THE USE OF THE COUNTING BOARD IN KINDERGARTEN’S MATHEMATICS


Published: Oct 8, 2018
Keywords:
counting board enumeration conservation subitizing verbal problems decomposition of numbers parents kindergarten teachers
Χρυσάνθη Σκουμπουρδή (Chrysanthi Skoumpourdi)
Abstract

In small ages the children usually function with auxiliary means and representations in order to support the abstract mathematic concepts that are taught to them. One teaching aid that might be used towards this end is the counting board. Its use for calculations includes the handling this manipulative through the movement of beads, the visualization of its structure, but it can also lead to the abstractive thought through its picture that the user can maintain in his mind. In this paper we studied kindergartners (5 years) ability in mathematical activities with the use of the counting board and we examined through a questionnaire the relative views of their parents as well as of kindergarten teachers.

The mathematical activities that were given included (a) enumeration, (b) conservation, (c) subitizing and matching quantities; recognition of symbols (1-6), (d) simple addition and subtraction word problems as well as (e) construction of number partners.

It was found that the counting board helped kindergartner s correspond in such activities as also that this auxiliary mean was familiar so much in the parents of the children as in kindergarten teachers. Indeed, it was available and was used in most the children 's houses, but also in the kindergartens. The observation and recording of particularities of kindergartner s in the handling of counting board led to a proposal for designing of a more functional assembled counting board.

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Author Biography
Χρυσάνθη Σκουμπουρδή (Chrysanthi Skoumpourdi), University of the Aegean
Lecturer
References
Ball, R. (1960). A Short Account of the History of Mathematics (pp. 123-127). Dover Publications Ine NY.
Bartolini Bussi, G. M. & Boni, M. (2003). Instruments for Semiotic Mediation in Primary School Classrooms. For the Learning of Mathematics Vol. 23, No 2, 15-22.
Bunt, L.N.H., Jones, P.S., Bedient, J.D., (1976). The Historical Roots of Elementary Mathematics, (pp. 223-228). Englewood Cliffs: Prentice Hall.
Burton, D. (1997). The history of mathematics: an introduction (pp. 237-243). McGray-Hill, NY.
Cotter, Α. J. (2000). Using Language and Visualization to Teach Place Value. Teaching Children Mathematics, Vol. 7, No 2, 109-114.
Eves, H. (1983). Great moments in mathematics: before] 650 (pp. 135-147). The Mathematical Association of American.
Fauvel, J. & Maanen, J. van, (eds) (2000). History in Mathematics Education The ICMI Study (pp. 257-258, 343-345). Kluwer Academic Publishers.
Fischer, P. S. & Hartmann, C. (2005). Math through the Mind's Eye. Mathematics Teacher Vol. 99, No 4, 246-250.
Gravenmeijer, K. (2000). Ένας διδακτικο-θεωρητικός συλλογισμός σχετικά με τη χρή­ ση χειρισμών. Στο Streefland, L. (ed.) Ρεαλιστικά Μαθηματικά στην Πρωτοβάθμια Εκπαίδευση (σελ. 59-82) (Επιμέλεια μετάφρασης: Ε. Κολέζα). Leader Books.
Gravenmeijer, Κ., Cobb, P., Bowers, J. & Whitenack, J. (2000). Symbolizing, Modelling, and Instructional Design. In Cobb, P, Yackel, E. & McClain K. (ed.) Symbolizing and Communicating in Mathematics Classrooms Perspectives on Discourse, Tools, and Instructional Design (pp. 225-273). Lawrence Erlbaum.
Gravenmeijer, K. & Stephan, M. (2002). Emergent Models as an Instructional Design Heuristic. In Gravenmeijer, K., Lehrer, R., Oers, B. van and Verschaggel, L. (ed.) Symbolizing Modeling and Tool Use in Mathematics Education (pp. 145-169). Kluwer Academic Publishers Netherlands.
Heath, T. (1981). Λ History of Greek Mathematics Volume 1 From Thaïes to Euclid (pp. 46- 52). Dover Publications, Inc. NY.
Heath, T. (2003). A Manual of Greek Mathematics (pp. 24-27). Courier Dover Publications. Ifrah, G. (1981). Παγκόσμια Ιστορία των Αριθμών (σελ. 114-121). Σμυρνιωτάκης. Mankiewicz, R., (2002). Η ιστορία των μαθηματικών (σελ. 67-76). (Τίτλος πρωτοτύπου: The Story of Mathematics, μετάφραση Αεωνίδας Καρατζάς). Εκδόσεις Αλεξάνδρεια.
Menne, J. (2001). Jumping ahead: an innovative teaching program. In
Anghileri, J. (ed) Principles and Practices in Arithmetic Teaching (pp 95-106). Open University Press.
Pimm, D. (1995). Symbols and Meanings in School Mathematics (pp. 76-88). Routledge London.
Σκουμπουρδή, Χ. (προ δημοσίευση). Υλικό για τα μαθηματικά της πρώτης σχολικής ηλικίας. Τόμος ΕνΕΔιΜ.
Σκουμπουρδή, Χ. & Καλαβάσης, Φ. (2007). Σχεδιασμός ένταξης του παιχνιδιού στη μαθηματική εκπαίδευση για την προσχολική και πρώτη σχολική ηλικία. Στο Φ. Καλαβάσης και Α. Κοντάκος (επιμ.) Θέματα Εκπαιδευτικού Σχεδιασμού (σ.σ. 137-156) Ατραπός, Αθήνα.
Smith, Ε. D. (1958) History of Mathematics Volume II (pp. 156-194). Dover Publications, INC. NY.
Smith, D. & Mikami, Y. (2004). A History of Japanese Mathematics (pp. 18-46) Courire Dover Publications.
StruiJk, J. C. (1987). Συνοπτική Ιστορία των Μαθηματικών (σελ. 139-140). Δαίδαλος.
Swetz, F. (1994) (eds). From five fingers to infinity: a journey through the history of mathematics (359-363). Open Court, Chicago.
Szendrei, J. (1996), Concrete Materials in the Classroom. Bishop, J. A. (eds.), International Handbook of Mathematics Education (pp. 411-434). Kluwer, Academic Publishers, Netherlands.
Treffers, A. (2000). To Διδακτικό Υπόβαθρο ενός προγράμματος Μαθηματικών στο Δημοτικό Σχολείο. Στο Streefland, L. (ed.) Ρεαλιστικά Μαθηματικά στην Πρω­ τοβάθμια Εκπαίδευση (σελ. 18-58) (Επιμέλεια μετάφρασης: Ε. Κολέζα) Leader Books.
van den Heu vel-Panhuizen, M. (2003). The Didactical Use of Models in Realistic Mathematics Educationa: An Example from a Longitudinal Trajectory on Percentage. Educational Studies in Mathematics 54, pp 9-35.
Wilson, R. (2001). Stamping Through Mathematics (pp. 16-17, 28-29,76-77) Springer.