Indicators

# Mathematics achievement: primary schooling

## What We Have Found

Although there has been a significant improvement in New Zealand Year 5 students' mathematics performance overall since 1994, there are signs of an emerging downward trend in recent years, with a significant decline between 2002 and 2011.

Date Updated: October 2013

## Indicator Description

Mathematics scores for Year 5 students.

## Why This Is Important

Building a strong foundation in mathematics at a primary school level is important because it provides children with the basis to better understand and acquire new and advanced knowledge in mathematics as they continue in schooling. For children, having a solid foundation in mathematics will also play a major role in their day-to-day lives. It helps children to understand the use of time and money, being fair to others, recognising and generalising from symbols and patterns and interpreting information. It helps children to develop the ability to think creatively, critically, strategically, and logically, to make things, and to solve problems.

This mathematics indicator draws on the Trends in International Mathematics and Science Study (TIMSS) assessments, which included questions on whole numbers, decimals and common fractions, two- and three- dimensional shapes, estimation, data representation, and patterns and relationships.

## How We Are Going

Although there has been a significant improvement in New Zealand Year 5 students' mathematics performance overall since 1994, there are signs of an emerging downward trend in recent years, with a significant decline between 2002 and 2011. The overall mean mathematics score for New Zealand Year 5 students in 2011 was 486, up from 469 in 1994, but down from 496 in 2002. These mean mathematics scores are significantly lower than the TIMSS Scale Centre Point (500).

The spread of scores, from the 5th to the 95th percentiles, reduced between 1994 and 2011. Most of this reduction results from an improvement in the scores of the lowest performing students, with the 5th percentile increasing from 297 to 339.

New Zealand Year 5 students' mean performance in mathematics was significantly higher than 16 of the countries that also tested at Year 5 level but was significantly lower than 29 countries including all English speaking Nations tested. New Zealand’s mean mathematics achievement was not significantly different from that of students in four other countries: Croatia, Spain, Romania, and Poland.

Figure 1: Distribution of New Zealand Year 5 mathematics achievement in TIMSS from 1994 to 2011

Notes:
1. Standard errors are presented in parentheses.
2. Data for the small proportion of students assessed in Māori in 2002 (~2%) are excluded from this table to ensure comparability with data reported for 1994, 1998, 2006 and 2011.

There are four points on the TIMSS mathematics scale which make up international mathematics benchmarks; the advanced benchmark (625), the high benchmark (550), the intermediate benchmark (475), and the low benchmark (400). The performance of students reaching each benchmark is described in relation to the types of questions they answered correctly. Four percent of students reached the advanced benchmark in 2011. Fifteen percent of New Zealand Year 5 students did not reach the lowest TIMSS benchmark. In terms of the benchmark definitions, these were students who did not demonstrate some basic mathematical knowledge.

The proportion of students reaching the high and intermediate benchmarks, which peaked in 2002 (27% and 62% respectively), reduced significantly (23% and 58% respectively) by 2011.  Note that the proportion shown for the low benchmark also includes students who performed at the advanced, high, and intermediate benchmarks. This is because, by definition, students who could do the more complex questions associated with, for example, the high benchmark, would also be able to complete the easier questions associated with the intermediate and low benchmarks.

Figure 2: Percentage of New Zealand Year 5 students reaching the TIMSS mathematics benchmarks (1994 to 2011
)

Notes:
1. Standard errors are presented in parentheses.
2. 'At or above' means that the proportion of students at the benchmark includes those that achieved at higher benchmarks also.
3. Data for the small proportion of students assessed in Māori in 2002 (~2%) are excluded from this table to ensure comparability with data reported for 1994, 1998, 2006 and 2011.

Items in TIMSS at the Year 5 level were designed around three content areas of mathematics: number; geometric shapes and measures; and data display. The content area scores were calculated on the same scale as the overall mathematics score and therefore can be compared with the overall score.  New Zealand Year 5 students achieved significantly higher in 2011 in the area of data display and significantly lower in the areas of geometric shapes and measures and number. Compared with 2006, there were significant declines in the average scores for the areas of data display and geometric shapes and measures. The score for the number content area remained unchanged (change not significant).

Significant increases in mean achievement were observed for both girls and boys over the 17-year period from 1994 to 2011. However, there has been a significant decrease in the 9 years since 2002. As was the case in the previous assessments, there was no significant difference between Year 5 girls' and boys' mean performance overall. In terms of the content areas in TIMSS 2011, girls scored significantly higher than boys in Data Display but there were no significant differences in other content areas.

Table 1: New Zealand Year 5 students' mean mathematics scores in TIMSS, by gender (1994 to 2011)
Year
Mean
Girls
Boys
Overall
1994
474 (4.3)465 (6.1)469 (4.4)
1998
480 (6.0)482 (5.8) 481 (5.6)
2002
495 (2.8)496 (2.4)496 (2.1)
2006
492 (2.4)493 (3.1)492 (2.3)
2008
486 (3.3)486 (2.8)486 (2.6)
Notes:
1. Standard errors are presented in parentheses.
2. Data for the small proportion of students assessed in Māori in 2002 (~2%) are excluded from this table to ensure comparability with data reported for 1994, 1998, 2006 and 2011.

The average mathematics achievement of both Pasifika and Pākehā/European students has shown a significant increase since 1994. The increases for Māori and Asian students between 1994 and 2011 are not statistically significant. Between 2006 and 2011 there has been a significant decrease in the average mathematics achievement of Asian students and a significant increase among Pasifika students.

Table 2: New Zealand Year 5 students' mean mathematics scores in TIMSS, by ethnic group (1994 to 2011)
Year
Mean
European
/Pākehā
MāoriPasifikaAsianOtherOverall
1994493 (3.9)427 (8.2)412 (11.0)483 (16.9)~469 (4.4)
1998502 (5.0)445 (7.3)416 (15.1)516 (9.9)~481 (5.6)
2002506 (2.7)479 (4.8)464 (6.3)500 (6.0)504 (9.8)496 (2.1)
2006510 (2.1)453 (4.4)427 (5.1)546 (4.9) 491 (6.0)492 (2.3)
2011505 (2.6)
443 (4.5)
444 (5.6)
512 (5.7)~486 (2.6)
Notes:
1. Standard errors are presented in parentheses.
2. Data for the small proportion of students assessed in Māori in 2002 (~2%) are excluded from this table to ensure comparability with data reported for 1994, 1998, 2006, and 2011.
3. For this indicator ethnicity is prioritised in the order of Māori, Pasifika, Asian, Other (except European/Pākehā) and European/Pākehā.
4. For this indicator European/Pākehā refers to people who affiliate as New Zealand European, Other European or European (not further defined).  For example, this includes and is not limited to people who consider themselves as Australian (excluding Australian Aborigines), British and Irish, American, Spanish, and Ukrainian.
5. ~ There were too few students in the 'Other' ethnic grouping to reliably report achievement.

## Where to Find Out More

Mathematics achievement: middle
schooling

Mathematics literacy achievement:
senior secondary schooling