Abstract
An understanding of linear measurement depends on principles that include standard unit size, iteration of units, numbering of a unit at its end, and partial units for measuring continuous length. Children may learn these principles at school, for example through experience with informal measurement, or they may learn them through use of measurement in society. This study compared the application of these principles by children aged 8 and 9 from the Philippines and New Zealand. These countries were selected because they have quite different curricula, societal influences and economies. Ninety-one children were interviewed individually on a common set of unusual tasks that were designed to tap underlying principles. Results showed many similarities and some differences between countries. Most tasks requiring visualisation and informal units were done more accurately by New Zealand children. Some tasks involving the use of a conventional ruler were done more accurately by Filipino children. These differences appear to be related to differences in curricula and possibly to differences in societal use of measurement. We suggest that these results, like those of other writers cited, demonstrate the need for extensive work on the underlying concepts in measurement through work on informal measurement and a careful transition between informal and formal measurement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bladen, E., Wildish, K., & Cox, J. A. (2000). The development of linear measurement in elementary school children: An empirical study.The Genetic Epistemologist, 28(3). Retrieved May 20, 2004, from http://www.piaget.org/GE/2000/GE-28-3.html.
Bragg, P., & Outhred, L. (2000). Students’ knowledge of length units: Do they know more about rules than rulers? In T. Nakahara & M. Koyama (Eds.),Proceedings of the 24th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 97–104). Hiroshima, Japan: PME.
Chamberlain, M., & Walker, M. (2001).Trends in Year 9 students’ mathematics and science achievement: Results from New Zealand’s participation in the repeat of the Third International Mathematics and Science Study. Wellington: Research Division, Ministry of Education.
Clements, D. H., Battista, M. T., Sarama, J., Swaminathan, S., & McMillan, S. (1997). Students’ development of length concepts in a Logo-based unit on geometric paths.Journal for Research in Mathematics Education, 28(1), 70–95.
Davydov, V. V. (1982). The psychological characteristics of the formation of elementary mathematical operations in children. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.),Addition and subtraction: A cognitive perspective (pp. 226–238). Hillsdale NJ: Erlbaum.
Gay, H., & Cole, M. (1967).The new mathematics and an old culture: A study of learning among the Kpelle of Liberia. New York: Holt Rinehart and Winston.
Hart, K. M. (1981). Measurement. In K. M. Hart, (Ed.),Children’s understanding of mathematics: 11–16 (pp. 9–22). Newcastle upon Tyne: John Murray.
Hart, K., Johnson, D. J., Brown, M., Dickson, L., & Clarkson, R. (1989).Children’s mathematical frameworks 8–13: A study of classroom teaching. Windsor, Berks: NFER-Nelson.
Irwin, K. C., & Ell, F. (2002). Visualising and the move from informal to formal linear measurement. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.),Mathematics education in the South Pacific.Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia (pp. 358–365). Sydney: MERGA.
Kamii, C., & Clark, F. B. (1997). Measurement of length: The need for a better approach to teaching.School Science and Mathematics, 97(3), 116–120.
Manila Bulletin. (2004, August 23). Retrieved August 30, 2004, from http://www.mb.com.ph/issues/2004/08/23/MTNN2004082316911.html
Millroy, W. L. (1992).An ethnographic study of the mathematical ideas of a group of carpenters. Reston, VA: National Council of Teachers of Mathematics.
Newcombe, R. G. (1998). Interval estimation for the difference between independent proportions: Comparison of eleven methods.Statistics in Medicine, 17, 873–890.
New Zealand Council for Educational Research [NZCER]. (2000).Assessment resource bank, mathematics [MS2087]. Retrieved May 11, 2001, from http://arb.nzcer.org.nz/nzcer3/maths/msrmnt/2000-099/ms2087.htm.
New Zealand Ministry of Education. (1992).Mathematics in the New Zealand curriculum. Wellington: Learning Media.
New Zealand Ministry of Education Numeracy Projects. (2003). Retrieved October 23, 2003, from http://www.nzmaths.co.nz/Numeracy/Index.htm.
New Zealand Official Yearbook on the Web. (n.d). Retrieved November 7, 2003, from http://www.stats.govt.nz/domino/external/PASfull/PASfull.nsf/0/4c2567ef0 0247c6acc25697a000442b0/Open Document.
Nunes, T., & Bryant, P. (1996).Children doing mathematics. Oxford: Blackwell Publishers.
Ortiz Munsayac, C. (1994).Book I measurements in metric: The SI units. Metro Manila: Tri-Copy Publishing House Co.
Philippine Department of Education. (2002).Handbook in elementary level (mathematics). The 2002 basic education curriculum. Pasig: Department of Education.
Piaget, J., & Inhelder, B., (1967).The child’s conception of space. New York: Norton.
Schliemann, A. D., & Carraher, D. W. (1992). Proportional reasoning in and out of school, In P. Light & G. Butterworth (Eds.),Context and cognition (pp. 47–73). London: Wheatsheaf.
Third International Mathematics and Science Study - Repeat (1999). Retrieved October 23, 2003, from http://timss.bc.edu/timss1999i/items.html.
Vistro-Yu, C. P. (2002). Filipino students’ achievement in mathematics: Results from TIMSS — Repeat.Matimyas Matematika, 25, 123–132.
Vistro-Yu, C. P. (2003).Children’s visualization skills and their understanding of concepts, necessary for linear measurement — Iterated units and fractional units. Unpublished report. Manila: Ateneo de Manila University.
Vuyk, R. (1981).Overview and critique of Piaget’s genetic epistemology 1965 – 1980. London: Academic Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Irwin, K.C., Ell, F.R. & Vistro-Yu, C.P. Understanding linear measurement: A comparison of filipino and new zealand children. Math Ed Res J 16, 3–24 (2004). https://doi.org/10.1007/BF03217393
Issue Date:
DOI: https://doi.org/10.1007/BF03217393