MUCH RESEARCH ON EARLY measurement learning is small-scale and dependent on the items used. While such research is helpful for indicating the key aspects of learning length, it does not give teachers a clear indication of the expectations for student learning of them. This paper presents substantial data from a large project that used individual interviews to assess student learning against ‘growth points' or key stages in children's learning, over a range of domains including length. Data from interviews conducted twice a year with more than 1000 children in each of the first three years of school are used to indicate appropriate targets for student achievement. Basically it is suggested that the key targets for the learning of length in the first three years of school are, respectively, learning to compare, learning to use a unit iteratively, and measuring using formal units.
References
1.
BattistaM. T. (2006). Understanding the development of students' thinking about length. Teaching Children Mathematics, 13(3), 140–146.
2.
BraggP., & OuthredL. (2000). What is taught versus what is learnt: The case of linear measurement. In BanaJ. & ChapmanA. (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.
3.
CarpenterT. (1976). Analysis and synthesis of existing research on measurement. In LeshR. (Ed), Number and measurement (pp. 47–83). Athens, Georgia: ERIC/SMEAC, University of Georgia.
4.
ClarkeD., CheesemanJ., GervasoniA., GronnD., HorneM., McDonoughA., MontgomeryP., RocheA., SullivanP., ClarkeB., & RowleyG. (2002). Early numeracy research project: Final report.Melbourne: Australian Catholic University and Monash University.
5.
ClementsD. H., & StephanM. (2004). Measurement in Pre-K to grade 2 mathematics. In ClementsD. H. & SaramaJ. (Eds), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 299–317). Mahwah, NJ: Lawrence Erlbaum.
6.
HattieJ., & TimperleyH. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.
7.
KamiiC. (2006). Measurement of length: How can we teach it better?Teaching Children Mathematics, 13(3), 154–158.
8.
LehrerR. (2003). Developing understanding of measurement. In KilpatrickJ., MartinW. G. & SchifterD. (Eds), A research companion to principles and standards for school mathematics (pp. 179–192). Reston, VA: National Council of Teachers of Mathematics.
9.
LehrerR., JaslowL., & CurtisC. (2003). Developing an understanding of measurement in the elementary grades. In ClementsD. H. & BrightG. (Eds), Learning and teaching measurement (2003 Yearbook, pp. 100–121). Reston, VA: National Council of Teachers of Mathematics.
10.
McClainK., CobbP., GravemeijerK., & EstesB. (1999). Developing mathematical reasoning within the context of measurement. In StiffL. V. & CurcioF. R. (Eds), Developing mathematical reasoning in grades K-12 (1999 Yearbook, pp. 93–106). Reston, VA: National Council of Teachers of Mathematics.
11.
NunesT., LightP., & MasonJ. (1993). Tools for thought: The measurement of length and area. Learning and Instruction, 3, 39–54.
12.
PiagetJ., InhelderB., & SzeminskaA. (1960). The child's conception of geometry.London: Routledge and Kegan Paul.
13.
RowleyG., & HorneM. (2000, December). Validation of an interview schedule for identifying growth points in early numeracy. Paper presented to the Australian Association for Research in Education Annual Conference, University of Sydney, New South Wales.
14.
StephanM., & ClementsD. H. (2003). Linear and area measurement in prekindergarten to grade 2. In ClementsD. H. & BrightG. (Eds), Learning and teaching measurement (2003 Yearbook, pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
15.
ThompsonC., & Van de WalleJ. (1985). Let's do it: Estimate how much. Arithmetic Teacher, 32(8), 8–12.
16.
WilsonP. A., & OsborneA. (1992). Foundational ideas in teaching about measure. In PostT. R. (Ed), Teaching mathematics in grades K-8: Researchabased methods (pp. 89–121). Needham Heights, Massachusetts: Allyn & Bacon.
17.
WilsonP. S., & RowlandR. (1993). Teaching measurement. In JensenR. J. (Ed), Research ideas for the classroom: Early childhood mathematics (pp. 171–194). Reston, VA: National Council of Teachers of Mathematics.