OVERVIEW

Year 8 students performed substantially better than year 4 students on mathematics tasks involving number knowledge, strategies and skills, with an average of 30% more year 8 than year 4 students succeeding on the same number task components. On average, there was no meaningful change in number task performance between 2005 and 2009, for either year 4 or year 8 students. There was clear evidence of substantial change in the number task strategies that students use. These appeared to help with some tasks and hinder with others.

The assessments included 56 tasks investigating students’ understandings, processes and skills in the areas of mathematics called number and algebra. Number includes the ways numbers are represented, their value, operations on number, accuracy and efficiency in calculating, estimating and making approximations. Algebra involves patterns and relationships in mathematics in the real world, the use of symbols, notation and graphs and diagrams to represent mathematical relationships and ideas, and the use of algebraic expressions for solving problems.

Twenty-six of the 56 tasks are trend tasks (fully described with data for both 2005 and 2009 – and for two tasks also from 2001). One is a longer-term trend task, with data from both 1997 and 2009. Three are released tasks (fully described with data for 2009 only) and 26 are link tasks (to be used again in 2010, so only partially described here). Trend tasks are presented first, then released tasks and finally link tasks.

There was major improvement in number and algebra knowledge and skills from year 4 to year 8. Averaged across 217 task components administered to both year 4 and year 8 students, 30% more year 8 than year 4 students succeeded with these components. Year 8 students performed better on every component. As expected, the differences were generally larger on more difficult components – often components that many year 4 students would not yet have had much opportunity to learn in school or to practise.

Overall, performance at both year levels was unchanged between 2005 and 2009. Averaged across 137 trend task components attempted by year 4 students in both years, the same percentage of students succeeded in 2009 as in 2005. Gains occurred on 66 of the 137 components. At year 8 level also, on average, the same percentage succeeded in 2009 as in 2005. Gains occurred on 79 of the 172 trend task components. The most notable change in performance was a decline for year 8 students on multiplication problems (p36), where changes in computation strategy were clearly evident.

The first three tasks allowed exploration of trends over periods longer than four years. Jumpers (p13) showed substantial improvement from 1997 to 2009 for year 4 students and smaller improvement for year 8 students. Number Facts (Multiplication) (p14) and Number Facts (Addition) (p15) had data for 2001, 2005 and 2009. There was very little change on these tasks at both year levels between 2005 and 2009, after substantial losses for year 4 students on both tasks between 2001 and 2005 and a small loss for year 8 students on multiplication facts.

Students at both levels scored poorly in tasks involving estimation and tasks involving fractions (especially fractions other than halves and quarters). There was clear evidence that students have adopted changes in number strategy taught in recent years. This appears to have been advantageous in responses to some tasks and disadvantageous in responses to other tasks.