New Zealand Research
Numicon Impact in NZ
Margi Leech
Lead consultant for NZ
Since Numicon was introduced to New Zealand in 2003, the excitement for its success has not faded, it has increased. Numicon is used in early childhood centres, primary schools, intermediate schools, secondary schools and special schools. It has a wide reach.
Numicon is now used in thousands of schools. The teachers see the immediate impact of engagement, joy and success This is particularly evident with students who have previously struggled with maths.
Numicon is a structured, whole school approach covering Levels 1 - 4 of the New Zealand Curriculum. It provides for all students including those who are gifted and those with special needs. There is a clear scope and sequence of learning progressions. These provide for a consistent experience for the students every year. Numicon’s approach has proved itself over and over again as you will read below.
During a recent visit to a school that teaches students in Years 1 - 8, the principal and senior staff showed me their results with beaming smiles. The first three table rows are results for whether students across the school had achieved more than below, no more than below or at or above the expected New Zealand Curriculum (NZC) level in maths. The third and fourth rows show results for students at Year 8 in their last year of school.
|
End of year |
More than below NZC |
No more than below NZC |
At expected level NZC |
Above expected level NZC |
|
2017 |
4 |
20 |
76% |
|
|
2018 Numicon purchased |
1 |
16 |
83% |
|
|
2019 End term 2 |
1 |
15 |
84% |
|
|
Year 8 2018 End of year
|
0 |
20 |
80% |
|
|
Year 8 2019 End Term 2 |
0 |
10 |
90% |
|
The results show a 12-percentage point increase between the end of 2017 and the end of term 2 2019 in the proportion of students across the school who were achieving at or above the expected NZC level, from 76% to 84%. There was also a 10-percentage point decrease in the proportion of Year 8 students who were no more than below the expected NZC level from 20% to 10%. This change meant 90% of Year 8 students were at or above the expected NZC level by the end of term 2 2019.
Besides the results from this one school, we have other systematic evidence of positive results. Three schools in different locations with students from different backgrounds have been participating in an evaluation of Numicon. Among other things, the evaluation has involved interviewing teachers about what they think of the Numicon Approach. Initial analysis of maths teachers’ experiences has revealed some encouraging outcomes for teachers and students.
Some key themes emerged from interviews with teachers about how they had found teaching with Numicon. According to teachers:
- Everyone has benefitted at different levels. “The enthusiasts fly”, and the other students “are starting to make real progress”. All children are loving Maths!
- Numicon has provided a common language for teachers across schools to talk about their students’ educational progress and to communicate and report results to parents. With all teachers using it, there are opportunities for teachers to help each other.
- The Numicon equipment allows teachers and students to show and model approaches. The equipment seems to help students who may not have understood approaches to learn. Numicon has more tools for students at younger ages who are starting from a low base or need to catch-up.
- Teachers like how Numicon is laid out. The planning is all done for them. All they need to do is organise the equipment and follow the medium to long-term plan, and the lesson handbooks.
- Numicon allows teachers to pick up exactly where students have finished at a previous Year level. The capacity to cycle-back over topics is also an advantage to achieve a sense of progress.
- Students who could not understand patterns now can.
- Another advantage is that teachers and students can discuss the language of maths first and some strategies for solving problems. Numicon gives teachers a model and encourages them to take time in their teaching to observe and listen to their children.
We saw these themes expressed in specific examples that teachers gave. For example, during the interviews, most teachers were asked how strongly they agreed Numicon produced the sorts of outcomes intended by its designers. Below is a summary of why teachers who responded this way strongly agreed Numicon had the intended outcomes.
- Numicon creates a supportive learning environment
Teachers generally thought all their students were involved using whole class teaching. No one was isolated. Every student could use the same resources. Students could own an activity by using the Numicon equipment.
For example, some teachers said their students absolutely love maths and are licking up mathematical language. Other teachers observed that their students find maths easy to learn, and can find patterns and understand concepts. These teachers said their students can now use concepts in context to solve problems. These teachers thought Numicon scaffolded their teaching well by having logical steps. Generally, teachers thought their students were eager for maths to begin and students challenged one another.
- Numicon encourages reflective thought and action
Most teachers said students who struggle with maths wanted to use the Numicon equipment. Teachers also generally thought students reflected during problem solving activities. These teachers said their students understood they could use the Numicon equipment to help solve problems if they were struggling with an exercise.
- Numicon provides for making connections with prior learning
Teachers generally understood that the Numicon approach includes deliberate feedback loops, basic skills tests or teacher observations. Most teachers said they could see how their students had responded by evaluating Numicon assessment results, as well as regular diagnostic testing.
- Numicon shows how new learning is relevant in real life
Teachers generally thought Numicon was relevant in real life since the approach helps teach students how to use money and to solve practical problems using measurement, statistics and geometry.
- Numicon encourages shared and individual learning
Most teachers said that Numicon provided opportunities for students to work in pairs, groups or as a whole class. Teachers said children could learn from each other and share. Some teachers said they had demonstrated mathematical concepts to mixed-ability groupings. Some of their students then helped each other.
- Numicon provides many opportunities for learning
Teachers generally agreed that students were learning maths by using different strategies in different contexts. Some teachers said their students had learnt their times tables quickly. For example, one teacher said,
“It’s a breeze”, [there’s] no rote learning. We take the activities from Numicon and play games. Some students are doing 9-12 times tables. Students are challenging each other to get through their times tables. Ever since Numicon was introduced, students have loved maths. My year 5 and 6’s are using Numicon 5 and 6. That is, about two years ahead of the NZ Curriculum.
Another teacher said a struggling student learned the concept of decimals “in a day”. That teacher said this student was able to calculate numbers with decimals with and without equipment after the student had been taught with Numicon.
From these results, we could see that the teachers from the three schools who were interviewed for this evaluation generally thought the resources worked well. While some investment in money and time was required to purchase and learn how to use the resources, Numicon helped give these teachers an edge in how they taught maths that they had not had before. Without Numicon, some of these teachers believed struggling students would not be able to learn mathematical concepts. These teachers believed that Numicon gave such students the opportunity to succeed and move forward.
Teachers could generally see an alignment between the NZC and the Numicon programme. For example, some teachers said they referred to relationships created by Numicon NZ between the NZC and Numicon benchmarks. These teachers said they thought this resource had helped them to understand the relationships better. Beforehand, some of these teachers said they had “no idea” about how to draw the connections.
Besides being able to draw better connections between Numicon and the NZC, some teachers said that because they were covering topics they had not done before, or did not have time to do, they felt like they were doing a better job. Before these teachers used Numicon, some were not sure they were teaching the whole curriculum well, or were trying to squeeze in topics. These teachers said they had become more confident that they were covering the whole curriculum.
In summary, these initial provisional results from our evaluation generally show that the teachers we interviewed had got to grips with the Numicon Approach reasonably quickly and had realised many of the benefits with their students. Their students who were disengaged at maths are now engaged, and those who were already engaged are being stretched. While using Numicon for the first time represented a learning curve for some of these teachers, any costs have been outweighed by the observed benefits to children’s progress at maths over a period of a few years or even months.
These initial results point to evidence of many of the merits of Numicon that we thought were true.
We are in the process of completing this project which has been over a three-year period.
International Research
The Numicon programme originates in the UK. A number of different organisations internationally have conducted their own research projects on using Numicon independently from Oxford University Press. They all agree on the effectiveness and possitive and sustained impact of this approach.
Cambridgeshire Local Authority Case Study
A summary of their research during 2006/7, conducting trials in the use of Numicon in the form of 10-week interventions.
This summary was commissioned by the National Teacher Research Panel for the 2004 Teacher Research Conference in the UK
Multi-sensory approach to the teaching and learning of mathematics - Leeds Report
A joint initiative by the Primary National Strategy team, the School Support Service and the Psychology and Assessment Service. Their plan was to develop an intervention for middle and upper primary students in particular, to explore the possibility of using Numicon.
Here is an overview of their findings. See the link above to read the full case study.
- Students improved their maths skills and visual memory skills (for some this was after a long period not making progress)
- High student confidence resulted from using the materials, with high levels of engagement and enjoyment;
- Participating schools were positive about the approach and materials, and keen to continue using them.
Multi-sensory Mathematics for Intervention
A case study by Doncaster Local Authority on the use of multi-sensory approaches, including using Numicon (2007 - 2008). This was run by 6 schools, each identifying 6 pupils who are currently working at least one level below age related expectations and have significant difficulties with maths.
Here is an overview of their findings. See the link above to read the full case study.
- Numicon equipment provides a unique and important structured imagery of the size of numbers and arithmetic processes.
- Children made progress in mathematical knowledge, skills and understanding
- Strong evidence of children’s increased confidence, willingness to 'have a go' and persistence
- Improved enjoyment in mathematics
- Using Numicon equipment and the teaching approach with whole class where appropriate, enhances the effectiveness of teaching.
- Numicon equipment and the teaching approach have relevance for all children.
Research in Early childhood and New Entrants - USA
Melissa Jenkins undertook research as part of the PhD. Her findings show a clear benefit for children using Numicon.
For further evidence and research links click here
The Numicon Project is a collaborative endeavour to facilitate children’s understanding and enjoyment of maths.
The Project was founded in the daily experience of intelligent children having real difficulty with maths, the frequent underestimation of the complexity of the ideas that we ask young children to face and a recognition of the importance of maths to them and to society as a whole.
We appreciate the complexity of these early number ideas and seek to foster the self-belief necessary to achieve in the face of difficulty; we are not about ‘making maths easy’.
We believe that the combination of action, imagery and conversation helps children to structure their experiences, which is such a vital skill for both their mathematical and their overall development.
By watching and listening to what children do and say, we and many others are finding that our developing multi-sensory approach provides learners with the opportunity to play to their strengths, thereby releasing their potential to enjoy, understand and achieve in maths. This enjoyment in achievement is also shared by teachers and parents.
We strive to support teachers’ subject knowledge and pedagogy with teaching materials, training and ongoing feedback as we continue to develop a better understanding of how we can work together to encourage all learners in the vital early stages of their own mathematical journey.