School of Education and Yewtree Primary School

A joint evaluation of the MaST programme

John Mower - Senior Lecturer in Primary Mathematics, School of Education

Numbers

Introduction

The purpose of this project was to review and evaluate the effects of the Mathematics Specialist Teacher (MaST) programme in one particular school, Yewtree Primary School in Hemel Hempstead. MaST is a two year Mathematics course with masters credits run by the School of Education at the University of Hertfordshire. It is designed for established teachers, maths co-ordinators and Headteachers to enhance and improve the teaching and learning of Mathematics in their class initially and then across the whole school.

MaST has several key aims that are explored over the two years. For the purposes of this project, the main aims of the MaST programme which were evaluated in the class were as follows:

To encourage mathematical thinking rather than mechanical ‘doing’
To implement effective use of maths-specific pedagogies such as ‘what do you notice?’
To initiate effective Mathematics talk in the classroom
To use of a range of resources and representations to help to foster understanding and express generalisations.

The teacher with whom I worked, Tia, completed the MaST programme in the summer of 2015 and has taught her class for the last two years, through Year 1 and 2, hence the children have been exposed to the MaST principles and philosophies over this two year process.

This project could only ever be a ‘snapshot’ of one class and one school and hence it was always going to be difficult to make generalisations after evaluating the impact in this specific case. However, any positive connections between the MaST principles and the learning and teaching seen at Yewtree would certainly add credence to the programme.

Implementation

At our first meeting we decided that we would team teach six sessions over a period of three weeks. This would enable us to plan sessions where we could evaluate according to the aims cited above. By team teaching, this would give both of us the opportunity to observe effective teaching and learning and form combined conclusions at the end of the process.

From our initial discussions it became clear that Tia’s view was that the MaST philosophies had been embedded well in to the children that she had taught for two years, but this was less evident throughout the school.It is not the intention of this report to document each of the sessions. Instead, the key aims of the project will be considered, using examples from particular sessions.

Meeting the aims

It was evident very early on that the children in Tia’s class are, for the most part, adept at thinking mathematically and justifying choices. In session 1, for example, the children were asked to create the biggest or smallest 3-digit number by rolling dice and choosing where to place these digits in their number. Quite complex issues of probability were expressed well; for example, one of the children commented ‘I’ve put this in the hundreds column because there is only one number that I can roll that is bigger.’ The follow-up task of allowing one of 4 rolls to be discarded in the ‘bin’ provided opportunity for an even greater amount of choice and justification and higher- attaining children could articulate their decisions very well. A further example of effective mathematical thinking was evident in sessions 3 and 4, where children had to work out missing numbers from ‘torn’ number grids. This required an ability to use their understanding of place value and to use logic to complete the grids.

It was very apparent during this task and the subsequent ones that, for children to be adept at mathematical thinking, they need to have been taught how to articulate their thinking and how to use specific answers to be able to form generalisations- both of which were key aims in this project and are fundamental principles of MaST. This was beautifully demonstrated when, after exploring specific grids, they began to apply the rules to any number. Photographs of the children’s efforts show a very high level of understanding for Year 2 children.

The children in Tia’s class use resources as a matter of course. ‘Maths packs’ are available on their tables at all times and the culture of the class is to use these to help to show, explain and justify. In session one, for example, I was struck by how confident most of them were with attacking questions such as: ‘Using your resource packs, find different ways of making the number 63.’ Numicon, money, Dienes blocks, multi-link cubes etc. were used naturally and creatively in this process. When a new resource, Cuisenaire rods, was introduced in sessions 5 and 6, the children were very happy to explore the relationship between the rods and soon used them to be able to recognise fractions and simple equivalent fractions.

Key to the success of this has been the use of open, pedagogical questions that children can explore at their own level. Throughout the last two years the children have become accustomed to questions such as ‘What do you notice?’, ‘What’s the same and what’s different?’ and ‘If I know this what else do I know?’ We have continued the use of these throughout these sessions and hence, when first introduced to the Cuisenaire rods, they were given the opportunity to explore what they noticed and subsequently could quickly articulate proportional relationships; for example, ‘I’ve noticed that 4 of the red ones fit in to the brown one.’ This starting point was essential in helping the children to explore proportionality later in the sessions and to begin to articulate why different fractions have the same value.

Next steps

It had always been the intention of Yewtree Primary School to develop these principles across all classes, using staff development sessions in Autumn 2016 as a direct stimulus for this.

Since her completion of the MaST course, Tia has implemented course pedagogies (e.g What do you notice? / How do you know etc?) across the school and she felt that the teachers are more confident in 'giving the children the lead' in terms of finding their own patterns and discussing them, allowing all of them to participate at their own level. However, as there were new staff who started in September 2016, there would be a need to revise these principles.

Tia and I met in early September 2016 to drive the initiative forward. Whilst resources were being used more confidently in KS1, staff in KS2 had asked for more support in the effective use of a range of resources. Following our discussion Tia then ran a further development session in October 2016 with the staff to try to embed both the principles discussed and the use of resources. Key to this would be dedicated time for staff to plan together and discuss impact in future staff meetings.

I spoke to Tia again in February 2017, after the school had had time to embed these principles, and her comments were extremely encouraging, as her training and passion for the subject is clearly beginning to pervade the school. She noted that every child now has Maths packs to support their learning and both staff and teaching assistants have had specific training in Numicon. Work scrutiny throughout the school is beginning to show children using both concrete and pictorial representations to help support abstract thinking, and the school has just completed a successful maths week, focussing on gaining a deep understanding of the equals sign.

Conclusions

Forming wide-ranging conclusions from such a small-scale and restrictive project is not possible. It was also not the intention of this project to compare a class that has been exposed to the principles to ones that haven’t - there are far too many variables which would question the validity of such a comparison. However, it is appropriate to summarise how a specific class have benefited directly both from good teaching and from the embedding of the MaST principles. The overarching feel when observing or teaching in Tia’s class is that her children both enjoy and are engaged by Mathematics. Through constant access to exploration and justification, her children, in the main, have developed a number sense and the confidence to develop a breadth of understanding. Several examples throughout the project served to emphasise this, especially when children were able to demonstrate an ability to form generalisations from specific examples.

As one of the key aims is for Mastees to implement these philosophies throughout the school, it was also very gratifying to see, several months after staff inset, that there is now a clear shift in emphasis across the whole school to further mathematical thinking.

The key aims of the National Curriculum are to develop fluency, reasoning and problem solving, as well as to develop a depth of understanding of age-related objectives. We can confidently use this case study with future ‘mastees’ to show how the fundamental principles of the course can help to meet these objectives and raise both interest and engagement in our children.

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