Abstract
The concept of base-10 numeral system is fundamental to other mathematical concepts such as decimal numbers and exponents, and yet for a variety of reasons, including differences in number naming language, many children in the early years of school find the concept of place value difficult. Renowned mathematics educator Freudenthal (Mathematics as an educational task. Reidel, Dordrecht, Holland, 1973) was critical of the way that mathematical content knowledge is often simplistically identified as the learning of ready-made mathematical objects, leaving the evolution and refinement process of mathematics unattended. It seems, therefore, that children’s experience of the evolution and construction of the base-10 numeral system should gain a position in young children’s mathematical experiences. This chapter outlines a possible learning trajectory for children in the early years of school for this purpose, together with a brief elaboration of its theoretical underpinnings. The ultimate goal is to open up possibility for young children to connect to the evolution of the base-10 number system, and so deepen their understanding of the concept of place value.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Askew, M. (2012). Tasks. In M. Askew (Ed.), Transforming primary mathematics: Understanding classroom tasks, tools and talk (pp. 97–108). UK, Oxon: Routledge.
Camos, V. (2008). Low working memory capacity impedes both efficiency and learning of number transcoding in children. Journal Experimental Child Psychology, 99(1), 37–57.
Chan, B. M. Y., & Ho, C. S. H. (2010). The cognitive profile of Chinese children with mathematics difficulties. Journal of Experimental Child Psychology, 107(3), 260–279.
Chan, W. W. L., Au, T. K., & Tang, J. (2014). Strategic counting: A novel assessment of place-value understanding. Learning and Instruction, 29(1), 78–94.
Collet, M. (2003). Diagnostic assessment of the understanding of the base-ten-system. Paper presented at the symposium current issues in assessment of learning disabilities of The Congress of the European Federation of Psychologists Associations (EFPA). Vienna.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, Holland: Reidel.
Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht/Boston/London: Kluwer Academic Publishers.
Fung, C. I. (1999). Teaching for Mathematising: From the dream to the reality (in Chinese). In N.-Y. Wong & K.-M. Wong (Eds.), Proceedings of the Symposium on the Optimisation of Basic Mathematics Education (pp. 4–46). Hong Kong: Department of Curriculum and Instruction, Faculty of Education, Chinese University of Hong Kong.
Fung, C. I. (2004). Teaching for Mathematising: Theory, practice, and prospect (in Chinese). In K.-M. Tang, K.-L. Wong, M.-S. Lee & N.-C. Mok (Eds.), Proceedings of Hong Kong Mathematics Education Conference 2004 (pp. 78–88). Hong Kong: Hong Kong Association for Mathematics Education.
Fuson, K. C., & Briars, D. J. (1990). Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction. Journal for Research in Mathematics Education, 21(3), 180–206.
Geary, D. C. (2000). From infancy to adulthood: The development of numerical abilities. European Child & Adolescent Psychiatry, 9(Suppl. 2), II/11–II/16.
Han, Y., & Ginsburg, H. P. (2001). Chinese and English mathematics language: The relation between linguistic clarity and mathematics performance. Mathematical Thinking and Learning, 3(2&3), 201–220.
Haylock, D. (2011). Number and place value. In D. Haylock (Ed.), Mathematics explained for primary teachers (4th ed., pp. 65–82). The UK, London: Sage.
Haylock, D., & Cockburn, A. (2008). Understanding mathematics for young children: A guide for foundation stage and lower primary teachers (pp. 30–58). The UK, London: Sage.
Ho, C. S. H., & Cheng, F. S. F. (1997). Training in place-value concepts improves children’s addition skills. Contemporary Education Psychology, 22(4), 495–506.
Lawton, F., & Hansen, A. (2011). Numbers and the number system. In A. Hansen (Ed.), Children’s error in mathematics: Understanding common misconceptions in primary schools (2nd ed., pp. 20–46). The UK, Exeter: Learning Matters Ltd.
McGuire, P., & Kinzie, M. B. (2013). Analysis of place value instruction and development in pre-kindergarten mathematics. Early Childhood Education Journal, 41(5), 355–364.
Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. C. (2011). Early place-value understanding as a precursor for later arithmetic performance—A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851.
Munn, P. (2008). Children’s beliefs about counting. In I. Thompson (Ed.), Teaching and learning early number (2nd ed., pp. 19–33). The UK, Buckingham: Open University Press.
Ng, S. S. N., & Rao, N. (2010). Chinese number words, culture, and mathematics learning. Review of Educational Research, 80(2), 180–206.
Ross, S. H. (1989). Parts, wholes, and place value: A developmental view. The Arithmetic Teacher, 36(6), 47–51.
Ryan, J., & Williams, J. (2007). Developing number. In J. Ryan & J. Williams (Eds.), Children’s mathematics 4–15: Learning from errors and misconceptions (pp. 53–78). The UK, Maidenhead: Open University Press.
Sharma, M. C. (1993). Place value concept: How children learn it and how to teach it. Math Notebook, 10(1–2), 3–26.
Valeras, M., & Becker, J. (1997). Children’s development understanding of place value: Semiotic aspects. Cognition and Instruction, 15(2), 265–286.
Van Oers, B. (2014). The roots of mathematising in young children’s play. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 111–123). The Netherlands, Dordrecht: Springer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Lai, M.Y., Fung, C.I. (2018). A Possible Learning Trajectory for Young Children’s Experiences of the Evolution of the Base-10 Positional Numeral System. In: Kinnear, V., Lai, M., Muir, T. (eds) Forging Connections in Early Mathematics Teaching and Learning. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-10-7153-9_6
Download citation
DOI: https://doi.org/10.1007/978-981-10-7153-9_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-7151-5
Online ISBN: 978-981-10-7153-9
eBook Packages: EducationEducation (R0)