Under Part 28 of the Education Act 1989 the Chief Review Officer has the power to administer reviews either general or relating to particular matters, of the performance of applicable (pre-tertiary) organisations in relation to the applicable services they provide, and prepare reports on the undertaking and results of such reviews.
An exemplar report may be produced when ERO finds an organisation demonstrates effective practice in relation to specific aspects of performance.
ERO reviewed Aberdeen School to investigate its mathematics teaching approaches and strategies that have led to a significant increase in the number of students at or above standards in the upper primary school years (Years 5 to 8). We wanted to learn more about any short-term interventions or long-term strategies that may have been influential in bringing about these positive achievement trajectories.
Aberdeen School was selected from a database of 129 schools, with rolls over 200. The school was chosen because increased numbers of students were achieving at or above as they moved through Year 4 to Year 5. The school’s achievement levels were also higher than the average for their decile.
Before the review, we sent the school a set of discussion points and questions for leaders to consider. We asked leaders what they saw as the reasons for their positive achievement trajectory. We then looked for evidence of the approaches and strategies used, and the outcomes, by:
talking with children, parents, teachers, leaders and, where possible, trustees
observing in classrooms
looking at documentation, student work, class displays and the school environment.
National data shows that while many New Zealand children make good progress during their first three to four years at primary school the rate of progress slows during Years 5 to 8.
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.
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
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.”
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).
Just over three-quarters of New Zealand Year 5 students said they ‘liked’ learning mathematics. However, 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.
Leaders managed successful professional learning for teachers through the use of a variety of strategies to cater for their strengths and needs. They recognised, also, that they needed to do something immediately for children who had not been succeeding in mathematics under previous teaching practices. As a result they provided targeted support for these children, which successfully raised their achievement. These interventions led to the trialling of some approaches that were subsequently introduced across the school.
This report highlights the steps that this school took to support the mathematical learning of teachers and students. Leaders used both outside expertise and the strengths of their own teachers to bring about improvement. They worked collaboratively with staff to get buy-in and they made well-considered adjustments to PLD in response to the very variable outcomes.
Leaders wanted to increase the number of children succeeding in mathematics, especially in Years 4 and above. They had identified that more and more children were requiring additional support as they moved through the year levels and they were determined to halt this negative trajectory.
At the same time as they were beginning to redevelop their mathematics programme, leaders were also reviewing the impact of previous PLD designed to improve students’ writing. They observed that there had been a considerable time lag between identifying the challenges and implementing changes in the classroom. Leaders wanted to ensure that new mathematics practices were put in place more quickly, in all classes, so that the children could start benefiting from them.
When introducing new strategies, the leadership team found it helpful to think of the teachers as if they were learners in their classroom. Some were early adopters, some would be swept along with the momentum, and the remainder would lag behind. All were on a learning continuum, with some requiring more support than others. Leaders noticed that sometimes less-experienced teachers were more open to new learning, especially when it was tailored to their needs. Leaders had to work differently to get teachers who were uncomfortable with change to adopt new ideas and build on existing successful practice. This meant understanding these teachers’ needs, and, sometimes, working one-on-one with them.
Leaders and teachers worked closely with external PLD facilitators to improve mathematics teaching and learning. The facilitators extensively modelled new teaching strategies and supported improved leadership practices. Facilitators always took a team leader with them when they observed a teacher, and then reflected on their practice with them. Over the two years of the mathematics PLD, every observation was followed by a reflection in which the focus teacher was a full participant. Some teachers initially found these two-person observations and reflections challenging because they were not used to their practice being under the spotlight in this way. But it was by being involved at this level that team leaders came to understand the strengths and needs of each teacher and provide ongoing, responsive PLD. At the same time, leaders had numerous opportunities to develop their own coaching and mentoring skills, which helped strengthen the sustainability of the new directions.
In the first year of the PLD mathematics achievement in some classes and levels did not improve as hoped. However, because the school leaders had worked so closely with individual staff they knew which teachers were not confident with the changes, and were able to provide them with additional support. Leaders were also aware that that they needed to overcome any change-induced confusion before the new approaches could be embedded and have a lasting positive impact on the children’s learning. Leaders strategically partnered confident teachers with those who were less confident for the purpose of observing and supporting each other’s practice. In many cases the benefits were reciprocal.
Teachers changed their assumptions about mathematics teaching and altered their practices in response to what the research was telling them. Year 4 to 6 mathematics programmes had previously been structured to support the linear acquisition of discrete bits of mathematics knowledge and discrete skills. Teachers had streamed students across the teaching teams based on what they had mastered. Mathematics was taught separately from the rest of the curriculum to allow for this streaming.
Following discussions with the PLD facilitators about the pros and cons of this practice, and possible alternatives, teachers recognised that streaming had been disadvantaging children in the lower mathematics class. Not only were these children unlikely to experience the whole mathematics curriculum, they were unlikely to develop positive attitudes towards mathematics. It was decided therefore that, as from the beginning of 2016, teachers would teach mathematics to all the students in their own class.
Teachers successfully implemented the new approach and trialled additional strategies. After making this change, teachers generally grouped their children by ability within the class when teaching mathematics. Because mathematics was no longer isolated from the other learning areas, teachers were able to integrate mathematics learning across the whole curriculum. Teachers also saw that children who were previously in the lower group class were beginning to experience a wider variety of mathematics strategies with their peers. As a result, teachers in some classes were starting to experiment by working with mixed-ability groups and were using more authentic mathematics tasks linked to learning from other curriculum areas.
Leaders carefully analysed data to determine their next steps. Analysis of whole-school data showed school leaders that knowledge gaps become more apparent as the children moved through the year levels. They decided to approach this challenge in three ways.
They set more specific charter targets.
They worked on a longer-term goal to improve mathematics teaching at all year levels, to develop a more positive mathematics achievement trajectory for their children.
They introduced a short-term strategy that focused on children in Years 4 and 5, where the most gaps were identified.
Leader usefully focused on setting more specific charter targets. During the first year of the PLD, the school’s charter target was for 85 percent of children to meet the national standard for mathematics. Such general targets are of limited use because they do not make it clear what teachers should focus on to accelerate the progress of identified children or groups. In the second year, when the anticipated progress had not been made, leaders established much more specific targets, identifying the year levels, groups of students and operational domains they should focus on. These new targets provided much clearer direction and less incentive for teachers to concentrate overly on aspects of the curriculum where the children were already succeeding.
Teachers worked collaboratively to continue to develop school-wide mathematics programmes.
All teachers were involved in developing the school’s 2016 Curriculum and Achievement Plan, which outlined agreed actions that in response to the new charter targets. This plan was to be reviewed and further developed into the future. The plan identified what children should know by the end of each of the Years 1 to 6. It described how to identify who was in need of additional support and how to provide responsive programmes for them. Teachers of Years 1 to 3 focused on what they needed to do to ensure that children understood each of the specified concepts and were ready for the more advanced learning they would encounter in Year 4 and beyond. By working collaboratively on the progressions and actions, teachers deepened their own understanding of the curriculum and of the kinds of teaching and assessment that promote children’s conceptual understanding.
Teachers increased sense of urgency required more responsive teaching. Instead of waiting until a child was confident with every concept before moving them to the next level, teachers moved them to the level or stage appropriate for their age and then taught them what they needed to know to succeed at that level or stage. This more responsive teaching meant teachers had to clearly understand the children’s strengths and gaps, so they could anticipate and plan for any misconceptions children may encounter with a new concept.
Leaders carefully reviewed assessment processes used for moderation and programme planning purposes, and teachers made sure that they were now assessing learning across all the mathematics strands.Accepting that it was not enough just to know which stage a child was at on the number framework, teachers now assessed how confident they were on each of the three operational domains. Teachers recognised that it can be hard to make overall teacher judgments (OTJs) about children’s achievement in relation to someMathematics Standardsafter teaching just one strand of the curriculum for a few weeks – some standards require performance to be evaluated across numerous curriculum achievement objectives. They decided therefore to integrate the strands and be more specific about what children can do and what they need to work on.
By looking in greater depth at children’s mastery of skills and concepts, teachers were able to change the way they grouped children for targeted instruction. They became more selective about who needed to attend a particular teaching session. Improved analysis of assessment data helped them identify that sometimes, by focusing on a particular domain, they could see considerable gains in the children. Teachers changed from planning and teaching that matched the strand they were to focus on, to thinking more about what could be done to set children up for success.
Learner also successfully focused on a short-term strategy to accelerate learning.A mathematics support teacher was selected to help achieve improvement across all the year levels. Her role was to lead an intervention programme for Year 4 and 5 children and help teachers try the new approaches advocated by the PLD.
The teacher was a keen learner and enjoyed good relationships with other staff, including those who were hesitant to make the required changes. However, she was not particularly confident with mathematics. To increase her confidence she undertook a university mathematics paper. She became excited about mathematics teaching and enthusiastically shared what she was learning with colleagues. This teacher’s ability to learn new skills and work successfully with children and teachers, and her empathy for those who were struggling, were crucial when it came to supporting teachers to engage with new approaches and strategies and try them for themselves.
As well as undertaking some co-teaching, the support teacher ran the intervention programme, which was mostly for Year 5 children. This programme focused initially on improving attitudes towards mathematics. She taught the children how to try different approaches and to view mistakes as a resource for learning rather than evidence of their failure.
Throughout the programme the teacher used aTeaching as Inquirymodel to formally reflect on what was working for both children and teachers, and for whom it wasn’t working. This process helped her identify approaches and strategies that were effective in accelerating the progress of children who had previously been struggling. These approaches and strategies included:
making connections between prior knowledge and new learning
using equipment and visual representations to aid conceptual understanding and support discussion
introducing purposeful tasks that connect mathematics with real life
sharing and discussing mathematical thinking with peers
using theGrowth Mindsetapproach to increase confidence and self-efficacy.
The strategies that proved most successful in terms of embedding changes in the classroom were:
collaboratively developing a Curriculum and Achievement Action Plan. As a result of this process, all teachers understood their responsibilities for getting children to achieve to expectations and helping those who needed additional support.
recognising and celebrating evidence that children who had not previously been succeeding were now making accelerated progress
listening to and understanding teachers’ difficulties and successes with mixed-ability groups
using more equipment and visual representations
using rich tasks and integrating the mathematics strands across the curriculum.
As these comments show, the attitides of the target children to mathematics had also improved:
|February 2016||July 2016|
|Child A||I don't like maths. I like plusses and take aways. Maths is boring. You just sit and answer things.||I want to learn maths now. I like that there is lots of ways to work things out. Maths is doing problems that might be division, you get your answer by using strategies.|
|Child B||I don't like maths, take aways, times tables and division are too hard to solve. I want to get better at maths in case I get a job as a teacher.||
Maths is more interesting and fun. I like explaining to the group how I got my answers.
I know that making mistakes is learning.
I like working with a group so we can help each other and see what different answers we get.
Having a buddy and drawing pictures about my thinking helps me learn to do maths.
|Child C||I don't like maths. I find it hard. Maths is adding and taking away numbers.||
I feel more excited about maths now. I've learned lots of different ways to do maths.
Maths is thinking about how to solve problems, like real-life problems. New strategies, sharing my thinking with others and using cubes equipment help me to learn maths.
Implementation of these strategies required the combined efforts of the PLD facilitators, the mathematics support teacher and individual teachers. Together they made a real difference for most of the target children.
It is vital all schools have organisational structures, processes and practices that enable and sustain collaborative learning and decision making designed to continuously improve student achievement.
Many schools are able to describe a wide variety of things they were doing, yet often with little knowledge about which of these are contributing to improved achievement. It is just as important to know what is working as it is to know what the achievement issues are. Schools that focus deeply on a small number of areas or systematically practise teaching as inquiry are better able to identify approaches that warranted continuation or extension. They are also better able to monitor the impact of new strategies to determine whether they are accelerating the progress of students who had been achieving below expectations.
The exemplar highlights how progress accelerated when leaders employedtwo complementary approaches: initial short-term interventions that focused on identified students and longer-term PLD designed to improve mathematics teaching school-wide. Teachers 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.
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.Sometimes the practice of teaching as inquiry triggered changes. 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.
ERO recommends that school leaders continue their improvements and share with other schools their approaches related to:
leadership for excellence and equity
educationally powerful connections and relationships
effectiveness of mathematics teaching
evaluation and inquiry.
Deputy Chief Executive Evaluation and Policy
On behalf of the Chief Executive/ Chief Review Officer
7 June 2018