Abstract
The present work shows how 4–6-year-old Spanish children interpret numbers and space intervals in the ruler when measuring length. To determine it, 4 ad hoc rulers are designed and used with a sample of 103 children from two schools of Toledo province (Spain). The sample is characterized respecting conservation and measurement with the standard ruler confirming that these children mostly neither conserve nor use the standard ruler correctly, regardless their time exposure to instruction. With the use of our rulers, we confirm that numbers hinder in measuring length, and discrete units imbedded in the ruler help children to measure correctly. A good scaffold is found to help children conceptualize space intervals as iterating objects consisting on the use of rulers with discrete units on them. Its use is recommended preceding the one of standard rulers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barrett, J. E., Jones, G., Thornton, C., & Dickson, S. (2003). Understanding children’s developing strategies and concepts for length. In D. H. Clements, & G. Bright (Eds.), Learning and teaching measurement : 2003 yearbook (pp.17–30). Reston, VA: National Council of Teachers of Mathematics.
Battista, M. T. (2006). Understanding the development of students’ thinking about length. Teaching Children Mathematics, 13(3), 140–146.
Belmonte, J. M. (2005). La construcción de magnitudes lineales en educación infantil [The building of length magnitudes in infant education]. In M. C. Chamorro (Ed.) Didáctica de las matemáticas para educación infantil (pp. 315–345). Madrid, Spain: Pearson Educación.
Boulton-Lewis, G. (1987). Recent cognitive theories applied to sequential length measuring knowledge in young children. British Journal of Educational Psychology, 57(3), 330–342.
Boulton-Lewis, G. M., Wilss, L. A., & Mutch, S. L. (1996). An analysis of young children's strategies and use of devices for length measurement. Journal of Mathematical Behavior, 15(3), 329–347.
Bragg, P., & Outhred, L. (2004). A measure of rulers—The importance of units in a measure. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 159–166). Bergen, Norway: Bergen University College.
Bush, H. (2009). Assessing children's understanding of length measurement: A focus on three key concepts. Australian Primary Mathematics Classroom, 14(4), 29–32.
Carpenter, T. P., & Lewis, R. (1976). The development of the concept of a standard unit of measure in young children. Journal for Research in Mathematics Education, 7, 53–58.
Castle, K., & Needham, J. (2007). First graders’ understanding of measurement. Early Childhood Education Journal, 35(3), 215–221.
Chamorro, M. C., & Belmonte, J. M. (1991). El problema de la medida: Didáctica de las magnitudes lineales [The problem of measurement: Didactics of linear magnitudes]. Madrid, Spain: Síntesis.
Clements, D. H. (1999). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5–11.
Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 299–317). Mahwah, NJ: Lawrence Erlbaum.
Cullen, C., & Barrett, J. E. (2010). Strategy use indicative of an understanding of units of length. Paper presented at the 34th Annual Conference of the International Group for the Psychology of Mathematics in Education, Belo Horizonte.
Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12(3), 197–211.
Kamii, C. (1995). Why is the use of the ruler so hard? Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.
Kamii, C. (2006). Measurement of length: How can we teach it better? Teaching Children Mathematics, 13(3), 154–158.
Kamii, C., & Clark, F. B. (1997). Measurement of length: The need for a better approach to teaching. School Science and Mathematics, 97(3), 116–121.
Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179–192). Reston, VA: National Council of Teachers of Mathematics.
Levine, S. C., Kwon, M., Huttenlocher, J., Ratliff, K. R., & Dietz, K. (2009). Children’s understanding of ruler measurement and units of measure: A training study. In N. A. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society (pp. 2391–2395). Austin, TX: Cognitive Science Society.
MacDonald, A. (2012). Young children’s photographs of measurement in the home. Early Years, 32(1), 71–85.
Mialaret, G. (1984). Las matemáticas: Cómo se aprenden, cómo se enseñan: Un texto base para psicólogos, enseñantes y padres [Mathematics: How they are learned and taught: A basic text for psychologist, teachers and parents]. Ed: Visor.
Nührenbörger, M. (2001). Children’s measurement thinking in the context of length. Paper presented at Annual Conference on Didactics of Mathematics, Ludwigsburg, Germany.
Nunes, T., Light, P., & Mason, J. (1993). Tools for thought: The measurement of length and area. Learning and Instruction, 3(1), 39–54.
Piaget, J. (1978). Psicología del niño [Child psychology]. Madrid, Spain: Morata.
Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child's conception of geometry. New York, NY: Basic Books.
Ryan, J., & Williams, J. (2007). Children’s mathematics 4–15: Learning from errors and misconceptions. New York, NY: McGraw-Hill.
Solomon, T. L., Vasilyeva, M., Huttenlocher, J., & Levine, S. C. (2015). Minding the gap: Children’s difficulty conceptualizing spatial intervals as linear measurement units. Developmental Psychology, 51(11), 1564–1573.
Sophian, C. (2007). Measuring spatial factors in comparative judgments about large numerosities. In D. D. Schmorrow & L. M. Reeves (Eds). Proceedings of the 3rd International Conference on Foundations of Augmented Cognition (Vol. 4565, pp. 157-165). Berlin, Germany: Springer.
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: 2003 yearbook (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
Stephan, M., Cobb, P., Gravemeijer, K., & Estes, B. (2001). The role of tools in supporting students’ development of measuring conceptions. In A. A. Cuoco (Ed.), The roles of representation in school mathematics: 2001 yearbook (pp. 63–76). Reston, VA: National Council of Teachers of Mathematics.
Wickstrom, M. H., & Jurczak, L. M. (2016). Inch by inch, we measure: Reflect and discuss. Teaching Children Mathematics, 22(8), 468–475.
Wilson, P. S., & Rowland, R. (1993). Teaching measurement. In Jensen & J. Robert (Eds.), Research ideas for the classroom: Early childhood mathematics (pp. 171–191). Reston, VA: National Council of Teachers of Mathematics, Inc.,: Macmillan Publishing Company.
Zöllner, J., & Benz, C. (2013). How four to six year old children compare lengths indirectly. Paper presented at the Eight Congress of European Research in Mathematics Education (Cerme 8), Antalya, Turkey.
Acknowledgements
We acknowledge the children, families, and teachers of Sta. Teresa and Galvez School for participating in our study.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gómezescobar, A., Fernández-Cézar, R. & Guerrero, S. Numbers and Space Intervals in Length Measurements in the Spanish Context: Proposals for the Transition to Measuring with the Ruler. Int J of Sci and Math Educ 16, 1375–1386 (2018). https://doi.org/10.1007/s10763-017-9835-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10763-017-9835-1