01 Using both long-term and short-term strategies to improve mathematics learning and achievement

ERO’s 2014 report Raising Achievement in Primary Schools identified that a quarter of the schools in the sample had strategically trialled and introduced new approaches to raise achievement. These schools implemented short-term strategies to improve achievement for groups of children and long-term developmental strategies to reduce achievement disparities.

Leaders at ABERDEEN SCHOOL 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 narrative highlights the steps 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 professional learning and development (PLD) in response to the very variable outcomes.

Leaders in this large school 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.

Focused professional learning and development

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.

“Relationships with our staff are as important as the relationships that they have with students. We model that. It’s about knowing your learners. Being a team leader enables you to get to know your staff really well.”

“When we started to see our teachers as learners, things changed. We reflected on that. We’ve seen that a one-size-fits-all model doesn’t work.”

Leaders

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.

Examining assumptions about mathematics teaching

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.

This image shows an example of prompts to remind children of strategies to use. In this image the are Think, Explain and Justify

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.

Managing improvements across the school

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.

  1. They set more specific charter targets.  
  2. 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.  
  3. They introduced a short-term strategy that focused on children in Years 4 and 5, where the most gaps were identified.

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.

Working collaboratively to develop school-wide mathematics programmes

All teachers were involved in developing the school’s 2016 Curriculum and Achievement Plan, which outlined actions that had been agreed in response to the new charter targets. This plan will 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 the kinds of teaching and assessment that promote children’s conceptual understanding.

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 gave teachers a greater sense of urgency and required more responsive teaching. 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 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 some Mathematics Standards after 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.

Focusing 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 Years 4 and 5 children and help teachers try the new approaches advocated by the PLD.

This 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.

This image shows some of the discussion prompts use which are I have a question about, Its ok take your time, how do you know your answer is correct, so what you are saying is, I dont understand, would someone like to add on, could you explain that to me another way and I agree because

Throughout the programme the teacher used a Teaching as Inquiry model 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 the Growth Mindset approach 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.

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.

At the beginning of the year, 27 Year 5 children were identified as ‘below’ or ‘well below’ national standards for mathematics. At the end of the year, six children were assessed as ‘below’ or ‘well below’ the relevant standard while 18 were assessed as ‘at’ the standard and three ‘above’.

As these comments show, the attitudes 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.

Working with individual children and their parents

At mid-year the deputy principal noticed that not enough Year 4 children who had previously been at the expected level were making sufficient progress for the school to meet its targets for mathematics. She analysed the data to determine which children were not progressing, and in which domains. She then took this information to the teachers of Year 4 children and asked for their suggestions on how to address it.

The teachers worked with the deputy principal on strategies to reduce the number of children in the ‘below expectations’ category by the end of the year. They saw that while the children were generally confident with addition/subtraction and multiplication/division, they were not confident with proportions/ratios. They immediately adjusted their programmes to address this. They also recognised that, when working with the 22 children who were below the expected level, they could increase the impact of their teaching by involving the parents.

“We contacted the parents and said something like, ‘Your child has the potential to reach the standard if we work together.’ They wanted to know how they could help. We said we would give the children things they needed to work on, and gave the parents really specific examples of how to help. The parents were all on board and were really pleased we were doing something."

Deputy principal

Before the school holidays, the teachers met with the target children. The children talked about what they needed to do to achieve the expected level and how they could take more responsibility for their learning. The teachers gave the children carefully chosen, manageable mathematical tasks to do at home in the holidays. They made personalised books for the children in which every activity was included for a specific purpose. They didn’t want to overload the children so some of the tasks consisted of family games and activities. The children responded really well to the extra mathematics. They enjoyed working with their parents and grandparents. They told ERO evaluators that they were keen to continue during the upcoming Christmas holidays.

“I’ve been learning lots and lots at school, and lots and lots at home. We did some holiday maths so that we could get onto Level 2. I got a lot of help because some was pretty hard and Grandad said, ‘I’ll come and help you.’ Since I kept practising, I moved up a level. Grandad was really proud of me.” “I got really, really better. It was awesome. You got to learn stuff that was easy but the right level. Everyone got the right level for them.”

Year 4 students

At mid-year interviews the teachers shared the children’s successes with theirparents and outlined next steps.

Leaders established that it was a variety of strategies, not just one thing, which had made the difference for these children. The most effective strategies were:

  • closely scrutinising the achievement data
  • working in partnership with parents
  • being vigilant and working with children every day in a targeted way, breaking down mathematics tasks as required to support their learning.

“Rather than just saying ‘this student is below’, it was about finding the one or two areas and realising that [success] is achievable. The information was framed to parents as: ‘Your child has the potential to get there. If we all work together, we can achieve this.’”

Leaders