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Hertfordshire mathematics research project 2011-12: Engaging and Motivating Pupils in Primary Mathematics

Teachers’ names: Angela Adams and Michelle Sage School: Holwell Primary School

Research project question / focus Can we improve the engagement and motivation of our children and staff through real maths and investigations? Abstract After much deliberation and discussion, we agreed upon a title that truly reflected our objectives of the project. We wanted to embed Maths in a real context for the children to engage and motivate them, initially in Year’s 2 and 3 and then widen the practice throughout the school. Questionnaires from staff and pupils gave us our entry and exit information and we focussed on 2 investigation type lessons each half term. Teacher assessment of Ma1 in Year’s 2 and 3 has shown an improvement in system using, confidence in independently tackling a problem and using Maths language to explain their conclusions. Introduction and project focus Holwell Primary is a popular, local, one form entry school. It has a school deprivation indicator which is above the national average and a higher than average number of children, on free school meals and on the SEN register. This year, our School Development Plan had a clear target to improve the teaching of Ma1 skills across the school. We had both been inspired by external maths training. We could see the potential benefits of engaging children through realistic maths tasks and investigations and this project gave us the opportunity to implement this and measure the impact. Through teacher assessment we had noted that when given a problem, children would struggle to know where to start and expected to be ‘fed’ the steps needed. This led us to think about how often we gave children the opportunity to tackle investigations, use Mathematical language in lessons and make links between what they know and what they needed to do. We hope our staff and children questionnaires will show a change in attitude towards maths lessons and they will be more engaged and motivated. We also hope that through teacher assessment, we will see an improvement in investigation skills. Review Jo Boaler (2009) describes maths as being narrow or real. Narrow maths is copying methods that teachers demonstrate and practicing them. She says that this is not mathematics as the whole subject involves problem solving, creating ideas and representations, exploring puzzles, discussing methods and many different ways of working. Gainsburg J (2003) says “Mathematics is not about numbers, but about life. It is about the world in which we live. It is about ideas. And far from dull and sterile, as it is so often portrayed, it is full of creativity.” Realistic Mathematics Education (RME) is the Dutch response to maths education reform. This started in the 70’s and the aim was to move away from the mechanistic style of teaching maths. Implementing these reforms is still a ‘work in progress’ as mechanistic maths still has a part to play in the classroom. ‘Education should give students the "guided" opportunity to "re-invent" mathematics by doing it… The present form of RME is mostly determined by Freudenthal’s (1977) view about mathematics. According to him, mathematics must be connected to reality, stay close to children and be relevant to society, in order to be of human value. Instead of seeing mathematics as subject matter that has to be transmitted, Freudenthal stressed the idea of mathematics as a human activity. Education should give students the "guided" opportunity to "re-invent" mathematics by doing it. This means that in mathematics education, the focal point should not be on mathematics as a closed system but on

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the activity, on the process of mathematization’ (Freudenthal, 1968). Pilot study and findings We have carried out 2 investigations each half term with years 2 and 3. For each investigation we have based the activity in a real context, initially scaffolding the investigation carefully. Children are now more confident at tackling an open ended problem, particularly in Year 3.

We have encouraged the use of systematic working, logical presentation and allowed plenty of time for discussion which nurtured the use of mathematical language.

We have shared our aims with the rest of the staff. We have shared a variety of OMS in staff meetings to start off thinking about open ended maths throughout the school. We recently had a staff inset, to share our findings so far and inspire others. Prior to the inset, staff had run a 10 minutes session with their class, asking the children to ‘make 10’ in as many different ways as possible. Staff brought along the children’s work and we analysed the systems and techniques children had chosen to use. We were pleased to see that children were applying their recently taught knowledge (brackets in Year 5 and dividing in Year 4), but only in Year’s 2 and 3 had the children consistently applied a systematic method to their work. This highlighted to the other staff the value in investigations, as well as mechanistic maths. Also at the inset, Deborah Mulroney shared ideas and games that would develop investigative thinking that would be easily employed in lessons. She also shared some mathematical based story books that could be used to create a ‘real’ context for the children. This linked with the investigations we have been trialling in our classes.

As in the Dutch RME study, we have realised that this is not an approach that be achieved overnight. In Primary maths especially, the children’s understanding and skill of manipulating numbers is still developing and so teaching of mechanistic maths is essential. As Gainsburg (2003) states, maths should be about real life. In reception, when children are developing their understanding of the conservation of numbers, all the teaching is based in a real context – counting cars, teddies etc. As children gain an abstract understanding of number, they need to extend and make links between what they know and new learning. If we dictate this to them they miss the chance to “re-invent” the maths and the connections will not stick!

3 children in each class participated in a maths questionnaire which told us many children had a closed idea of what maths is (‘It’s adding!’). They found big numbers and dividing tricky. Overall they all liked and enjoyed maths, including challenging activities. Reflection, evaluation and interpretation of the outcomes We have been re-motivated by our research and changes in practice. The next step is to widen the use of real investigation throughout the school. Our Inset started this process and it will continue to be a focus for the school. We will have staff meetings to discuss the next steps and to evaluate the impact. The children’s voice (appendix 1) has shown that they are not frightened of ‘hard work’. Challenge and the process of investigating helped their learning and this is recognised by them. They have found real maths investigations enjoyable and motivating. Across the school, the children have a broader understanding of what maths is, realising that it is more than just ‘sums’. The children in Year 2 and 3 both saw a change in their maths lessons this year, with a clear move from ‘book’ based lessons to more practical and in all the year groups, the children obviously enjoy the activity based lessons the most.

We have seen a very positive impact, following this project in Years 2 and 3. The children’s ability to independently approach a mathematical problem has improved, as we would have hoped. In addition, we have noted that children are linking their learning in lessons where previously we would have needed to point out the connections. Hopefully children will use this realistic contextual learning to see maths as a whole subject and not discreet units of teaching.

We have begun, with the staff inset, to develop real maths investigations in other year groups. We will continually review the impact in future staff meetings and allow the opportunity to share good

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practice for the rest of this academic year and next.

As teachers, we need to find the balance between practising and extending skills, and giving them the opportunity to use and develop their skills in a real context. Reference List Boaler, J (2009) The Elephant in the Classroom, Helping Children Learn and Love Maths. London: Souvenir Press Gainsburg, J (2003) The Mathematical Behavior of Structural Engineers. Stanford: Stanford University Early Grade Mathematics Assessment (EGMA): A Conceptual Framework Based on Mathematics Skills Development in Children (2009) http://pdf.usaid.gov/pdf_docs/PNADS439.pdf