03 Working collaboratively to develop and implement an agreed mathematics curriculum and consistent, high quality teaching practices

ERO’s 2014 report Raising Achievement in Primary Schools identified that, in many schools, the processes for reviewing the mathematics curriculum and assessing teaching and learning were not well connected. Some used the same long-term plans each year without analysing or responding to their assessment information. Many lacked a deliberate and relentless whole-school focus on improving student achievement.

This narrative shares what leaders and teachers at HOKOWHITU SCHOOL in Palmerston North did to understand, review, develop and introduce a carefully structured mathematics and statistics curriculum. New teaching guidelines synthesised the curriculum strands, characteristics of the mathematics standards and aspects of the earlier Numeracy Projects. Agreed teaching approaches were established and implemented to provide consistent strategies for children across year levels.

When ERO visited Hokowhitu School, it had recently experienced major leadership, teaching and environmental change. Leaders and teachers had introduced flexible learning spaces, which gave children greater choice about how and what they would learn. Most teachers now worked collaboratively in groups of three in the new spaces, leading workshops and acting as learning coaches. In this latter role they reinforced workshop learning or coached children while their colleagues led workshops.

Reviewing and developing curriculum content

Leaders wanted teachers to fully understand the learning progressions for Years 1 to 6. Working collaboratively with the professional staff, they developed a set of expectations and practices to be consistently applied school-wide so that when children transitioned from one learning space to another they would know what to expect. They also put in place a policy of moving one of the three teachers in each learning space to a different learning space at the start of each new school year so that they would understand the curriculum requirements at different levels. This policy underscored the importance of teachers knowing what prior learning children were bringing with them.

Leaders and teachers closely reviewed the school’s mathematics programme and teaching practice and made many changes as a result. Over a period of three years teachers worked with an outside expert to:

  • look in depth at the knowledge and strategies children should be taught for each of Levels 1 to 4 of the mathematics and statistics curriculum
  • make sure that teachers were confident to teach not only the number and algebra strand of the curriculum, but also the geometry and measurement and statistics strands
  • bring the strands together by integrating number into algebra, geometry, measurement and statistics topic overviews
  • introduce the expectation that no child would be classified as ‘no good at mathematics’ (this has sometimes meant changing parents’ own expectations of their children)
  • identify, understand, introduce and establish clear expectations about effective teaching practices.

Leaders developed topic overviews for the first four levels of the mathematics and statistics curriculum. Each of the algebra, geometry, measurement and statistics overviews:

  • explained the percentage of teaching time that teachers should allocate to each strand
  • brought together what children should learn by combining detail from the relevant number strategies from the Numeracy Projects and the national standards
  • provided indicative examples of what should be seen and heard in the classroom.

The overview included progressions for Levels 1 to 4. The Level 1 overview called for investigations that focus on ‘all about me’, which children would do as a class. The Level 4 overview called for investigations that required multiple displays and analyses of data on relevant newsworthy issues.
The excerpt below shows the progressions from Level 2 and 3 statistics overview.

Statistics overview (excerpt)

Level 2
In class you will see and hear:

Level 3
In class you will see and hear:

Statistical investigations about my class/my school, as groups or individuals following teacher model

  • Vertical and horizontal bar graph
  • Strip graphs (bars end to end)
  • Pie graphs from strip or cubes and string
  • Pictograph 1:2 or 1:5 or 1:10
  • Single dot plot
  • Present and interpret data in table format
  • Mark axis in ones/twos/fives
  • Include key where appropriate
  • Use a sample
  • Collect data before deciding on presentation

Statistical investigations about our community

  • Multiple bar graph (vertical or horizontal)
  • Line graph (to join continuous data)
  • Stem and leaf
  • Scatter plot
  • Dot plot – back to back
  • Pictograph (1 to many)
  • Present and interpret data in table formats
  • Mark axis in chunks
  • Use lots of number data
  • Ask/present own survey question
  • Use the enquiry cycle independently

Statistical Literacy

  • Accurate transfer of data to presentation
  • Present same data two ways
  • Identify best categories
  • Identify the most appropriate axis marking
  • Mark even lines – not spaces
  • Talk about most/least from combined bars
  • Discussion of obvious outliers and clusters

Statistical Literacy

  • Choose own (appropriate) data display
  • Numerical analysis using fractions
  • Range, spread, average, outliers and clusters
  • Inferences, predictions and trends beyond
  • literal statements of the raw data
  • Evaluate statements others make about data
  • Present same data several ways


  •  Likely, certain, possible, impossible, maybe, almost always
  • ‘Shades of grey’ statements
  • Find possible outcomes (tree diagrams)
  • Order events – flow charts
  •  Use unequal spinners, cards and dice


  • Certain, good, even or poor chance, possibility, impossibility
  • Fair testing
  • Interpret frequency tables
  • Find possible outcomes (tree diagrams) – discuss with simple fractions

While the overviews unpacked the mathematics and statistics achievement objectives from The New Zealand Curriculum it was not intended that they be used as assessment checklists. Rather, leaders saw them as a means of ensuring that all children experienced the whole curriculum and as a tool for increasing teachers’ content knowledge. By describing which mathematics standards related to each of algebra, geometry, measurement and statistics topics, the overviews provided a range of opportunities for teachers to make overall teacher judgements in relation to each of the mathematics national standards.

Although the overviews took time to develop, leaders considered it was time well spent to ensure that teachers fully understood how children’s mathematical learning should progress. Equally important, the overviews would help ensure that children were exposed to the full curriculum and experience less repetition of already-familiar concepts. The overviews encouraged high expectations and provided a wide variety of content to keep children engaged and achieving.

Outlining expectations about teaching practice

Instructional strategies include:

  • Using a context (story word problems)
  • Modelling
  • Class starters
  • Teacher think alouds
  • Use of the most appropriate equipment
  • Grouping (ability and flexible)
  • Rotations
  • Discussions, sharing and justifying.
  • Deliberate acts of teaching
  • Making explicit links between mathematics and real life

In addition to the overviews, the school’s leaders also developed additional teaching guidelines they called ‘essence statements’. For mathematics, these statements highlighted:

  • what should be present in the learning environment
  • what teachers should know
  • what the learning space programme must include
  • instructional strategies to be used
  • what teachers should say and do
  • what effective pedagogy looks like.

Successfully implementing new approaches

We observed mathematics lessons at different year levels where children were working in a mix of mixed-ability and streamed groups. Leaders told us that they were gradually moving to mixed-ability groups, and that, from 2017, all children would be in mixed-ability groups for at least part of their programmes.

In the Year 4 to 5 learning space we observed two workshops being led by two teachers while the third worked with individual children, checking, carifying and encouraging their efforts. Children had selected which of the workshops they would attend based on what they believed they needed to learn. The workshops had short, specified timeframes. The teacher leading the workshop either demonstrated strategies or got children to demonstrate and explain their use of a strategy. Teachers also encouraged those who were still developing the confidence share their ideas to verbalise their thinking to the group.

Our mathematics programmes are enriched through the use of rich tasks that support open-ended thinking skills and the key competencies

The tasks include:

  • Using a context (story word problems)
  • Thinking with what you already know (link to numeracy knowledge and strategies)
  • Connected concepts (cross-strand mathematics)
  • Problem solving (using multiple strategies, approaches and tools
  • Investigations
  • Cross-curricular links

Class starters are used for ‘front loading’ and ‘backfilling’ of key concepts, strategies and strand-based teaching. The purpose of starters is to ensure students are exposed to a variety of types of questions and thinking tasks.

Monday: Modelling using different types of equipment
Tuesday: Tick a box (multi-choice)
Wednesday: Word problems
Thursday: Thinking skills problem solving/application
Friday: Fast and furious – quickfire questions.

The children not in the workshops were highly engaged in activities that they were working on either independently or in pairs. They had been given nine activities on ‘must do’ sheets and were required to complete four. The sheets were designed for four different ability levels. Some children told us they were striving to move up to a harder level.

Some children were very aware of and supportive of others near them. One asked the girl next to her if she needed help, and the two then worked together to solve the problem. Some children were accessing world population data on digital devices as an authentic activity to practise comparing very large numbers and sorting them into numerical order. All were motivated and keen to make progress.

As a result of collaboratively reviewing and developing their mathematics and statistics curriculum, the leaders and teachers of Hokowhitu School had ensured that their students came into the upper primary school well set up to progress, confidently apply strategies to solve problems, and achieve.