# Developing measurement concepts within context: Children’s representations of length

- 1.6k Downloads
- 9 Citations

## Abstract

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.

### Keywords

Young children Measurement Representations Context### References

- Aldridge, S., & White, A. (2002). What’s the time, Ms White?
*Australian Primary Mathematics Classroom, 7*(2), 7–12.Google Scholar - 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.Google Scholar - Bobis, J., Mulligan, J., & Lowrie, T. (2009).
*Mathematics for children: Challenging children to think mathematically*(3rd ed.). Frenchs Forest: Pearson Education Australia.Google Scholar - Boulton-Lewis, G. (1987). Recent cognitive theories applied to sequential length measuring knowledge in young children.
*British Journal of Educational Psychology, 57*, 330–342.CrossRefGoogle Scholar - Boulton-Lewis, 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.CrossRefGoogle Scholar - Bronfenbrenner, U. (1974). Developmental research, public policy, and the ecology of childhood.
*Child Development, 45*, 1–5.CrossRefGoogle Scholar - Bronfenbrenner, U. (1979).
*The ecology of human development: Experiments by nature and design*. Cambridge: Harvard University Press.Google Scholar - 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.Google Scholar - 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.Google Scholar - 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.Google Scholar - 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.Google Scholar - Civil, M. (2002). Culture and mathematics: a community approach.
*Journal of Intercultural Studies, 23*(2), 133–148.CrossRefGoogle Scholar - Clarke, D. (1998a). Children’s understanding of the clock in the digital age.
*Primary Educator, 4*(3), 9–12.Google Scholar - 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.CrossRefGoogle Scholar - Clements, D. H., & Sarama, J. (2000). The earliest geometry.
*Teaching Children Mathematics, 7*(2), 82–86.Google Scholar - Clements, D. H., & Stephan, M. (2004). Measurement in pre-K 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.Google Scholar - 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.Google Scholar - 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.Google Scholar - Hiebert, J. (1981). Cognitive development and learning linear measurement.
*Journal for Research in Mathematics Education, 12*(3), 197–211.CrossRefGoogle Scholar - Hughes, M., Desforges, C., & Mitchell, C. (2000).
*Numeracy and beyond: Applying mathematics in the primary school*. Buckingham: Open University Press.Google Scholar - Kamii, C., & Clark, F. (1997). Measurement of length: the need for a better approach to teaching.
*School Science and Mathematics, 97*(3), 116–121.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - Lowrie, T. (2004a). Problem solving in out-of-school settings: Children “playing” in ICT contexts. In G. Jones & S. Peters (Eds.),
*New development and trends in mathematics education at pre-school 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.icme-10.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.Google Scholar - Masingila, J. O., & de Silva, R. (2001). Teaching and learning school mathematics by building on students’ out-of-school 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.Google Scholar - Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development.
*Mathematics Education Research Journal, 21*(2), 33–49.Google Scholar - Nunes, T., & Bryant, P. (1996).
*Children doing mathematics*. Oxford: Blackwell Publishers Ltd.Google Scholar - Nunes, T., Light, P., & Mason, J. (1995). Measurement as a social process.
*Cognition and Instruction, 13*(4), 585–587.CrossRefGoogle Scholar - 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.Google Scholar - 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.Google Scholar - Piaget, J., Inhelder, B., & Szeminska, A. (1960).
*The child’s conception of geometry*. London: Routledge and Kegan Paul.Google Scholar - Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2007).
*Helping children learn mathematics*(8th ed.). Hoboken: John Wiley & Sons, Inc.Google Scholar - 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.Google Scholar - Smith, T., & MacDonald, A. (2009). Time for talk: the drawing-telling process.
*Australian Primary Mathematics Classroom, 14*(3), 21–26.Google Scholar - 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.Google Scholar - 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.Google Scholar - Sullivan, P., & Lilburn, P. (1997).
*Open-ended maths activities: Using “good” questions to enhance learning*. Melbourne: Oxford University Press.Google Scholar - Sullivan, P., Mousley, J., & Zevenbergen, R. (2005). Increasing access to mathematical thinking.
*Gazette, 32*(2), 105–109.Google Scholar - Vygotsky, L. (1978).
*Mind in society: The development of higher psychological processes*. Cambridge: Harvard University Press.Google Scholar - 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.Google Scholar - Wright, S. (2003). Ways of knowing in the arts. In S. Wright (Ed.),
*Children, meaning-making and the arts*(pp. 1–33). Frenchs Forest: Pearson Education Australia.Google Scholar - Wright, S. (2006). Children’s multimodal meaning making: Giving voice to children through drawing and storytelling. In W. D. Bokhorst-Heng, M. D. Osborne, & K. Lee (Eds.),
*Redesigning pedagogy: Reflections of theory and praxis*(pp. 175–190). Rotterdam: Sense Publishers.Google Scholar - Wright, S. (2007). Young children’s meaning-making through drawing and ‘telling’: analogies to filmic textual features.
*Australian Journal of Early Childhood, 32*(4), 37–48.Google Scholar - Zevenbergen, R., Dole, S., & Wright, R. J. (2004).
*Teaching mathematics in primary schools*. Crows Nest: Allen & Unwin.Google Scholar