Abstract
The ruler is the standard measuring instrument used for measuring lengths. However, measuring lengths with a ruler is a challenge for children. For this reason, this study explores how children who have not received specific school instruction on its use, measure lengths with a conventional ruler. The relative object-ruler position, the strategy to justify the measurement, and the combination between them are analysed. Additionally, the possible influence of the grade and the transition from Kindergarten to Primary School is also studied. To achieve this aim, 99 children were asked to measure a cardboard strip in both a free and a directed situation. The results showed that in free measurements children tend to situate the object in the 2 hash mark of the ruler, the reading of the endpoint was identified as the most used strategy, and the combination of this strategy with lining up the object at 0 was the most commonly used in correct measurements. On the other hand, the results also showed marginal significant differences between age groups in such a way that children in the last year of kindergarten measured better than those in the first year of primary school. To conclude, the educational implications of these results are discussed.
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., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., et al. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14(1), 28–54. https://doi.org/10.1080/10986065.2012.625075.
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. The Journal of Mathematical Behavior, 15(3), 329–347.
Bragg, P., & Outhred, L. (2000a). What is taught versus what is learnt: The case of linear measurement. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000, Proceedings of the twenty-third annual conference of the Mathematics Education Research Group of Australasia, Fremantle, WA. (Vol. 1, pp. 112–118). Perth, WA: Mathematics Education Research Group of Australasia.
Bragg, P., & Outhred, L. (2000b). Students' knowledge of length units: Do they know more than rules about rulers? In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 97–104). Hiroshima, Japan: International Group for the Psychology of Mathematics Education.
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, 2, (pp. 159–165). Bergen: Bergen University College.
Castle, K., & Needham, J. (2007). First graders’ understanding of measurement. Early Childhood Education Journal, 35(3), 215–221. https://doi.org/10.1007/s10643-007-0210-7.
Chamorro, C., & Belmonte, J. M. (1991). El problema de la medida: Didáctica de las magnitudes lineales [The problem of measurement: Didactics of linear magnitudes]. Madrid: Síntesis.
Clements, D. H., Barrett, J. E., Sarama, J., Cullen, C. J., Van Dine, D. W., Eames, C. L., Kara, M., Klanderman, D., & Vukovich, M. (2017). Length: A summary report. In J. E. Barrett, D. H. Clements, J. Sarama (Eds.), A longitudinal account of children’s knowledge of measurement (JRME Monograph No. 16). Reston, VA: National Council of Teachers of Mathematics.
Congdon, E. L., Kwon, M. K., & Levine, S. C. (2018). Learning to measure through action and gesture: Children’s prior knowledge matters. Cognition, 180, 182–190. https://doi.org/10.1016/j.cognition.2018.07.002.
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.
Cullen, C. J. (2009). A comparative analysis: Two representational models for units of length. Doctoral dissertation, Illinois State University, IL.
Decreto 54/2014, de 10 de julio, por el que se establece el currículo de la Educación Primaria en la Comunidad Autónoma de Castilla-La Mancha. Diario Oficial de Castilla-La Mancha, no. 132, 2014, 10 de julio. [Decree 54/2014].
Gómezescobar, A., Fernández-Cézar, R., & Guerrero, S. (2017). Numbers and space intervals in length measurements in the Spanish context: Proposals for the transition to measuring with the ruler. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-017-9835-1.
González, J. A., Muñoz, M. P. E., & Zubizarreta, A. C. (2011). Metáforas de la transición: la relación entre la escuela infantil y la escuela primaria y la perspectiva de futuros docentes de educación infantil [Transition metaphors: the relationship between kindergarten and primary school and the outlook for future kindergarten teachers]. Educación XX1, 14(1), 135. https://doi.org/10.5944/educxx1.14.1.265
Ho, S. Y., & Lowrie, T. (2013, November 11). Grade 6 students’ performance on a measurement task. In CoSDEd 2013: 5th Proceedings of the International Conference on Science and Mathematics Education. Penang, Malaysia.
Irwin, K. C., Ell, F. R., & Vistro-Yu, C. P. (2004). Understanding linear measurement: A comparison of Filipino and New Zealand children. Mathematics Education Research Journal, 16(2), 3–24. https://doi.org/10.1007/BF03217393.
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, USA.
Kamii, C. (2006). Measurement of length: How can we teach it better? Teaching Children Mathematics, 13(3), 154–158.
Kellman, P. J., & Massey, C. M. (2013). Perceptual learning, cognition, and expertise. In G. H. Bower (Ed.), Psychology of learning and motivation (Vol. 58, pp. 117–165). Boston: Academic Press. https://doi.org/10.1016/B978-0-12-407237-4.00004-9
Kotsopoulos, D., Makosz, S., Zambrzycka, J., & McCarthy, K. (2015). The effects of different pedagogical approaches on the learning of length measurement in kindergarten. Early Childhood Education Journal, 43(6), 531–539. https://doi.org/10.1007/s10643-014-0686-x.
Lehrer, R. (2003). Develo** understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. 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.
Ley orgánica para la mejora de la calidad educativa (LOMCE). Ley Orgánica 8/2013, 9 de diciembre. Boletín Oficial del Estado, nº 295, 2013, 10 diciembre. [Organic law for the improvement of educational quality. Organic Law 8/2013. Spanish Kingdom Official Bolletin, 295, 2013, December, 10].
McDonough, A., & Sullivan, P. (2011). Learning to measure length in the first three years of school. Australasian Journal of Early Childhood, 36(3), 27. https://doi.org/10.1177/183693911103600305.
National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). Reston: National Council of Teachers of Mathematics.
Northcote, M., & Marshall, L. (2016). What mathematics calculations do adults do in their everyday lives? Australian Primary Mathematics Classroom, 21(2), 8–17.
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., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. New york, NY: Basic Books.
Sisman, G. T., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293–1319. https://doi.org/10.1007/s10763-015-9642-5.
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. https://doi.org/10.1037/a0039707.
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, VA: NCTM
Tamayo, S. (2014). La transición entre etapas educativas: de Educación Infantil a Educación Primaria [The transition between educational stages: From Infant Education to Primary Education]. Participación educativa, 3(5), 131–138.
Acknowledgements
The authors would like to thank Dr. Ignacio Rieiro for his collaboration in the review of this paper. The first author acknowledges the Spanish Ministry of Education, Culture and Sports for her Erasmus Practice scholarship.
Funding
Funding was provided by Fundación Española para la Ciencia y la Tecnología, FECYT (Grant No. FCT-16-10952).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gómezescobar, A., Guerrero, S. & Fernández-Cézar, R. How Long Is It? Difficulties with Conventional Ruler Use in Children Aged 5 to 8. Early Childhood Educ J 48, 693–701 (2020). https://doi.org/10.1007/s10643-020-01030-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10643-020-01030-y