# Mathematics/Pāngarau: primary schooling

## What We Have Found

National Standards results for Year 1 to 8 students show that 75.4% of students are achieving at or above the standards for mathematics in 2016, a decrease of 0.1 percentage points from 2015. The proportions of Māori and Pasifika that are reaching the standard are lower than the overall proportion of students reaching the standard.

Ngā Whanaketanga Rumaki Māori Pāngarau results show that, in 2016, 55.9% of students learning Te Ine me te Āhuahanga, 62.0% learning Te Tau me te Taurangi and 53.4% learning Te Tauanga me te Tūponotanga achieved either manawa ora or manawa toa.

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

## Indicator Description

This mathematics indicator draws on three sources of information:

For state and state-integrated schools that use the New Zealand Curriculum, a summary of the National Standards mathematics results are provided. National Standards results are based on Overall Teacher Judgements (OTJs) about whether students in Years 1-8 were achieving at a level 'well below', 'below', 'at', or 'above' the standard in mathematics for their year level.

For state and state-integrated kura and schools that use Te Marautanga o Aotearoa (mainly Māori medium education schools), the Ngā Whanaketanga Rumaki Māori results in the pāngarau (mathematics) skill area are used. Ngā Whanaketanga Rumaki Māori (NWRM) are the Māori medium equivalent of National Standards.

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

### National Standards: Mathematics

Since 2011, schools which use the New Zealand Curriculum were required to report their National Standards results. Student achievement is reported at four levels: 'at', 'above', 'below' or 'well below' for the standard at their year level. The 2011 year saw the transition into National Standards data collection, and the data from that transition year has been excluded from analysis in this indicator . Of the 2,081 schools with Year 1-8 students which used the New Zealand curriculum in 2015, 2,063 provided National Standards data for mathematics.

#### How We Are Going

Since 2015, the percentage of students achieving at or above the National Standard in mathematics for their year level has decreased slightly by 0.1 percentage points, from 75.5% to 75.4%.

The difference in achievement between genders is least prominent in mathematics. However, Māori and Pasifika continue to achieve at a much lower rate than other ethnicities.

Figure 2: Proportion of students achieving at or above the National Standard for mathematics (2012-2016)

### Ethnic Group

In 2016 Asian students had the highest proportion of students learning at or above the math standard (83.7%), which was 2.9 percentage points higher than European/Pākehā (80.8%). Māori (65.3%) and Pasifika (62.7%) had the lowest rates.

The proportion of students achieving 'at' or 'above' has decreased slightly or had no change for most ethnicities apart from Asian which has had a slight increase. The proportion of Māori and Pasifika at or above the standard has decreased by 0.3 and 0.6 percentage points respectively with European/Pākehā having no change since 2015. The proportion of Asian students learning at or above the math standard has increased by 0.2 percentage points since 2015.

Figure 3: Proportion of students achieving at or above the National Standard for mathematics,
by ethnic group (2013-2016)

### Gender

The proportion of Year 1 to 8 male students achieving at or above the standard in mathematics is slightly lower than for female students. In 2015, 75.9% of females achieved at or above the standard compared to 75% of males.

Findings from TIMSS show no significant difference in mathematics performance for Year 5 males and females. These findings are discussed further in the International Comparison part of this indicator. It is important to note that the TIMSS findings are based on a sampling study of Year 5 students, whereas the National Standards results are based on the majority of all Year 1 to 8 students in New Zealand.

Figure 4: Proportion of students achieving at or above the National Standard for mathematics,
by gender (2012-2016)

### Decile

Decile provides a measure of the socio-economic status of a school's student body: the lower a school's decile is, the lower their school community's socio-economic status is. There is a clear relationship between school decile and National Standards achievement; as decile increases so does the proportion of students achieving at or above the standards for mathematics. In 2015 and 2016 the same general trend from lowest to highest decile is seen. The difference between decile 1 (58.9%) and decile 10 (86.0%) in 2016 was 27.1 percentage points.

This general relationship between mathematics and socio-economic status is consistent with international evidence from TIMSS which shows higher mathematics performance among students from areas of higher affluence. It is important to note that the TIMSS findings are based on a sampling study of Year 5 students, whereas the National Standards results are based on the majority of all Year 1 to 8 students in New Zealand.

Figure 5: Proportion of students achieving at or above the National Standard for mathematics,
by decile (2015-2016)

### Year Level

National Standards information is collected after a student has been at school for one year, after two years' attendance, after three years' attendance, and then annually for students in year levels four to eight. Because of differing assessment criteria and assessment tools for the different year level standards, direct comparisons of performance between year levels are fraught. Comparisons within year levels, across time, do not carry the same issues.

Between 2015 and 2016, there has been a decrease in the proportion of students at or above standard in mathematics within the first four years of schooling by 0.4 to 0.9 percentage points. Over this same period, there has been an increase in achievement for students in their last four years of schooling by 0.4 to 0.7 percentage points.

Figure 6: Proportion of students achieving at or above the National Standard for mathematics,
by year level (2012-2016)

### Ngā Whanaketanga Rumaki Māori: Pāngarau

The 2016 year was the fourth year for which kura and schools using Te Marautanga o Aotearoa reported their results for Ngā Whanaketanga Rumaki Māori. Due to a large difference in the sample of schools that supplied data over the last few years and an update in assessments, only figures from 2014 onwards are included in this indicator.

The Pāngarau (mathematics) component of Ngā Whanaketanga is made up of three categories: Te Ine me te Āhuahanga (Measurement/ Geometry), Te Tau me te Taurangi (Number/ Algebra) and Te Tauanga me te Tūponotanga (Statistics).

For each category in Ngā Whanaketanga students can be assessed as:

Manawa Toa
Kei runga noa atu. The student is progressing and achieving higher than expected for particular learning areas.

Manawa Ora
Kua tutuki Ngā Whanaketanga Rumaki Māori. The student is progressing and achieving as expected for particular learning areas.

Manawa Āki
E whanake tonu ana kia tutuki Ngā Whanaketanga Rumaki Māori. The student is progressing but requires further support to assist their achievement for particular learning areas.

Manawa Taki
Me āta tautoko kia tutuki Ngā Whanaketanga Rumaki Māori. The student requires in-depth support to assist their achievement for particular learning areas.

Of the 202 schools and kura with Year 1-8 students that were using Te Marautanga o Aotearoa in 2016, 131 provided Ngā Whanaketanga Rumaki Māori data. Of these, 96 provided data about students assessed for Te Ine me te Āhuahanga, 116 for Te Tau me te Taurangi, and 89 for Te Tauanga me te Tūponotanga.

### How We Are Going

In 2016, 55.9% of students learning Te Ine me te Āhuahanga, 62.0% learning Te Tau me te Taurangi and 53.4% learning Te Tauanga me te Tūponotanga achieved at either manawa ora or manawa toa. In comparison with 2015, this is a decrease of 1.4, 1.0 and 8.0 percentage points respectively.

Figure 1: Proportion of students achieving manawa ora or manawa toa in Ngā Whanaketanga for pāngarau (mathematics) categories (2015-2016)

### Ethnic Group

Over 99% of students that are assessed under Ngā Whanaketanga are Māori. There is only a very small absolute number of non-Māori students assessed using Ngā Whanaketanga. For this reason ethnic groups have not been separated out for comparison.

### Gender

The gender difference for pāngarau runs in the same direction as the National Standards differences for mathematics.

Kōtiro (girls) were more likely to be assessed as achieving either manawa ora or manawa toa than tama (boys) for Te Ine me te Āhuahanga (59.1% compared to 52.5%), Te Tau me te Taurangi (64.8% compared to 59.1%) and Te Tauanga me te Tūponotanga (57.1% compared to 49.5%). Both kōtiro and tama have seen decreases in achievement across most pāngarau strands with the exception of Te Ine me te Āhuahanga where achievement has increased by 0.3 percentage points for kōtiro since 2015.

Figure 2: Proportion of students achieving manawa ora or manawa toa in Ngā Whanaketanga for pāngarau
(mathematics) categories, by gender (2015-2016)

### Quintile

Decile provides a measure of the socio-economic status of a school's student body: the lower a kura or school's decile is, the lower their school community's socio-economic status is. Due to the small number of kura and schools (and therefore students) assessed using Ngā Whanaketanga, deciles have been grouped into quintiles. Because of the low number of kura and schools in quintiles 4 and 5, these quintiles have been further grouped for analysis. There were 80 kura and schools in quintile 1 (deciles 1 and 2), 23 in quintile 2 (deciles 3 and 4), 8 in quintile 3 (deciles 5 and 6) and 6 in quintiles 4 and 5 (deciles 7 to 10).

The relationship between quintile and the proportion of students achieving either manawa ora or manawa toa in pāngarau is not straightforward. Patterns differ based on pāngarau category and, even when pāngarau categories are grouped, the clear linear relationship that is seen for the mathematics National Standards is not seen clearly for Ngā Whanaketanga Rumaki Māori pāngarau.

Figure 3: Proportion of students achieving manawa ora or manawa toa in Ngā Whanaketanga for pāngarau
(mathematics) categories, by quintile (2015-2016)

### Whanaketanga Level

Rather than examining Ngā Whanaketanga results by year level, Ngā Whanaketanga is split up into Whanaketanga levels, much like how deciles are grouped into quintiles. Whanaketanga 1 includes Year 1 and 2 students, Whanaketanga 2 includes Year 3 and 4 students, Whanaketanga 3 includes Year 5 and 6, and Whanaketanga 4 includes Year 7+.

Drawing conclusions about the achievement of students in one Whanaketanga level compared to another within the same year is not advisable because of how assessment standards may differ from Whanaketanga level to Whanaketanga level. Comparisons within Whanaketanga levels, across time, do not carry the same issues.

Between 2015 and 2016 most Whanaketanga levels have shown a decrease in the proportion of students achieving manawa ora or manawa toa by pāngarau strand. Students in Whanaketanga level 1 had a decrease in achievement across all three strands by 2.6 to 8.5 percentage points. Other Whanaketanga levels had a mixure of increases and decreases in achievement (See Figure 9).

Figure 4: Proportion of students achieving manawa ora or manawa toa in Ngā Whanaketanga for pāngarau
by Whanaketanga level (2015-2016)

### International Comparison

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.

##### Table 1: Relative rankings of selected countries participating in 3 cycles of TIMSS
Notes:
1.   means the country mean score was significantly higher than the mean for all 12 countries.
2.   means the country mean score was signficantly lower than the mean for all 12 countries.
3. The mean for all 13 countries has been calculated by pooling all student results for the 13 countries and weighting so that each country contributes equally to the mean.
4. Standard errors are in parentheses.
Mean Mathematics Score
1994/95 2002/03 2014/15
Singapore 590 (4.5) Singapore 594 (5.6) Singapore 618 (3.8)
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)
Netherlands 549 (3.0) Netherlands 540 (2.2) England 546 (2.8)
Hungary 521 (3.5) England 531 (3.7) USA 539 (2.3)
USA 518 (2.9) Hungary 529 (3.2) Netherlands 530 (1.7)
Australia 495 (3.5) USA 518 (2.4)
Hungary 529 (3.2)
England 484 (3.3) Cyprus 510 (2.4)
Cyprus 523 (2.7)
Norway 476 (3.0) Australia 499 (3.9) Slovenia 520 (1.9)
Cyprus 475 (3.2) New Zealand 496 (2.2) Australia 517 (3.1)
New Zealand 469 (4.4) Slovenia 479 (2.5) Norway 493 (2.3)
Slovenia 462 (3.2) Norway 451 (2.2) New Zealand  491 (2.3)
Iran, Islamic
Rep. Of
387 (4.9) Iran, Islamic
Rep. Of
389 (4.2) Iran, Islamic
Rep. Of
431 (3.2)
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)

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, 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.

### Gender

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)

Note:
1.  Error bars on the graph provide a 95 percent confidence interval for the estimate of the mean.

### Socio-economic Status

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)

Note:
1.  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.

## References

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:

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

## Where To Find Out More

Education Data Requests