number  : Introduction   

The assessments included twenty-three tasks which investigated students understandings, processes and skills in the area of mathematics called Number. Number includes the ways numbers are represented, their value, operations on number, accuracy and efficiency in calculating, estimating and making approximations.

Four tasks were identical for both year 4 and year 8. Nine tasks had overlapping versions for year 4 and year 8 students, with some parts common to both levels. Four tasks were attempted by year 8 students only, and three by year 4 only. Eight of the twenty-three tasks have been selected as link tasks to be used again in the year 2001, and therefore are not described in detail here. The other tasks are released tasks for which full details are given.

The chapter presents the assessment tasks in the following order:

  • The released tasks attempted by both year 4 and year 8 students;
  • The released tasks attempted separately by year 4 and year 8 students;
  • The eight tasks which will be used as link tasks.

High percentages of students at year 4 and year 8 were accurate with basic addition tables, but many students at both year levels struggled with recalling multiplication facts. A large percentage of students at both levels had difficulty performing subtraction algorithms that required adjustments (renaming), and results show that skilfulness in performing division algorithms is not high at year 4 or year 8. The majority of students at both levels showed inability to recognise values and perform calculations with fractional numbers (common fractions and decimals). Students at both levels managed more accurate answers when using calculators than when calculating mentally or with pencil and paper. Results for tasks which investigated important conceptual understandings and processes with number, and their practical application, show a wide spread of confidence at both levels, with year 8 students achieving consistently higher scores than year 4 students. This difference is also particularly noticeable in number and word items. Large percentages of year 4 and year 8 students struggled with communicating their ideas and understandings about the meaning of number. On task components common to both year levels, on average about 35 percent more year 8 students than year 4 students achieved success.