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.
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 know, think and 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, 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 materials. Their responses are presented orally, by demonstration, in writing, in computer files, or through other physical products. Many of the responses are recorded on videotape for subsequent analysis.
Key Results
Number and alegebra
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.
Measurement
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.
Geometry
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.
Statistics
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.
Mathematics Survey
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.
Performance of subgroups
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 Māori, 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 Māori 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.