This Education Review Office (ERO) report is one of a series of reports on teaching strategies that work. It features strategies and approaches that we observed in 40 primary schools selected from across New Zealand. These schools came from a database of 129 schools, all with rolls of 200 or more, in which the proportion of students in the upper primary years (Years 5 to 8) achieving at or above the national standard had increased. In each case achievement levels were also above average for the decile.

We asked leaders in each school what they saw as the reasons for their school’s positive achievement trajectory and then investigated the teaching strategies that had been implemented, and the outcomes.

This report shares some of the strategies and approaches used by schools that had focused on improving achievement in mathematics. It also shares some of the simple strategies used in classrooms where achievement in mathematics had been accelerated.

Why did we focus on mathematics in the upper primary school?

Recent National Monitoring Study of Student Achievement (NMSSA) reports have found that many more Year 4 than Year 8 students are achieving at the expected curriculum level. The most recent report, NMSSA mathematics and statistics report, 2013, found that while 81 percent of Year 4 students were performing at Level 2 as expected, only 41 percent of Year 8 students were performing at the expected Level 4. The report also found that Year 8 students were less positive about mathematics than Year 4 students. The box-and-whisker chart at right highlights this decline in positive dispostion.

This figure show the maths scale score.  It is a box and whisker chart that shows from 2013 81% of year 4 students were performing at level 2 but that only 41% of year 8 students were performing as expected level.

Assessment Tools for Teaching and learning (asTTle) norm data also indicates the need for many children to progress through the levels more quickly in the upper primary school. If most children were progressing well, our national norms would show changes of about three sublevels every two years. However, data for the mathematics asTTle norms for the 2010 cohort indicated that the achievement trajectory does not ensure most children will reach Level 4A by the end of Year 8.

These concerns, based on primary school data, are reinforced by Programme for International Student Assessment (PISA) testing of high school students. PISA reports that New Zealand is one of very few countries in which the mathematics and science achievement of 15-year-olds is on a trajectory of accelerated decline.

Further, PISA data show that within the same school young people can experience widely divergent opportunities to learn. This within-school disparity, one of the highest in the participating countries, means that within-school variation in student achievement is very large compared with that of countries in a similar position on the table.

PISA data also show that New Zealand has one of the highest proportions of students attending schools where they are grouped by ability across and within mathematics classes. And, in New Zealand, the impact of these four factors on mathematics achievement is particularly significant:

  • exposure to formal mathematics
  • teacher–student relations
  • disciplinary climate
  • truancy
Quarter Year Mean Score

Mathematics: Mean 

Curriculum Levels

1 4 1358 2P
2 4 1364 2P
3 4 1375 2P
4 4 1389 2A
1 5 1400 2A
2 5 1410 2A
3 5 1420 3B
4 5 1430 3B
1 6 1441 3P
2 6 1451 3P
3 6 1460 3P
4 6 1466 3P
1 7 1472 3P
2 7 1479 3A
3 7 1489 3A
4 7 1500 3A
1 8 1512 4B
2 8 1521 4B
3 8 1529 4P
4 8 1535 4P

The 2014/15 Trends in International Mathematics and Science Study (TIMMS) found that “although New Zealand’s mean achievement in mathematics has increased since 1994/95, many other countries have increased by more. New Zealand Year 5 students’ mean mathematics achievement was significantly higher than 13 countries, but lower than the mean score of 33 countries, including all the other predominantly English-speaking countries who participated.”

The TIMSS test contained questions that went beyond what the New Zealand curriculum requires of Year 5 students, but even when these were removed, the mean outcome was that students correctly solved fewer than half the items. Six percent of the tested students were classified as ‘advanced’ performers while 16 percent were classified as ‘below low’, unable to perform simple mathematical tasks. This wide range of achievement was greater in New Zealand than in other high performing countries and in the predominantly English-speaking countries.

The TIMMS report found that, compared with Year 5 teachers in other countries, New Zealand teachers made less use of whole-class teaching and more of group activities. They frequently used ability grouping and more often had students work on problems, individually or with peers, while they occupied themselves with other tasks. In New Zealand classrooms, activities that involved the teacher explaining new mathematics content or how to solve problems or asking students to memorise rules, procedures and facts were less likely to be part of nearly every lesson.

Although New Zealand teachers reported that at least eight in every 10 students had been taught all the topics tested, some specific strengths and weaknesses were revealed in the results. Students did significantly better at applying their knowledge and reasoning, compared with the cognitive behaviour of knowing (a consistent pattern since 2006/07). They did best on data display questions, which was the curriculum area most likely to be covered by their teachers. The topics least likely to be covered in class were comparing and drawing angles (40 percent); concepts of decimals, including place value and ordering, and adding and subtracting with decimals (62 percent); and using informal coordinate systems to locate points in a plane (67 percent).

Although just over three-quarters of New Zealand Year 5 students said they ‘liked’ learning mathematics, the score on this indicator was less positive than the mean for all participating countries. More students described themselves as ‘not confident’ and fewer as ‘very confident’ in mathematics. They were positive about how their teacher engaged with them in the mathematics classroom, but fewer found their mathematics lessons ‘very engaging’ compared with the international average.

What does ERO already know about mathematics in primary schools?

Mathematics in Years 4 to 8: Developing a responsive curriculum (February 2013)

This report identified the need for more schools to use their achievement information as a basis for regularly reviewing and adapting their mathematics curriculum to make sure it responds to the strengths and needs of all students.

Most schools were able to identify those learners who were not achieving at the relevant national standard but many persisted with the same teaching strategies, programmes and initiatives instead of using the information they had to develop or replace them in response to known needs.

Most teachers used ability grouping within or across classes and many were relying on teacher aides to accelerate the progress of priority learners. Few had evidence that such strategies were actually working to enhance learning or achievement. ERO cautioned against the use of inadequately qualified adults to work with those learners who most needed expert teaching. A key finding of the report was that grouping by ‘ability’, whether in-class or across classes, disadvantages students.

Raising achievement in primary schools: Accelerating Learning in Mathematics (ALiM) and Accelerating Literacy Learning (ALL) June 2014

This report shared how some primary schools were using the Ministry-funded support projects Accelerated Learning in Mathematics (ALiM) and Accelerated Learning in Literacy (ALL) to enhance learning and raise achievement.

The report found that, in schools where teachers’ involvement in the ALiM and ALL projects had accelerated children’s progress,

  • students were active partners in designing their own learning plans; they were supported to monitor their own progress; they knew what they needed to learn next; and they were able to provide feedback about the teaching actions that worked for them. 
  • parents and whānau were formally invited to be part of the process; they were involved in workshops to develop home activities and in frequent, regular, three-way conferencing in which teachers emphasised progress and success.
  • teachers knew they were expected to critique the effectiveness of their practice and to make changes; they had a willingness to seek both positive and negative evidence of progress; and they were open to new practices that make a difference.

Raising Achievement in Primary Schools June 2014

In this June 2014 document ERO described how strategic and successful schools had a long-term commitment to improvement through deliberate, planned actions designed to accelerate student progress. These effective schools were highly strategic and evaluative when trialling new approaches and innovations.

The report found that, for schools to be effective in accelerating student progress,they needed:

  • leadership capability
  • teacher capability
  • leaders and teachers with assessment and evaluative capability
  • leaders with the capability to develop relationships with students, parents,whānau, trustees, and other teaching professionals
  • leaders and teachers with the capability to design and implement a curriculum that engaged students.

These schools also had a focus on equity and excellence.

What did we find overall?

In schools where mathematics achievement was improving, and leaders knew the reasons for this improvement, teachers had usually participated in well-planned and targeted professional learning and development (PLD). Leaders had identified each teacher’s strengths and needs and then organised internally or externally facilitated PLD to respond specifically to those needs. They carefully selected teachers from within the school who could lead development work successfully with their colleagues to spread the agreed practices. They made time available for these selected leaders to increase their own knowledge and to work with others.

Many of the 40 schools we visited had successfully identified the children who needed additional support in mathematics. What made the difference in the schools that had succeeded in accelerating achievement was that they had employed two complementary approaches: initial short-term interventions that focused on identified students and longer-term PLD designed to improve mathematics teaching school-wide. These schools moved from an intervention model aimed at ‘fixing the children’ to a collaborative model where teaching professionals assumed collective responsibility for improving teaching, thereby reducing the need for future interventions. They refused to accept that so many children were simply not good at mathematics.

The PLD could not be rushed because it often took teachers time to come to terms with the fact that they needed to teach the whole mathematics and statistics curriculum. They gained confidence to do this as they grew their knowledge of all the strands and looked in detail at what children should be learning at each of the first three or four curriculum levels. Some schools integrated number concepts across the strands and/or collaboratively documented the specific knowledge and skills children needed to acquire at each level.

In other schools, the changes were triggered by the practice of teaching as inquiry. Either individually or in groups, teachers recognised that they needed to do something different if they were to accelerate the progress of particular students. They researched best practice, tried something new, and then checked its impact on the students concerned. As a further step, they worked collaboratively with other teachers to spread practices that proved effective.

PLD and inquiries usually focused on both content knowledge and teaching practice. Teachers examined their assumptions about what children need for success in mathematics – particularly their own assumptions about their teaching for children who needed additional support.

Most of the schools that had improved achievement in mathematics had reviewed and completely changed the way they taught students. Some had previously paid little attention to or even omitted sections of the curriculum and now wanted to ensure that their students engaged with the whole curriculum. Teachers revised their long-term plans and guidelines and/or extended children’s opportunities to learn by integrating mathematics into other curriculum areas. They recognised that although number and algebra are vital, if students are to be successful in mathematics they must also engage fully with learning in geometry, measurement and statistics.

For many of the schools the most fundamental change was the implementation of mixed-ability group instruction within an authentic and rich curriculum. Teachers realised that their previous practice of grouping by ability within or across classes seriously disadvantaged children in the lower groups, who were denied access to the whole curriculum and had negative perceptions about their mathematical ability reinforced. Streaming children into different classes for mathematics separates mathematics from the rest of the curriculum. By abandoning this practice, teachers found they were able to more effectively integrate mathematics into authentic contexts that they were using in their classrooms.

As a first step teachers usually tried mixed-ability grouping for some of the time while they monitored outcomes. They used strategies such as talk moves to deliberately teach the children how to engage in problem-solving discussions with peers, facilitating workshops with groups of children who needed to practise particular processes or skills.

talk moves
Teacher move: What a teacher does:

Repeats some or all of what the student is saying and then asks the student to respond and verify whether it is correct

Repeating Asks students to restate someone else’s reasoning
Reasoning Asks students to apply their own reasoning to someone else’s reasoning
Adding on Prompts students for further participation
Waiting Waits in silence

One of the principles of ‘talk moves’ is to carefully orchestrate talk to provide for equitable participation by all learners.

Over time, teachers saw that mixed-ability grouping practices also had benefits for more able mathematicians, who, when working with peers, had to think deeply about alternative solutions. Teachers found that children in mixed-ability groups had greater understanding of their learning, were better able to recognise achievement and progress, and knew what they had to do to improve. Many of those who had previously been in ‘bottom’ groups talked to us about how their confidence in and enjoyment of mathematics had increased since working in flexible, mixed-ability groups.

When introducing new approaches and strategies, the teachers in some schools worked closely with parents and whānau. This was particularly important for schools abandoning the practice of cross-grouping. At special mathematics evenings, leaders in some schools provided parents with group problem-solving activities to help them understand the benefits of working in mixed-ability groups. Other schools focused on communicating regularly with the parents and whānau of children in need of additional support so that they were kept fully aware of what was working for the child and what progress they were making.

Some schools, which had been involved in the Ministry of Education’s ALiM, had triggered the need for more extensive PLD. For others, it had involved replacing withdrawal-type interventions with in-class interventions, where ALiM leaders supported teachers to provide children with additional assistance while they continued to learn alongside and with their peers. The ALiM teachers were able to introduce collaborative reflection and sharing of practices that extended into other areas of the curriculum. Some approaches were so successful that the board of trustees in two schools allocated resources to enable them to be introduced more widely.

Leaders played a crucial role in ensuring a coherent approach to professional learning. They identified and developed internal expertise. They accessed external expertise that was relevant to teachers’ needs and aligned with the school’s vision and values. They actively involved parents and whānau, seeking their perspectives and communicating changes. They identified teachers who needed extra support to implement change and they provided the necessary support in innovative ways. They made time available for teachers to look deeply into their own content knowledge and pedagogy. These were all factors contributing to positive achievement trajectories for students.