Student performance in mathematical literacy

Means and distributions of performances

As shown in Figure 1, the mean mathematical literacy performance of New Zealand 15-year-olds was 522 scale score points, significantly above the mean for the 30 OECD countries (hereafter referred to as the OECD mean). The mean mathematical literacy scores for New Zealand in 2003 and 2006 are not significantly different. Figure 1 also includes other participating countries, with an indication of whether their results were higher, similar or lower than those for New Zealand. The 15-year-old students in only five countries - Chinese Taipei (549), Finland (548), Hong Kong-China (547), Korea (547), and the Netherlands (531) - had significantly higher mean mathematical literacy achievement than New Zealand 15-year-olds. This is the same group of countries as in 2003, with the addition of Chinese Taipei, a new participant in PISA in 2006.

Students in Switzerland (530), Canada (527), Macao-China (525), Liechtenstein (525), Japan (523), Belgium (520), and Australia (520) had similar mean scores to New Zealand 15-year-old students (that is, tests of significance showed no statistical difference). Students in the United Kingdom (495) and the United States (474) had significantly lower mean mathematics literacy than in New Zealand.

Figure 1 also shows the distribution of achievement across 15-year-olds within each country. The outer limits of achievement among New Zealand 15-year-old students range from 368 scale score points at the 5th percentile to 674 at the 95th percentile. Presentation of the percentiles demonstrates that there is a range in mathematical literacy achievement in New Zealand: from students that would be considered average in lower-achieving countries to those that would be considered exceptional in nearly all countries. An examination of this range shows that in comparison to other countries there was a relatively wide range of achievement in New Zealand (306). Finland (266), Macao-China (276), Canada (281) and Australia (289) were among the countries with narrower ranges of achievement than New Zealand. However, the range in Hong Kong-China (306) was the same as that of New Zealand, while Chinese Taipei had a much wider range (333).

Although the range from the 5th to the 95th percentiles is shown, it may be more beneficial to look at the interquartile range, as the 5th and 95th percentiles tend to have a greater degree of uncertainty associated with them. The interquartile range for New Zealand in 2006 is 129, similar to the OECD average (125) and to the interquartile ranges found in Hong Kong-China (128), the Netherlands (129) and Korea (127). This range is also similar to that found in 2003 (138). Of the other high-performing countries, Finland had a lower interquartile range (111), and Chinese Taipei had a larger one (148).
 

Interpretation of percentiles

The percentages of students performing below or above particular points on the scale are shown for each country.  The lowest outer limit is the 5th percentile – the score at which only 5% of students achieved a lower score. The highest outer limit is the 95th percentile – the score at which only 5% of students achieved a higher score. The middle 50% of students achieved scores between the 25th and 75th percentiles, shown on Figure 1 as the darkly shaded section of each bar.

 
Figure 1: Means and distributions of mathematical achievement in PISA 2006

Note: * denotes non-OECD (partner) countries. These countries are not included in the OECD average.

Proficiency levels and relative performances across countries

Nearly six percent of New Zealand students were proficient at the highest proficiency level, Level 6, and were deemed capable of advanced mathematical thinking and reasoning. A further 13 percent of students were proficient at the second highest level, Level 5. At the lower end of the spectrum, ten percent of students were proficient at Level 1; these students were deemed capable of answering questions involving familiar contexts and clearly defined questions. Four percent of students achieved below proficiency Level 1, and were therefore deemed unlikely to demonstrate success on the most basic type of mathematics that PISA seeks to measure. The proportions of students achieving at each proficiency level have not changed since 2003.

As illustrated in Figure 2, a larger proportion of New Zealand students (6% and 13%), when compared with the average internationally, were found in the top two proficiency levels (3% and 10% for Levels 6 and 5, respectively, on average for OECD countries). The Czech Republic (18%), Japan (18%), Liechtenstein (18%), Canada (18%), Belgium (22%), and the Netherlands (21%) had similar proportions of students in the top two proficiency levels, while Chinese Taipei (32%), Hong Kong-China (28%), Finland (24%), Korea (27%), and Switzerland (23%) had significantly higher proportions in these top two levels.

Compared to other countries, New Zealand had a high proportion of students proficient at least at Level 3, with two-thirds proficient at this level or higher. Other OECD countries with notably large proportions of students (higher than two-thirds) proficient at Level 3 or higher include Korea, Switzerland, Canada, Finland, the Netherlands and Japan.

There has been some concern in New Zealand about the ‘tail of under-achievers’. Lower achievers can be defined in PISA as those who performed at Level 1, which means they can only complete simple mathematical tasks, and those who performed below Level 1 on the PISA mathematics questions. At this end of the proficiency scale it is most desirable to have a small proportion or no students performing at this level. New Zealand had fewer lower achievers than on average across OECD countries, with 14 percent performing at Level 1 or below compared with 21 percent on average across OECD countries. However, a number of countries had a smaller proportion of students performing at Level 1 or below, notably the higher-performing countries such as Finland (6%), Korea (9%), Hong Kong-China (10%), Macao-China (11%), the Netherlands (12%), and Chinese Taipei (12%). In comparison, Australia had a similar proportion of students performing at Level 1 or below (13%), while the United Kingdom (20%) and the United States (28%) had much larger proportions of students performing at these levels.

Although New Zealand’s overall performance is very high in comparison with most other participating countries, a relatively wide spread of achievement persists. In seeking to understand the reasons for this distribution in mathematical literacy it is important to put the achievement of students in context. In the following sections, the distributions of mathematical literacy achievement are compared for major sub-groupings in the population in order to build a better understanding of factors associated with variations in student achievement.
 

Figure 2: Percentage of students at each of the mathematical literacy proficiency levels

Note: * denotes non-OECD (partner) countries. These countries are not included in the OECD average.