Developing measurement concepts within context: Children’s representations of length
 Amy MacDonald,
 Tom Lowrie
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This article presents data gathered from an investigation which focused on the experiences children have with measurement in the early years of schooling. The focus of this article is children’s understandings of length at this early stage. 32 children aged 4–6 years at an Australian primary school were asked to draw a ruler and describe their drawing, once in February at the beginning of school, and again in November towards the end of their first year of school. The drawings and their accompanying descriptions are classified within a matrix which, informed by Bronfenbrenner’s ecological theory and literature regarding the development of length concepts, considers conceptual understanding and contextual richness. The responses revealed that children have a good understanding of length at the start of school, but that as their ability to contextualise develops so too does their conceptual understanding. This article suggests that participation in tasks such as these allows children to create their own understandings of length in meaningful ways. Additionally, the task and its matrix of analysis provide an assessment strategy for identifying children’s understandings about length and the contexts in which these understandings develop.
Inside
Within this Article
 Literature context
 Method
 Results
 Discussion and implications
 References
 References
Other actions
 Aldridge, S., & White, A. (2002). What’s the time, Ms White? Australian Primary Mathematics Classroom, 7(2), 7–12.
 Boaler, J. (1993). The role of contexts in the mathematics classroom: do they make mathematics more “real”? For the Learning of Mathematics, 13(2), 12–17.
 Bobis, J., Mulligan, J., & Lowrie, T. (2009). Mathematics for children: Challenging children to think mathematically (3rd ed.). Frenchs Forest: Pearson Education Australia.
 BoultonLewis, G. (1987). Recent cognitive theories applied to sequential length measuring knowledge in young children. British Journal of Educational Psychology, 57, 330–342. CrossRef
 BoultonLewis, G. M., Wilss, L. A., & Mutch, S. L. (1996). An analysis of young children’s strategies and use of devices of length measurement. Journal of Mathematical Behavior, 15, 329–347. CrossRef
 Bronfenbrenner, U. (1974). Developmental research, public policy, and the ecology of childhood. Child Development, 45, 1–5. CrossRef
 Bronfenbrenner, U. (1979). The ecology of human development: Experiments by nature and design. Cambridge: Harvard University Press.
 Bronfenbrenner, U. (1988). Interacting systems in human development. Research paradigms: Present and future. In N. Bolger, A. Caspi, G. Downey, & M. Moorehouse (Eds.), Persons in context: Developmental processes (pp. 25–49). Cambridge: Cambridge University Press.
 Bronfenbrenner, U. (2005). Interacting systems in human development: Research paradigms: Present and future. In U. Bronfenbrenner (Ed.), Making human beings human: Bioecological perspectives on human development (pp. 67–93). Thousand Oaks: SAGE.
 Carraher, D. W., & Schliemann, A. D. (2002). Is everyday mathematics truly relevant to mathematics education? In J. Moshkovich & M. Brenner (Eds.), Everyday and academic mathematics in the classroom: Monographs of the Journal for Research in Mathematics Education, 11, 238–283.
 Chinnappan, M. (2008). Productive pedagogies and deep mathematical learning in a globalised world. In P. Kell, W. Vialle, D. Konza, & G. Vogl (Eds.), Learning and the learner: Exploring learning for new times (pp. 181–193). Wollongong: University of Wollongong.
 Civil, M. (2002). Culture and mathematics: a community approach. Journal of Intercultural Studies, 23(2), 133–148. CrossRef
 Clarke, D. (1998a). Children’s understanding of the clock in the digital age. Primary Educator, 4(3), 9–12.
 Clarke, D. (1998b). Making a difference: Challenging and enthusing children for mathematics in the early years. In Keys to life. Conference proceedings of Sharing the Journey: Early years of schooling conference. (pp. 1–5). Melbourne: Department of Education. Retrieved November 26, 2008, from: http://www.sofweb.vic.edu.au/eys/pdf/proc98.pdf
 Clements, D. (1999). Teaching length measurement: research challenges. School Science and Mathematics, 99(1), 5–11. CrossRef
 Clements, D. H., & Sarama, J. (2000). The earliest geometry. Teaching Children Mathematics, 7(2), 82–86.
 Clements, D. H., & Stephan, M. (2004). Measurement in preK to grade 2 mathematics. In D. H. Clements, J. Sarama, & A. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 299–320). Mahwah: Lawrence Erlbaum Associates, Inc.
 Ginsburg, H. P., Inoue, N., & Seo, K. H. (1999). Young children doing mathematics: Observations of everyday activities. In J. V. Copley (Ed.), Mathematics in the early years (pp. 88–99). Reston: National Council of Teachers of Mathematics.
 Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 397–430). Mahwah: Lawrence Erlbaum Associates, Inc.
 Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12(3), 197–211. CrossRef
 Hughes, M., Desforges, C., & Mitchell, C. (2000). Numeracy and beyond: Applying mathematics in the primary school. Buckingham: Open University Press.
 Kamii, C., & Clark, F. (1997). Measurement of length: the need for a better approach to teaching. School Science and Mathematics, 97(3), 116–121. CrossRef
 Kendrick, M., & McKay, R. (2004). Drawings as an alternative way of understanding young children’s constructions of literacy. Journal of Early Childhood Literacy, 4(1), 109–128. CrossRef
 Lowrie, T. (2004a). Problem solving in outofschool settings: Children “playing” in ICT contexts. In G. Jones & S. Peters (Eds.), New development and trends in mathematics education at preschool and primary level. Refereed proceedings of the Early Childhood Topic Study Group (TSG, 1) of the International Congress of Mathematics Education, Copenhagen, Denmark. Available online from http://www.icme10.dk/
 Lowrie, T. (2004b). Making mathematics meaningful, realistic and personalised: Changing the direction of relevance and applicability. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.), Proceedings of the 41st annual Mathematics Association of Victoria (MAV) conference (pp. 301–315). Brunswick: MAV.
 Masingila, J. O., & de Silva, R. (2001). Teaching and learning school mathematics by building on students’ outofschool mathematics practice. In B. Atweh, H. Forgaz, & B. Nebres (Eds.), Sociocultural research on mathematics education: An international perspective (pp. 329–344). Mahwah: Lawrence Erlbaum Associates, Inc.
 Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.
 Nunes, T., & Bryant, P. (1996). Children doing mathematics. Oxford: Blackwell Publishers Ltd.
 Nunes, T., Light, P., & Mason, J. (1995). Measurement as a social process. Cognition and Instruction, 13(4), 585–587. CrossRef
 Perry, B., & Dockett, S. (2005). “I know that you don’t have to work hard”: Mathematics learning in the first year of primary school. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education (PME), 4 (pp. 65–72). Melbourne: PME.
 Piaget, J. (1999). The stages of the intellectual development of the child. In A. Slater & D. Muir (Eds.), The Blackwell reader in developmental psychology (pp. 35–42). Maiden: Blackwell Publishing Ltd.
 Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. London: Routledge and Kegan Paul.
 Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2007). Helping children learn mathematics (8th ed.). Hoboken: John Wiley & Sons, Inc.
 Schoenfeld, A. (1989). Problem solving in context(s). In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 82–92). Hillside: Lawrence Erlbaum Associates.
 Smith, T., & MacDonald, A. (2009). Time for talk: the drawingtelling process. Australian Primary Mathematics Classroom, 14(3), 21–26.
 Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 3–16). Reston: National Council of Teachers of Mathematics.
 Stephens, M., & Sullivan, P. (1997). Developing tasks to assess mathematical performance. In F. Biddulph & K. Carr (Eds.), People in mathematics education: Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia (MERGA) (pp. 470–477). Rotorua: MERGA.
 Sullivan, P., & Lilburn, P. (1997). Openended maths activities: Using “good” questions to enhance learning. Melbourne: Oxford University Press.
 Sullivan, P., Mousley, J., & Zevenbergen, R. (2005). Increasing access to mathematical thinking. Gazette, 32(2), 105–109.
 Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.
 Woleck, K. R. (2001). Listen to their pictures: An investigation of children’s mathematical drawings. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (pp. 215–227). Reston: National Council of Teachers of Mathematics.
 Wright, S. (2003). Ways of knowing in the arts. In S. Wright (Ed.), Children, meaningmaking and the arts (pp. 1–33). Frenchs Forest: Pearson Education Australia.
 Wright, S. (2006). Children’s multimodal meaning making: Giving voice to children through drawing and storytelling. In W. D. BokhorstHeng, M. D. Osborne, & K. Lee (Eds.), Redesigning pedagogy: Reflections of theory and praxis (pp. 175–190). Rotterdam: Sense Publishers.
 Wright, S. (2007). Young children’s meaningmaking through drawing and ‘telling’: analogies to filmic textual features. Australian Journal of Early Childhood, 32(4), 37–48.
 Zevenbergen, R., Dole, S., & Wright, R. J. (2004). Teaching mathematics in primary schools. Crows Nest: Allen & Unwin.
 Title
 Developing measurement concepts within context: Children’s representations of length
 Journal

Mathematics Education Research Journal
Volume 23, Issue 1 , pp 2742
 Cover Date
 20110301
 DOI
 10.1007/s1339401100027
 Print ISSN
 10332170
 Online ISSN
 2211050X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Young children
 Measurement
 Representations
 Context
 Authors

 Amy MacDonald ^{(1)}
 Tom Lowrie ^{(2)}
 Author Affiliations

 1. Research Institute for Professional Practice, Learning and Education (RIPPLE), Charles Sturt University, P.O. Box 789, Albury, NSW, 2640, Australia
 2. Research Institute for Professional Practice, Learning and Education (RIPPLE), Charles Sturt University, Locked Bag 588, Wagga Wagga, NSW, 2678, Australia