Mathematics/Pāngarau: primary schooling
What We Have Found
International testing shows a significant improvement in New Zealand Year 5 students' mathematics performance over the period 1994 to 2014, but there has not been a significant change in their performance since 2002/03; the overall mean mathematics achievement of New Zealand Year 5 students in 2014 is not significantly different from 2002, 2006, and 2011.
Date Updated: August 2017
This mathematics indicator draws on the following sources of information:
An overview of selected findings from the Trends in International Mathematics and Science Study 2014/2015 (TIMSS 2014/2015) is also included. The TIMSS assessments included questions on whole numbers, decimals and common fractions, two- and three- dimensional shapes, estimation, data representation, and patterns and relationships.
Why This Data is Important
In 2017, the Government set a target of 80% of Year 8 students will be achieving at or above the National Standard in mathematics, or at Manawa Ora or Manawa Toa in Ngā Whanaketanga Rumaki Māori pāngarau.
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 use of time and money, being fair to others, recognising and generalising from symbols and patterns, interpreting information, thinking systematically, making things, and solving problems.
A healthy knowledge of mathematics and pāngarau will mean that children and young people will have more opportunities to progress in their learning and more choices in their transition into further education, training and employment.
Progress against Target
The Government has set a target of 80% of Year 8 students will be achieving at or above the National Standard in mathematics, or at Manawa Ora or Manawa Toa in Ngā Whanaketanga Rumaki Māori pāngarau.
In 2016, 70.6% of students at the end of year 8 were achieving at or above the National Standard in mathematics, or at Manawa Ora or Manawa Toa in Ngā Whanaketanga Rumaki Māori pāngarau. This is an increase of 3.8 percentage points since 2012. Limited progress is being made towards this target, but faster improvement is required to reach it by the end of 2021.
Figure 1: Proportion of students achieving 'At' / 'Above' or 'Manawa Ora' / 'Manawa Toa' in Mathematics/Pāngarau
In addition to using National Standards and Ngā Whanaketanga Rumaki Māori to examine mathematics achievement trends within New Zealand, the Trends in International Mathematics and Science Study (TIMSS) results are used to examine primary-aged students' (Year 5 students in New Zealand) mathematics performance in relation to other nations and education systems. TIMSS has been conducted every 4 years since 1994. The tests are run at the end of the school year. The sixth cycle of TIMSS was conducted in 2014 in Southern Hemisphere countries and in 2015 in Northern Hemisphere countries. Hence it is referred to as TIMSS 2014/15 in New Zealand. New Zealand is one of 49 countries that took part in this cycle.
How We Are Going
New Zealand Year 5 students' mean performance in mathematics was significantly higher than 13 of the countries that also tested at Year 5 level in TIMSS 2014/15 but was significantly lower than 33 countries including Singapore, England, the United States, and Australia. New Zealand's mean mathematics achievement was not significantly different from that of students in two other countries: France and Turkey. New Zealand had the second lowest mean score of all English speaking nations tested after South Africa.
The table below presents New Zealand's relative ranking in mathematics achievement compared with the other countries who have participated in TIMSS in 1994/95, 2002/03, 2014/15. Of all the 49 countries that participated in TIMSS 2014/15 at the middle primary level, only 13 have participated in all these three cycles.
The mean mathematics achievement in New Zealand has been below the mean for the 13 trend countries in each cycle. In addition, while the mean for New Zealand has increased compared with 1994/95, so has the mean for all 13 countries. Therefore the ranking of New Zealand among these 13 countries is at its lowest in 2014/15 compared to the previous cycles. Note that relative rankings do not demonstrate significant differences between countries. Standard errors are provided so that significance between two countries can be calculated if desired.
|Mean Mathematics Score|
|Japan||567||(1.9)||Hong Kong SAR||575||(3.1)||Hong Kong SAR||615||(2.9)|
|Hong Kong SAR||557||(4.0)||Japan||565||(1.6)||Japan||593||(2.0)|
|Mean for all 13||504||Mean for all 13||514||Mean for all 13||534|
There has been a significant improvement in New Zealand Year 5 students' mathematics performance in TIMSS over the period 1994 to 2014, but there has not been a significant change in their performance since 2002/03. The overall mean mathematics score for New Zealand Year 5 students in 2014 was 491, up from 469 in 1994 and not significantly different 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 2014, however has been widest since 2002. Most of the reduction results from an improvement in the scores of the lowest performing students, with the 5th percentile increasing from 297 in 1994 to 335 in 2014.
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. Six percent of New Zealand Year 5 students reached the advanced benchmark in 2014, while sixteen percent did not reach the lowest TIMSS benchmark. In terms of the benchmark definitions, these were students who did not demonstrate some basic mathematical knowledge.
Figure 2: Percentage of New Zealand Year 5 students reaching the international TIMSS mathematics benchmarks (1994 to 2014)
- Standard errors are presented in parentheses.
- At or above" means that the proportion of students at the benchmark includes those that achieved at higher benchmarks also.
- 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, 2011 and 2014.
The proportions of students reaching the high and advanced benchmarks significantly increased from 23% and 4% respectively in 2011 to 26% and 6% respectively in 2014. Due to these increases, the proportions of students reaching each benchmark in 2014 were similar to those in 2002. 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.
Significant increases in mean achievement were observed for both girls and boys overall for the 20-year period from 1994 to 2014, even though the achievements for both genders in 2014 are similar to those in 2002. As was the case in the previous assessments, there was no significant difference between Year 5 girls' and boys' mean performance overall. This is consistent with findings for the international male and female average scores in mathematics in TIMSS 2014/2015: no significant difference was found. In terms of the content areas in TIMSS 2014, there were no significant differences between the achievement of boys and girls. However, boys scored significantly higher than girls in the cognitive domain of knowing, while being similar in applying and reasoning.
The 2014 international gender comparison in mathematics achievement differs from the 2014 National Standards data where there is a slight gender difference in females' favour. Ngā Whanaketanga 2014 results also show a gender disparity, with females more likely to be manawa ora or manawa toa in Te Ine me te Āhuahanga and Te Tau me te Taurangi categories. It is important to note that the TIMSS research is based on a sample of only Year 5 students, whereas National Standards and Ngā Whanaketanga include all Year 1 to 8 students under at least one of the two assessment types.
Figure 3: Mean TIMSS mathematics scale scores, by gender (2014)
- Error bars on the graph provide a 95 percent confidence interval for the estimate of the mean.
Principals in all TIMSS countries were asked to provide estimates, using a four-point scale—'0–10%', '11-25%', '26-50%', and 'more than 50%'—of the proportions of students in their school that came from economically disadvantaged backgrounds and the proportion coming from economically affluent homes. Analysis showed that New Zealand principals' estimates of economic composition aligned very well with the Ministry of Educations decile for their schools and vice versa.
Internationally, all principals' responses to the questions on the two socio-economic measures (economically disadvantaged vs. economically affluent) were then aggregated in order to describe the overall student body: schools that had proportionally more disadvantaged than affluent students (i.e. more than 25% from economically disadvantaged homes and 25% or fewer from economically affluent homes) and schools with more affluent than disadvantaged students (i.e. 25% or fewer students from economically disadvantaged homes and more than 25% of students from economically affluent homes).
The mean mathematics performance of Year 5 students increases as the aggregated level of socio-economic rating increases both for New Zealand and internationally. However, the gradient of change in performance between the levels is steeper for New Zealand than internationally. Economic differences seem to have a greater impact on New Zealand student achievement than internationally.
Figure 4: Mean TIMSS mathematics scale scores by economic composition (2014)
- The points represent the mean scores, and the lines extending from the points represent the 95% confidence interval, i.e. the range in which we are 95% confident that the true population value lies.
Evidence about what works for this indicator can be found in:
- Caygill, R., Singh, S., & Hanlar, V. (2016). TIMSS 2015: New Zealand Year 5 Mathematics Results. Wellington: Ministry of Education.
- Mullis, I.V.S., Martin, M.O., Foy, P. & Arora, A. (2016). TIMSS 2015 International Results in Mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
- Ministry of Education (2008). Te Marautanga o Aotearoa. Wellington: Ministry of Education.
- Ministry of Education (2007). The New Zealand Curriculum. Wellington: Ministry of Education.
The Ministry of Education has established an Iterative Best Evidence Synthesis Programme to systematically identify, evaluate, analyse, synthesise and make accessible, relevant evidence linked to a range of learner outcomes. Evidence about what works for this indicator can be found in:
- Quality Teaching for Diverse Students in Schooling: Best Evidence Synthesis
- Spotlight on Mathematics/Pāngarau: Best Evidence Synthesis
The Ministry of Education also reports on results from the National Standards School Sample Monitoring and Evaluation Project 2010-2013, a three year project on National Standards implementation in a representative sample of schools. Recent results can be found in the National Standards: School Sample Monitoring and Evaluation Project 2011 publication.
Summaries of the National Standards and Ngā Whanaketanga Rumaki Māori data that includes the years that were transitions into collection are available at: National Standards/Ngā Whanaketanga Rumaki Māori on Education Counts.Regional and territorial authority data on current year educational measures, including National Standards and Ngā Whanaketanga Rumaki Māori, are available at: Know Your Region
School level data for individual schools, including National Standards and Ngā Whanaketanga Rumaki Māori information, can be found at: Find a School