4. Successfully responding to an achievement issue in mathematics

Cover of 4th narrative

West Gore School in Southland has a roll of around 250 students in Years 1 to 6. Most are Pākehā/European. About one-sixth are Māori.

Leaders believe that one of the features that contributed to their school’s positive achievement trajectory is their focus on interrogating the data to determine how their teaching is impacting on children’s outcomes. The rigour and honesty with which they do this helped them address an identified dip in mathematics achievement.

Addressing the issue involved:

  • identifying the achievement issue and the associated learning needs of children and teachers
  • deciding on and applying short-term strategies to help children who were below the expected level
  • introducing new teaching strategies and approaches to reduce the risk of an achievement dip in the future.

Identifying the achievement issue and related needs

Achievement data always came under close scrutiny when reports were being prepared for the board of trustees. When scrutinising the data, leaders and trustees asked:

  • What do we know from the data?
  • How do we know this?
  • What do we still need to know?
  • What do we need to do?

In a report to the board in mid 2014, the principal identified that numeracy achievement was at crisis point. The finding of most concern was that 43 percent of children in Years 4 to 6 were below the expected level. Most of the children in this category had experienced some form of targeted learning at least once during their time at the school, so clearly this hadn’t had the desired effect. More needed to be done, and probably something different, to help teachers accelerate their progress.

The principal and staff established a small set of questions for themselves to answer:

  •  is our professional development making a difference?
  •  is our teaching making a difference?
  •  why are we seeing only shifts in achievement and no ‘really accelerated’ achievement?
  • how do we build whānau involvement with a focus on learning?

"There is no sweeping this under the carpet.  This is what it is. What are we going to do about it?  It's not about blaming, but putting it on the table."

Responding to the data with short-term measures and longer-term strategies

The teachers and board scrutinised the data to determine whom to support and in what. The teachers discussed possible strategies and identified gaps in their own content knowledge. They felt they needed to know more about the numeracy progressions so they were always aware of what came before and what came next. They recognised that if they did not have this content knowledge it was unlikely that the children would be clear about their next learning steps.

The issues identified in this preliminary phase informed the development of a long-term strategy to reduce underachievement. The board discussed the data, possible strategies and recommendations. They updated the charter to respond to the report. Groups, especially year cohorts with high levels of underachievement, became charter targets.

Once unwieldy, with lots of strategies and actions, reports to the board now focused on the priority students and areas where the biggest difference could be accomplished within a specified timeframe. The aim was to focus on achieving deep learning in a small number of quite specific content areas and, in this way, to ensure substantial gains in achievement.   

Teachers analyse data
Teachers analysing data

For example, the action plan for Year 4 focused on the 17 out of 39 children achieving ‘below’ or ‘well below’ the level for mathematics. A lead teacher worked with the Year 4 teachers and the 17 target children to identify specific content and teaching gaps and found, for example, that understanding of place value and knowledge of basic facts were two areas of need.

While the focus was on the target students, the board insisted that professional learning and development (PLD) and other improvement actions had positive benefits for all children, in this way making sure all children could fulfil their mathematical potential.

Here are two goals, together with initial actions:


All Year 4 children that are below and well below the standard will improve mathematics levels and stages.


  • Teachers of the Year 4 target group will provide explicit teaching and modelling of strategies children need to accelerate progress. 
  • The lead teacher will work with the Year 4 group to monitor progress and advise class teachers of the next step.
  • The lead teacher will support the Year 4 teachers in the classroom with the target group of children.
  • Discussions about the target group’s progress will occur in syndicates.


Develop systems and opportunities to involve whānau and the community with mathematics.


  • All teachers to have a current maths display in their classroom that reflects current learning and shows children’s work.
  • Have a maths week in Term 3, week 4 with school-wide activities and home challenges
  • The school will have an open hour for maths in the classroom.
  • Hold a parent maths evening during the maths week.
  • During three-way conferences, children will share their maths learning.

The board immediately provided extra teacher aide time to support the school’s short-term strategy. This additional time was to be used to implement the targeted maths programme with the identified students, supported by the lead teacher. Further assessment of the 17 target students identified the extent of their knowledge gaps and plans were developed for the teacher aides to follow. The lead teacher modelled the teaching to the teacher aide and demonstrated how they should run the additional teaching session. The teacher aide generally worked with groups of four or five children who had similar learning needs.

Group activities

Once the teachers had inquired more deeply into their own learning needs, leaders recognised external and internal expertise would be required to meet them, and PLD should extend beyond numeracy to include the wider mathematics curriculum. To supplement what their own lead teacher could do, they engaged a respected external facilitator to lift the quality of professional practice and deepen teachers’ content knowledge.   

The external facilitator focused on:

  • the mathematics progressions
  • moderation of teacher judgments
  • making sure children experienced the whole mathematics curriculum.

The facilitator used many of the strategies teachers were already familiar with from recent writing PLD. Teachers reported subsequently what they most wanted was to be totally familiar with the curriculum levels so they knew exactly where the children were at, and where they needed to be.     

"My confidence around knowing the curriculum area grew really well and knowing the progressions that came before and after without even having to look at the book. It feels amazing. It’s about giving the kids a good deal.”


The following are some of the approaches introduced by teachers into their classes because of the PLD.

Double and flexible grouping recognises children may need to practise using some strategies many times before they really understand them and can use them confidently. Flexible groups are organised around the mastering of specific skills. By participating in more than one group during a mathematics class, children can engage in new learning and revisit earlier learning.

I have very flexible grouping. I double group all of the time. Sometimes children who are just lower, listen in and then I see what they think of that. Maths is so huge – some children might be great at an aspect but not good at something else, so they can flick in and out of a group depending on what they need. If the child already knows it, there is no point in keeping them there. It’s about keeping the level of challenge.”


Spider graph shows child's level of achievements in mathematics

A spider graph can be used to show a child’s level of achievement in different areas of mathematics. Teachers created a graph for every targeted child. They filled it in regularly, annotating it with notes about what the graph was telling them and the child’s strengths, needs and interests. Those who were ‘well below’ the expected level had individual education plans (IEPs). Used in this way, a spider graph provides a picture of a child’s achievement and progress, as well as their engagement with different areas of the mathematics curriculum. West Gore later extended the use of spider graphs to all students.

In backwards learning the teacher does not share the WALT (‘we are learning to’) with the children at the start of the lesson. Instead, children are asked at the end to share what they have learnt. This practice can help children become more reflective learners. It also ensures the WALT is written in language the children can understand and recall later.

Wherever possible, authentic contexts are used so the learning relates to real life and children can put themselves in the problem. This helps make sure they can make any necessary connections.

“I have three children in my class who have some knowledge of te ao Māori. The biggest thing for me was incorporating Māori perspectives into a normal maths lesson. On one occasion the children made a connection between the waka and the tens-frame.  I wouldn’t have even thought about that but they made the connection. The children would light up when they got to make those connections and share them with others.”


One teacher’s inquiry focused on how to successfully help three Māori children who had come from a kōhanga reo. Recognising that establishing a partnership with whānau was going to be essential, the teacher began engaging with them more frequently.

The learning environment was managed in ways that supported participation, enjoyment and agency. Children were engaged in purposeful follow-up activities to practise and extend their learning. In some classes, the children were able to choose from several learning activities once the teacher had explained the learning they would be practising. In some classes, each group would have a box of learning activities for the children to do when they weren’t working with the teacher. Some of these activities would focus on one or two specific skills while others provided opportunities for revision.

In Years 5 and 6, teachers created an environment where the emphasis was on progress rather than achievement. They recognised that if the children, especially the boys, were not experiencing success, they could think they were dumb and disengage.

"We make the celebration public in ways such as getting them to share their think board with their previous teacher to show what the can do now."


talk moves is a participation strategy designed to help children learn through talking mathematics. It gives them the tools to clarify their mathematical thinking and resolve disagreements. It can also help teachers reduce the time they spend explaining while increasing the time children spend explaining. One of the principles of talk moves is that talk must be carefully orchestrated to ensure equitable participation by all learners.2

talk moves

Teacher move

What a teacher does

Benefit of the move


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

Makes one student’s ideas available for the teacher and other students to understand 

Provides thinking space for students to track what is going on mathematically


Asks students to restate someone else’s reasoning

Gives students more time to process an idea, as well as another way to hear it.

Provides evidence that other students did indeed hear the idea of another student.

Shows the students that mathematical ideas they have are important and taken seriously.


Asks students to apply their own reasoning to someone else’s reasoning

Entry point to eliciting student thinking.

Positions student ideas as important mathematical ideas and builds on them.

Adding on

Prompts students for further participation

Encourages students to weigh in on ideas.

Helps establish a norm around connecting mathematical ideas and building on them.


Waits in silence

Brings important contributions from students into the discussion.

Communicates an expectation that everyone has important ideas to contribute.

Teachers reported that after using this strategy in mathematics they introduced it to other curriculum areas too.

Children’s posters were an effective form of assessment when used to demonstrate what they had learned. In one class, the children were able to add to the teacher’s modelling book and photograph themselves demonstrating mathematical ideas using equipment. Their photos were then displayed on the learning wall as evidence of their achievement and progress.

When making assessment judgments teachers were encouraged to use a wider range of evidence, including:

  • children workbooks
  • modelling books with formative assessment notes in them
  • photographs
  • videos of student voice
  • artwork relevant to maths with student voice attached
  • written assessment tasks (not just the test scores)
  • think board
  • GloSS and JAM assessments
  • children’s written reflections.

 “Yesterday in maths it was the first day of Term 4. We forgot the maths strategy so me and the other two went and got the maths books. I felt good because I problem solved. Next time I will get the book again.”

“When I was learning my 5 times strategy I used abacus [Slavonic] to help me and I did it. Next time I will keep it up by using equipment to help me.”


Students thought that it was useful to reflect on their learning:      

“We know what helped us to learn. Things like using the modelling book, asking a buddy, using a certain piece of equipment.”

“By going back to our reflections to see what I said helped me last time I was doing this sort of problem – I can use that same thing.”                         

Group activities

The curriculum was reviewed and then fully revised to ensure that long-term plans and teaching guidelines incorporated all the strands and what must be taught at each year and curriculum level. For each topic (such as time and temperature), at each of the Levels 1 to 4, the curriculum now provided:

  • curriculum level descriptors
  • National Standards descriptors
  • progression of learning
  • number strategies      
  • required mathematical language.

The school offered parents increased opportunities to be involved in their child’s mathematics learning. They were invited to mathematics’ evenings and open days to learn the games that children played in mathematics and to observe lessons. Games were then sent home for the parents to play with their children. If a child was selected to be in the targeted learning group the teacher or a leader would contact the parents and explain why.

Parents we spoke to felt well supported by the school and said that they now felt more confident and better equipped to support their child’s mathematical learning at home.  

“The evenings and open days made me understand where our daughter was at [with her maths learning] and gave me ideas of what to ask her and how to include numeracy in our daily conversations.”

“It highlighted to us that at home we could work better with our child. For my husband, he realised he could support our child even though he felt he hadn’t had a successful time at school.”

 “It was a lot more positive to get our son to do his homework. It got the family more involved in playing the games. His confidence grew because he had a better idea of his maths. He got his basic facts reinforced. He stayed on the target programme for one or two terms. He is at ‘above’ now and has stayed there for the last 18 months. It was a more positive experience at home, it was fun because it was games. Reinforcing at home helped. It was easy to see how much he had improved.”


Although some teachers were still developing confidence with the new teaching strategies, reports to the board in 2015 revealed continuing increases in the number of students achieving at or above the expected level. By the end of 2014, 10 of the 17 target students were achieving at or above the expected level and only four had not improved their achievement level. By the end of 2015, 81 percent of students in Years 4 to 6 were achieving at or above the expected level. Reports to the board continued to describe what was working and where further efforts were required.

2 Chapin, S., O’Connor, C., & Anderson, N. (2003). Classroom Discussions: Using Math Talk to Help Students Learn, Grades 1–6 (2nd ed). Boston: Math Solution.