Australasian Journal of Early Childhood

■■72 per cent of the project school students wereusing standard units or beyond by the end of thethird year of school (Grade Two in Victoria). Thecomparable number was only 39 per cent forthe reference school students, suggesting thatexpectations for students generally should besomewhere between these figures for studentswho have been taught well. It also suggests thatthe third year of school is an appropriate level forspecific attention to ensuring that students canprogress toward using standard units.Nearly all students moved to comparing lengths duringthe first year of school, but some did not progressbeyond that by the end of the third year. This hasimplications for teaching.It is interesting to note the extremes of achievement atthe end of the third year of school, even with teacherswho had had substantial professional development andactive supportive professional learning teams at theirschools. While on one hand 12 per cent of the cohortcould not respond successfully to the unit iterationitem (meaning they could not measure a straw withpaperclips), on the other hand 19 per cent could solvequite sophisticated application problems. This also hasimplications for teaching.Comparing lengthsThe first length task involved presenting the studentswith a skewer and a length of string, and inviting themto say which is longer, first estimating then physicallycomparing, with the expectation that they will both holdthe string taut and compare the lengths accurately,perhaps by having one end of the string aligned with anend of the skewer.Table 2 shows the number of students in the first yearof school (Grade Prep in Victoria) in each of the years ofthe data collection not comparing lengths of the stringand the skewer. The reason for using the negative ofthe data is to allow exploration of the characteristics ofthe students who could not complete the task.Table 2. Students (per cent) not Comparing lengths inthe first year of schoolMarch Novembernpercentnpercent1st year of the project 1238 34 1524 62nd year of the project 1488 24 1483 43rd year of the project 543 21 566 7While there is some variation in the March scores overthe years, the November scores are consistent. Aboutone-quarter of the students at the start of school couldnot perform this basic measurement task, but most ofthese were able to perform the task by the end of the year(at least in the project schools). Being able to completethis task is a reasonable indication of this fundamentalmeasurement skill, and it is appropriate that teachersin the first year of school find out about each individualstudent’s capacity to perform such tasks and providewhatever experiences and support are necessary.Note that the improvement in the March scores overthe three years is not attributable to the project, giventhat the students are just beginning their first year atschool in each case.While the breadth of the entire interview limited thedepth of the items in a particular domain, it did allowsome comparisons between domains of mathematics.For example, we can gain insights into characteristicsof the students in the first year of the project who couldnot compare the string and the skewer as follows:■■At the commencement of school, of the 34 percent who could not compare the objects, 34 percent could count a collection of 20 objects, and15 per cent could add 9 and 4 more seen itemscounting them all.■■At the end of the first year of school, 71 per cent ofthe students who could not compare the skewerand the string could count a collection of 20 objects,59 per cent could add 9 and 4 by counting eachobject, and a further 13 per cent could add 9 and 4objects with the 9 objects hidden (e.g. by countingon from the 9).The addition was presented as two groups of objectswhich were to be added. Initially nine objects werecovered and four objects seen, and the total sought but,if not given, then the nine objects were uncovered. Inboth forms, this seems to be much more complicatedthan comparing the string and the skewer.We can conclude that an ability to count does not implyan ability to compare lengths, neither does an ability tocombine and count two groups, and even the imaginingof a group where some counters are hidden does notseem to be related to a capacity to compare lengths.This suggests that the development of this lengthconcept is quite independent of the development ofnumber concepts, and that mathematics (and science)programs in the first year of school should offer specificexperiences on comparing lengths and conservation.Note that the distribution of the responses of the girlsand boys were indistinguishable.32A u s t r a l a s i a n J o u r n a l o f E a r l y C h i l d h o o d