The assessments included 50 tasks investigating students’ understandings, processes and skills in the areas of 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, graphs and diagrams to represent mathematical relationships and ideas, and the use of algebraic expressions for solving problems.

Sixteen tasks were identical for both year 4 and year 8. Eleven tasks had overlapping versions for year 4 and year 8 students, with some parts common to both levels. Seventeen tasks were attempted by year 8 students only and six tasks were attempted by year 4 students only. Sixteen are trend tasks (fully described with data for both 2001 and 2005), ten are released tasks (fully described with data for 2005 only) and 24 are link tasks (to be used again in 2009, so only partially described here).

The tasks are presented in three sections: trend tasks, then released tasks and finally link tasks. Within each section, tasks attempted (in whole or part) by both year 4 and year 8 students are presented first, then tasks where year 4 and year 8 students did parallel tasks, then tasks attempted by only year 4 students, followed by tasks attempted by year 8 students.

Averaged across 143 task components administered to both year 4 and year 8 students, 31 percent more year 8 than year 4 students were successful. Year 8 students performed better on every component. As might be expected, the differences were larger on the more difficult tasks. These tasks are ones where the year 4 students might not yet have had much opportunity to learn those skills in school. Also, the relatively lower percentages of success at year 4 allows for more room to grow by year 8.

Averaged across 109 task components, five percent fewer year 4 students in 2005 were successful than in year 2001. This decrease was almost entirely attributable to task components involving addition, subtraction, multiplication and division facts and simple problems. There were a total of 71 task components in these areas (60 were addition and multiplication facts), and nine percent more 2001 year 4 students were successful than 2005 year 4 students. On the other hand, on eight of the nine remaining tasks (with 38 task components), 2005 year 4 students outperformed 2001 students by three percent. These tasks involved algebra, logic, finding patterns, estimation and identifying sequences.

Averaged across 145 task components, there was no change in net performance for year 8 students from 2001 to 2005. Mirroring the year 4 results, year 8 students did not perform as well on facts and simple problems (a net decrease of three percent averaged across 84 tasks). On the positive side, averaged across 61 tasks, there was a four percent gain from 2001 to 2005 on tasks involving algebra, logic, finding patterns, estimation and identifying sequences.

There are several results in this area that stand out: first, there are strong increases from year 4 to year 8. This indicates a substantial growth in mathematical achievement across these years, particularly in areas such as fractions, number patterns and estimation. Second, even in areas where solid year 4 to year 8 growth is seen, there is room for improvement. An examination of performance levels on the individual tasks is the best way to look for areas of improvement. Third, there is a clear shift in performance from 2001 to 2005. Students are improving in tasks that require quantitative reasoning skills, but declining in basic mathematics facts and solving simple number problems.