Australasian Journal of Early Childhood

In other words, the difficulties these students experiencewith using standard units are not because of countingdifficulties, nor problems with reading the numbers, normanipulating numbers overall, nor being able to operatewith images. Indeed, many such tasks seem substantiallymore sophisticated than using the ruler to measure thestraw. It is possible that teachers have emphasised thenumber skills in their programs, but it also may be that usingstandard units requires specific structured experiences.ConclusionThe intention of this paper is to explore lengthunderstandings in light of experiences from the EarlyNumeracy Research Project (ENRP) and reflect uponthe value of the fundamental ideas underpinning thelearning of length in the early years of schooling.In terms of the results presented above, we confidentlyrecommend the following to teachers.Teachers of children in the first year of school canreasonably aim that nearly all students are able tocompare the length of two objects, to order three objectseven if not necessarily directly comparing them, andbegin to move towards quantifying lengths. It is relevantto note that in the ENRP an active decision was madenot to have assessment items that measure the transitiveproperty of length; nevertheless, structured activities thatprovide experiences in this element of length learning areimportant (e.g. asking students to compare the lengthsof two objects that cannot be placed next to each other).Teachers of children in the second year of school couldemphasise activities that facilitate the movement ofall students toward using informal units iteratively toquantify lengths, both using a single unit repeatedlyand using multiple versions of the one unit. It is worthnoting that approximately two-thirds of the students atthis level are either using or will become ready for usingstandard units during the year.Teachers of children in the third year of school shouldexpect most children to be moving towards usingstandard units such as the centimetre. Again it is notedthat many students are ready for more sophisticatedtasks involving measuring length.It is evident that the capacity to operate with numbersand these fundamental measurement concepts seemto be quite independent of each other, suggestingthat teachers need to incorporate measurement in astructured way in their teaching programs.It is noted that, even with well-supported teachers,there is great diversity of readiness after three years ofschool and, from the third year of schooling onwards,it is difficult to imagine that teachers can teachmeasurement without making specific provision for thedifferences in their planning.It is important to consider the implications of thesefindings for teaching and teacher learning. Hattieand Timperley (2007) argued that the most importantdeterminant of student learning is the feedback theyreceive. This includes the students knowing what theyare meant to be doing, how well they are doing it, andwhat they will do next. If the teacher is clear about theparticular learning goals, (s)he will be in a better positionto communicate those goals to the students, and toprovide ongoing feedback on their progress towardsachieving those goals. Having clear goals also allowsteachers to choose or create activities that can allowstudents to construct the fundamental ideas of, in thiscase, measurement of length for themselves.AcknowledgementsThe Early Numeracy Research Project (ENRP) wassupported by grants from the Victorian Departmentof Employment, Education and Training, the CatholicEducation Office (Melbourne) and the Association ofIndependent Schools Victoria.ReferencesBattista, M. T. (2006). Understanding the developmentof students’ thinking about length. Teaching ChildrenMathematics, 13(3), 140–146.Bragg, P., & Outhred, L. (2000). What is taught versus whatis learnt: The case of linear measurement. In J. Bana &A. Chapman (Eds), Mathematics education beyond 2000(Proceedings of the Twenty-third Annual Conference of theMathematics Education Research Group of Australasia,Fremantle, WA. Vol. 1, pp. 112–118). Perth, WA: MathematicsEducation Research Group of Australasia.Carpenter, T. (1976). Analysis and synthesis of existingresearch on measurement. In R. Lesh (Ed), Number andmeasurement (pp. 47–83). Athens, Georgia: ERIC/SMEAC,University of Georgia.Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne,M., McDonough, A., Montgomery, P., Roche, A., Sullivan,P., Clarke, B., & Rowley, G. (2002). Early numeracy researchproject: Final report. Melbourne: Australian Catholic Universityand Monash University.Clements, D. H., & Stephan, M. (2004). Measurement in Pre-Kto grade 2 mathematics. In D. H. Clements & J. Sarama (Eds),Engaging young children in mathematics: Standards for earlychildhood mathematics education (pp. 299–317). Mahwah, NJ:Lawrence Erlbaum.Hattie, J., & Timperley, H. (2007). 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