Different Types of Subitizing Activity: A Teaching Experiment with Preconservers

Arp, S., & Fagard, J. (2005). What impairs subitizing in Cerebal Palsied children? Wiley Periodicals, Inc., 47, 89-102. https://doi.org/10.1002/dev.-20069 Search in Google Scholar

Beckwith, M., & Restle, F. (1966). Process of enumeration. Psychological Review, 73(5), 437.10.1037/h0023650 Search in Google Scholar

Brownell, W. A. (1928). The Development of Children’s Number Ideas in the Primary Grades. Chicago: University of Chicago. Search in Google Scholar

Carper, D. V. (1942). Seeing numbers as groups in primary-grade arithmetic. The Elementary School Journal, 43, 166-170.10.1086/458144 Search in Google Scholar

Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5, 400-405.10.5951/TCM.5.7.0400 Search in Google Scholar

Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38(2), 136-163.10.2307/748360 Search in Google Scholar

Clements, D. H., & Sarama, J. A. (2009). Learning and teaching early math. New York: Routledge.10.4324/9780203883389 Search in Google Scholar

Clements, D. H., & Sarama, J. (2017/2019). Learning and teaching with learning trajectories. Retrieved from www.LearningTrajectories.org10.4324/9781003083528 Search in Google Scholar

Clements, D. H., Sarama, J., & MacDonald, B. L. (2019). Subitizing: The neglected quantifier. In A. Norton, & M. W. Alibali (Eds.), Constructing Number. https://doi.org/10.1007/978-3-030-00491-0_210.1007/978-3-030-00491-0_2 Search in Google Scholar

Cobb, P., & Steffe, L. P. (2011).The constructivist researcher as teacher and model builder. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education: Insights from the work of Paul Cobb (pp. 19-32). NY: Springer Science+Business Media. Search in Google Scholar

Demeyere, N., Rotshtein, P., & Humphreys, G. W. (2012). The neuroanatomy of visual enumeration: Differentiating necessary neural correlates for subitizing versus counting in a neuropsychological voxel-based morphometry study. Journal of Cognitive Neuroscience, 24(4), 948-964.10.1162/jocn_a_00188 Search in Google Scholar

Deringöl, Y. (2019). Parents’expectation of mathematics education and their engagement in education and homework habits of children. Acta Educationis Generalis, 9(3), 16-40. https://doi.org/10.2478/atd-2019-001210.2478/atd-2019-0012 Search in Google Scholar

Douglass, H. R. (1925). The development of number concept in children of preschool and kindergarten ages. Journal of Experimental Psychology, 8, 443-470.10.1037/h0065267 Search in Google Scholar

Fitzhugh, J. I. (1978). The role of subitizing and counting in the development of the young children’s conception of small numbers. Dissertation Abstracts International, 40, 4521B-4522B. Search in Google Scholar

Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press. Search in Google Scholar

Klahr, D., & Wallace, J. G. (1976). Cognitive Development: An Information-Processing View. Mahwah, NJ: Erlbaum. Search in Google Scholar

Leibovich, T., Kadhim, S. A. R., & Ansari, D. (2017). Beyond comparison: The influence of physical size on number estimation is modulated by notation, range and spatial arrangement. Acta Psychologica, 175, 33-41.10.1016/j.actpsy.2017.02.004 Search in Google Scholar

Logan, G. D., & Zbrodoff, N. J. (2003). Subitizing and similarity: Toward a pattern-matching theory of enumeration. Psychonomic Bulletin & Review, 10(3), 676-682.10.3758/BF03196531 Search in Google Scholar

MacDonald, B. L. (2013). Subitizing Activity: Item Orientation with Regard to Number Abstraction (Unpublished Doctoral dissertation). Virginia: Virginia Polytechnic Institute and State University. Search in Google Scholar

MacDonald, B. L. (2015). Ben’s perception of space and subitizing activity: A constructivist teaching experiment. Mathematics Education Research Journal, 27(4), 563-584. https://doi.org/10.1007/s13394-015-0152-010.1007/s13394-015-0152-0 Search in Google Scholar

MacDonald, B. L., & Shumway, J. F. (2016). Subitizing games: Assessing preschool children’s number understanding. Teaching Children Mathematics, 22(6), 340-348.10.5951/teacchilmath.22.6.0340 Search in Google Scholar

MacDonald, B. L., & Wilkins, J. L. M. (2016). Seven types of subitizing activity characterizing young children’s mental activity. In S. Marx (Ed.), Qualitative research in STEM (pp. 256-286). New York, NY: Routledge. Search in Google Scholar

MacDonald, B. L., & Wilkins, J. L. M. (2019). Subitising activity relative to units construction: A case study. Research in Mathematics Education, 21(1), 77-95.10.1080/14794802.2019.1579667 Search in Google Scholar

Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 3(1), 1-22. Search in Google Scholar

Piaget, J. (1965). The Child’s Conception of Number. New York, NY: W.W. Norton & Company, Inc. Search in Google Scholar

Piaget, J. (1970). Genetic Epistemology. New York, NY: Columbia University Press.10.7312/piag91272 Search in Google Scholar

Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435.10.1016/j.jmathb.2003.09.002 Search in Google Scholar

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.10.4324/9780203883785 Search in Google Scholar

Siegler, R. S. (2007). Cognitive variability. Developmental Science, 10(1), 104-109.10.1111/j.1467-7687.2007.00571.x Search in Google Scholar

Starkey, G. S., & McCandliss, B. D. (2014). The emergence of “groupitizing” in children’s numerical cognition. Journal of Experimental Child Psychology, 126, 120-137. https://doi.org/10.1016/j.jecp.2014.03.00610.1016/j.jecp.2014.03.006 Search in Google Scholar

Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. Von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 171-194). Netherlands: Kluwer Academic Publishers. Search in Google Scholar

Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 267-306). Mahwah, NJ: Lawerence Erlbaum Assoc. Search in Google Scholar

von Glasersfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. NY: Taylor & Francis Group. Search in Google Scholar

Whelley, M. M. (2002). Subitizing and the Development of Children’s Number Knowledge (Doctoral dissertation). Retrieved from ProQuest dissertations and theses (3037768). Search in Google Scholar