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Mathematics Education Research Journal

, Volume 26, Issue 2, pp 131–150 | Cite as

Investigating young children’s learning of mass measurement

  • Jill Cheeseman
  • Andrea McDonough
  • Sarah Ferguson
Original Article
First Online:

Abstract

This paper reports results of a design experiment regarding young children’s concepts of mass measurement. The research built on an earlier study in which a framework of “growth points” in early mathematics learning and a related, task-based, one-to-one interview to assess children’s understanding of the measurement of mass were developed. Prompted by the results and recommendations from the earlier study, five lessons were developed that offered rich learning experiences regarding concepts of mass. The 119 Year 1 and 2 children participating in the study were interviewed using the same protocol before and after the teaching period. The assessment data showed that the majority of these children moved from using nonstandard units to using standard units and instruments for measuring mass. The findings from this study challenge the traditional approach of using informal units for an extended period before the introduction of standard units.

Keywords

Young children’s mathematics concepts Measurement of mass 
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References

  1. Australian Curriculum Assessment and Reporting Authority (2012). Australian curriculum: Mathematics http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10.
  2. Baroody, A. J. (2009). Fostering early numeracy in preschool and kindergarten. Encyclopedia of Language and Literacy Development, 1–9. from <http://literacyencyclopedia.ca/pdfs/topic.php?topId=271>.
  3. 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. The Journal of Mathematical Behavior, 15, 329–347.CrossRefGoogle Scholar
  4. Brainerd, C. J. (1974). Training and transfer of transitivity, conservation, and class inclusion of length. Child Development, 45(2), 324–334.CrossRefGoogle Scholar
  5. Brown, M., Blondel, E., Simon, S., & Black, P. (1995). Progression in measuring. Research Papers in Education, 10(2), 143–170.CrossRefGoogle Scholar
  6. Carpenter, T. (1976). Analysis and synthesis of existing research on measurement. In R. Lesh (Ed.), Number and measurement (pp. 47–83). Athens: ERIC/SMEAC, University of Georgia.Google Scholar
  7. Cheeseman, J. (2008). Young children’s accounts of their mathematical thinking. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the joint meeting of PME 32 and PME-NA XXX, vol. 2 (pp. 289–296). Morelia: International Group for the Psychology of Mathematics Education.Google Scholar
  8. Cheeseman, J. (2010). Challenging children to think: An investigation of the behaviours of highly effective teachers that stimulate children to probe their mathematical understandings. Unpublished thesis, Monash University, Melbourne.Google Scholar
  9. Cheeseman, J., McDonough, A., & Clarke, D. (2011). Investigating children’s understanding of the measurement of mass. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Mathematics: Traditions and [new] practices, vol. 1 (pp. 174–182). Adelaide: Australian Association of Mathematics Teachers and the Mathematics Education Research Group of Australasia.Google Scholar
  10. Cheeseman, J., McDonough, A., & Ferguson, S. (2012). The effects of creating rich learning environments for children to measure mass. In J. Dindyal, L. Pien Cheng, & S. Fong Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia). Singapore: MERGA.Google Scholar
  11. Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, A. G. Howson, & M. Otte (Eds.), Perspectives on mathematics education (pp. 243–307). Holland: Reidel.CrossRefGoogle Scholar
  12. Clarke, D. M., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., et al. (2002). Early numeracy research project final report. Melbourne: Mathematics Teaching and Learning Centre, Australian Catholic University.Google Scholar
  13. Clarke, D. M., Cheeseman, J., McDonough, A., & Clarke, B. A. (2003). Assessing and developing measurement with young children. In D. H. Clements & G. W. Bright (Eds.), Learning and teaching measurement (2003 Yearbook ) (pp. 68–80). Reston: National Council of Teachers of Mathematics.Google Scholar
  14. Clements, D. (1999). Teaching length measurement: research challenges. School Science and Mathematics, 99, 5–11.CrossRefGoogle Scholar
  15. Clements, D. H., & Battista, M. T. (1986). Geometry and geometric measurement. Arithmetic Teacher, 33(6), 29–32.Google Scholar
  16. Clements, D., & Bright, G. (2003). Learning and teaching measurement (2003 yearbook). Reston: National Council of Teachers of Mathematics.Google Scholar
  17. Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.Google Scholar
  18. Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: a large-scale, cluster, randomized trial. Journal for Research in Mathematics Education, 42(2), 127–166.Google Scholar
  19. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  20. Copley, J. V. (2006). “Are you bigger than me?” A young children’s mathematical thinking about measurement. Lecture presented at the International Conference on Logical Mathematical Thinking. http://www.waece.org/cdlogicomatematicas/ponencias/juanitaycopley_pon_ing.htm.
  21. De Klerk, J. (2007). Illustrated maths dictionary. Pearson.Google Scholar
  22. Department of Education and Early Childhood Development (DEECD) (2006). Mathematics Online Interview. http://www.education.vic.gov.au/studentlearning/teachingresources/maths/interview/moi.htm.
  23. Ferguson, S. (2012). Like a bridge: Scaffolding as a means of assisting low-attaining students in mathematics during cognitively challenging tasks. Unpublished doctoral dissertation, Australian Catholic University, Melbourne.Google Scholar
  24. Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, vol. 1 (pp. 371–404). Charlotte: Information Age.Google Scholar
  25. Hiebert, J., & Wearne, D. (1997). Instructional tasks, classroom discourse and student learning in second grade arithmetic. American Educational Research Journal, 30(2), 393–425.CrossRefGoogle Scholar
  26. Johnson, P. (1996). What’s a substance? Education in Chemistry, 33, 41–42.Google Scholar
  27. Johnson, P. (2000). Children’s understanding of substances, part 1. Recognizing chemical change. International Journal of Science Education, 22, 719–737.CrossRefGoogle Scholar
  28. Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137–168). Mahwah: Lawrence Erlbaum.Google Scholar
  29. Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurement in the elementary grades. In D. H. Clements & G. W. Bright (Eds.), Learning and teaching measurement (2003 Yearbook ) (pp. 100–121). Reston: National Council of Teachers of Mathematics.Google Scholar
  30. MacDonald, A. (2011). Young children’s representations of their developing measurement understandings. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Mathematics: Traditions and [new] practices, vol. 1 (pp. 420–490). Adelaide: Australian Association of Mathematics Teachers and the Mathematics Education Research Group of Australasia.Google Scholar
  31. Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. Milton Keynes: The Open University.Google Scholar
  32. McDonough, A., & Sullivan, P. (2011). Learning length in the first 3 years of school. Australasian Journal of Early Childhood, 36(3), 27–35.Google Scholar
  33. McDonough, A., Cheeseman, J., & Ferguson, S. (2012). Insights into children’s understandings of mass measurement. In T. Y. Tso (Ed.), Proceedings of the 36th conference of the International Group for the Psychology of Mathematics Education, vol. 3 (pp. 201–208). Taipei: PME.Google Scholar
  34. McKenney, S., & Reeves, T. (2012). Conducting educational design research. London: Routledge.Google Scholar
  35. Nunes, T., Light, P., & Mason, J. H. (1993). Tools for thought: the measurement of length and area. Learning and Instruction, 3, 39–54.CrossRefGoogle Scholar
  36. Outhred, L., & McPhail, D. (2000). A framework for teaching early measurement. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000. Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia (pp. 487–494). Fremantle: MERGA.Google Scholar
  37. Outhred, L., & Mitchelmore, M. (1992). Representation of area: A pictorial perspective. In W. Geeslin & K. Graham (Eds.), Proceedings of the sixteenth PME conference, vol. 11 (pp. 194–201). Durham: Program Committee of the 16th PME Conference.Google Scholar
  38. Papageorgiou, G., & Johnson, P. (2005). Do particle ideas help or hinder pupils’ understanding of phenomena? International Journal of Science Education, 27(11), 1299–1317.CrossRefGoogle Scholar
  39. Piggott, J. (2008). Rich tasks and contexts. http://nrich.maths.org/5662.
  40. Spinillo, A., & Batista, R. (2009). A sense of measurement: What do children know about the variant principles of different types of measure. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education, vol. 5 (pp. 161–168). Thessalonika: PME.Google Scholar
  41. 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: National Council of Teachers of Mathematics.Google Scholar
  42. van den Akker, J., McKenney, S., & Neiveen, N. (2006). Introduction to educational design research. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Neiveen (Eds.), Educational design research (pp. 67–90). London: Routledge.Google Scholar
  43. van den Berg, O. (1995). ‘Progression in measuring’–some comments. Research Papers in Education, 10(2), 171–173.CrossRefGoogle Scholar
  44. Wilson, P. A., & Osborne, A. (1992). Foundational ideas in teaching about measure. In T. R. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (2nd ed., pp. 89–121). Needham Heights: Allyn & Bacon.Google Scholar
  45. Wilson, P. S., & Rowland, R. (1993). Teaching measurement. In R. J. Jensen (Ed.), Research ideas for the classroom: Early childhood mathematics (pp. 171–194). Reston: National Council of Teachers of Mathematics.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2013

Authors and Affiliations

  • Jill Cheeseman
    • 1
  • Andrea McDonough
    • 2
  • Sarah Ferguson
    • 2
  1. 1.Monash UniversityMelbourneAustralia
  2. 2.Australian Catholic UniversityMelbourneAustralia

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