J. H. (2000). Standard progressive matrices. Oxford7 Psychology Press.

Reys, R. E., Reys, B., Emanuelsson, G., Johansson B., Mcintosh, A., & Yang, D. G. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61-70.

Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth-and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29, 225-237.

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. Cognition, 102(3), 361-395. doi: 10.1016/j.cognition.2006.01.005

Rubinsten, O., & Henik, A. (2005). Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology, 19, 641–648.

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.

Shalev, R. S. (2004). Developmental dyscalculia. Journal of Child Neurology, 19(10), 765-771.

Shalev, R.S., Manor, O., & Gross-Tsur, V. (2005). Developmental dyscalculia: a prospective six-year follow-up. Developmental Medicine and Child Neurology, 47, 121-125.

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. doi: 10.1037/a0014239

Siegler, R. S., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444.

Siegler, R. S. & Booth, J. L. (2005). Development of numerical estimation. In J. I. D. Campell (Ed.), Handbook of Mathematical Cognition. New York and Hove: Psychology Press.

Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11, 655–661.

Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Developmental science, 10(1), 89-96.

Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts math achievement in early childhood. Proceedings of the National Academy of Sciences, 110, 18116– 18120.

Yaman, H. (2014). Sınıf düzeylerine göre öğretmen adaylarının sayı duyusu performansları [Number sense performances of prospective teachers according to grade levels]. Kastamonu Education Journal, 23(2), 739-754.

Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic--evidence from brain imaging studies. Neurosci Biobehav Rev, 33(6), 909-925. doi: 10.1016/j.neubiorev.2009.03.005

Xue, F., & Spelke, E. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1-B11.

Whyte, J. C., & Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Developmental Psychology, 44, 588–596.

Wilson, A. J., & Dehaene, S. (2007). Number sense and developmental dyscalculia. In D. Coch, G. Dawson ve K. Fischer (Eds.), Human Behavior, Learning, and the Developing Brain: Atypical Development. New York: Guilford Press.

Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1), 20. doi:






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