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:
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.