New
Zealand’s National Education Monitoring Project commenced
in 1993, with the task of assessing and reporting on the achievement
of New Zealand primary school children in all areas of the school
curriculum. Children are assessed at two class levels: year 4 (halfway
through primary education) and year 8 (at the end of primary education).
Different curriculum areas and skills are assessed each year, over
a four-year cycle. The main goal of national monitoring is to provide
detailed information about what children can do so that patterns
of performance can be recognised, successes celebrated and desirable
changes to educational practices and resources identified and implemented.
Each year,
small random samples of children are selected nationally, then assessed
in their own schools by teachers specially seconded and trained
for this work. Task instructions are given orally by teachers, through
video presentations, on laptop computers, or in writing. Many of
the assessment tasks involve the children in the use of equipment
and supplies. Their responses are presented orally, by demonstration
in writing, in computer files or through submission of other physical
products. Many of the responses are recorded on videotape for subsequent
analysis.
The use of many tasks with both year 4 and year 8 students allows
comparisons between the two levels. Because some tasks have been
used twice, in 2001 and 2005, trends in performance across the four-year
period can also be analysed.
In 2005, the third year of the third cycle of national monitoring,
three areas were assessed: mathematics, social studies and information
skills. This report presents details of the mathematics assessments.
Chapter
2 explains the place of mathematics in the New Zealand
curriculum and presents the mathematics framework. It identifies
four areas of content (number and algebra, measurement, geometry,
and statistics) linked to eight processes. The importance of attitudes
and motivation is also highlighted.
Chapter
3 presents the students’ results on 50 number and
algebra tasks. Averaged across 143 task components administered
to year 4 and year 8 students, 31 percent more year 8 than year
4 students succeeded with these components. Year 8 students performed
better on every component. Differences were larger on the more difficult
tasks, possibly reflecting tasks where year 4 students had yet to
receive much instruction.
There was a moderate net decline in performance in year 4 from 2001
to 2005. Averaged across 109 task components, five percent fewer
year 4 students in 2005 were successful than in year 2001. This
difference is attributable to 71 task components that involved recall
of facts or simple calculations with the four basic arithmetic operations,
where students in 2001 outperformed 2005 students by nine percent.
On the other hand, on the 38 task components involving algebra,
logic, finding patterns, estimation and identifying sequences, year
4 students in 2005 outperformed the 2001 cohort by three percent.
There were 145 task components in common for 2001 and 2005 for year
8, with no net difference between the two years. Following the pattern
of 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 task components
involving algebra, logic, finding patterns, estimation and identifying
sequences.
Chapter
4 presents the results for 27 measurement tasks. Averaged
across 79 task components administered to both year 4 and year 8
students, 29 percent more year 8 than year 4 students succeeded
with these components. Year 8 students performed better on 78 of
79 components.
There was little evidence of change between 2001 and 2005. Averaged
across 53 trend task components attempted by year 4 students in
both years, one percent more students succeeded in 2005 than in
2001. Gains occurred on 28 of the 53 components. At the year 8 level,
with 65 task components included, again there was one percent gain
from 2001 to 2005. Gains occurred on 29 of 65 components.
The measurement tasks represented a broad range of skills related
to the processes and applications of making and using measurements.
There were some problems in basic measurement tasks, especially
in year 4. However, student performance was uniformly stronger in
the areas of making and reading measurements in straightforward
applications than in the areas related to using measurements and
measurement processes to solve problems.
Chapter
5 presents the results for 15 geometry tasks. There were
31 task components administered to both year 4 and year 8 students.
In each of these, the year 8 students showed a higher success rate
than the year 4 students. On average, year 8 students outperformed
year 4 students by 21 percent. Differences between year 4 and year
8 students were fairly consistent across the tasks.
There were 16 task components in common for 2001 and 2005 for year
4 students. Eight of those components showed a gain over the four-year
period, and the other eight showed a decline. The net difference
over the 16 task components was a decline of one percent. There
were 19 task components in common for 2001 and 2005 for year 8.
Eleven of those components showed a gain over the four years and
eight showed a decline, with a net gain of one percent.
Chapter
6 presents the results of seven statistics tasks. The two
tasks administered to both year 4 and year 8 show substantial growth
over those years. On average, there was a 36 percent increase in
performance on tasks from year 4 to year 8. There was also a small
improvement from 2001 to 2005 at year 4 level (an average of two
percent) and a moderate improvement between 2001 and 2005 at year
8 level (average of five percent). These trends were based on a
small number of task components, so should be interpreted cautiously.
Chapter
7 focuses on the results of a survey that sought information
from students about their strategies for, involvement in, and enjoyment
of mathematics. Mathematics was the second most popular option for
year 4 students and the third most popular option for year 8 students,
at both levels – one place higher than in 2001. At year 4
level it was chosen by seven percent more students in 2005 than
in 1997, and at year 8 level it was chosen by 6 percent fewer students
in 2005 than in 1997. It should be noted that two additional options
(dance and drama) were added between 1997 and 2005, which might
have reduced the percentages choosing mathematics.
An open-ended question asked students, “What are some interesting
maths things you do in your own time?” The emphasis on basic
facts and tables among year 4 students declined substantially between
2001 and 2005, mentioned by 56 percent of students in 2001 but only
36 percent of students in 2005.
The student responses to 11 rating items showed that about 10 percent
more year 8 than year 4 students have distinctly negative views
about studying mathematics in school and about their own capabilities,
while 33 percent more year 8 than year 4 students are negative about
doing maths in their own time. These patterns have stayed quite
consistent from the first survey in 1997 to the 2005 survey. Over
the same period, there have been worthwhile reductions, at both
year levels but especially year 8, in the percentages of students
who said that they didn’t know how good their parents thought
they were at maths, or how good their teacher thought they were
at maths. There is considerable scope for further reduction in the
percentage of students who do not know what their teacher thinks
about their mathematical capabilities.
Chapter
8 details the results of analyses comparing the performance
of different demographic subgroups. Community size, school size,
school type (full primary, intermediate, or year 7 to 13 high school),
and geographic zone did not seem to be important factors predicting
achievement on the mathematics tasks. The same was true for the
2001 and 1997 assessments. However, there were statistically significant
differences in the performance of students from low, medium and
high decile schools on 62.5 percent of the tasks at year 4 level
(compared to 87 percent in 2001 and 85 percent in 1997) and 65 percent
of the tasks at year 8 level (compared to 76 percent in 2001 and
77 percent in 1997). The change for year 4 students is noteworthy.
For the comparisons of boys with girls, Pakeha with Mäori,
Pakeha with Pasifika students, and students for whom the predominant
language at home was English with those for whom it was not, effect
sizes were used. Effect size is the difference in mean (average)
performance of the two groups, divided by the pooled standard deviation
of the scores on the particular task. For this summary, these effect
sizes were averaged across all tasks.
Year 4 boys averaged slightly higher than girls, with a mean effect
size of 0.08 (very similar to the mean effect size of 0.10 in 2001).
Year 8 girls averaged slightly higher than boys, with a mean effect
size of 0.03 (the same as in 2001). Pakeha students averaged moderately
higher than Mäori students, with mean effect sizes of 0.37
for year 4 students and 0.35 for year 8 students (the corresponding
figures in 2001 were 0.46 and 0.42). Year 4 Pakeha students averaged
moderately higher than Pasifika students, with a mean effect size
of 0.35 (compared to 0.59 in 2001). This is a noteworthy change.
Year 8 Pakeha students averaged substantially higher than Pasifika
students, with a mean effect size of 0.51 (compared to 0.53 in 2001).
Compared to students for whom the predominant language at home was
English, students from homes where other languages predominated
averaged slightly lower, with mean effect sizes of 0.10 for year
4 students and 0.10 for year 8 students. Comparative figures are
not available for the assessments in 2001.
| SUMMARY
OF TREND INFORMATION |
In the 2001
report on Mathematics, evidence was reported on gains (from 1997
to 2001) in the areas of number, algebra and statistics. There was
little change in measurement or geometry at Year 4, and a small
decline in geometry at year 8. Linked with the current trend results,
this suggests that gains are continuing in algebra/statistics, but
that the gains in number have not been maintained. It should be
pointed out that from 1997 to 2001, gains were seen in number facts
as well as tasks involving more complex thinking skills. In 2005,
there is a clear decline in tasks involving number facts, but a
continued increase in the more complex tasks.
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