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

Teacher’s name: Rebecca Smith

School: Aboyne Lodge School

Research project question / focus: Exploring the impact of different strategies for incorporating real life maths. What impact does ‘real life maths’ have on disengaged children. Abstract I have carried out research on exploring different strategies for incorporating real life maths. I focused my research on short term projects, long term projects, oral mental starters and plenaries. I have found that contexts work particularly well for shape and measures but can become forced and unnecessary in lessons with number objectives. I have suggested that the projects are used for assessment opportunities whilst active learning takes place in all lessons. Children were engaged by the investigative approach to maths and the use of interesting equipment, scenarios and contexts. It was a combination of approaches that led to children becoming more engaged with maths and motivation came about by setting a clear and interesting aim for the lesson. The more regularly real life links are discussed, the more I found that children were beginning to make connections themselves. Introduction and project focus Over the last 2 years, our school has focused on using assessment activities in maths at the beginning of each unit to assess the children’s knowledge and understanding. This, together with a mixed ability approach to each lesson has had a great impact on the children’s enjoyment and confidence. The children have been able to focus on their individual learning rather than the ‘ability level’ of their group and, as a teacher, I have been able to pitch the teaching to their current level of understanding. I noticed that the class particularly enjoyed the independence and active approach of the assessment days, but there were a group of children (Group A) who seemed to remain disengaged and lacking in confidence.

The children in my chosen group often became disengaged and unenthused as soon as they saw maths on the timetable. During the initial pupil interviews, it became apparent that many of them were unable to see any relevance to maths, it was a lesson of ‘numbers’ and ‘remembering’, which to the creative children of the group immediately became something that they were convinced that they could not do. ‘ I am not good at working out sums and other people always do it quicker than I can.’ Another explained that they did not enjoy fractions and decimals as ‘we never really use it, it is not needed.’ The class consists of many able children, and as a cohort, can be taught at a high level. Yet, when they were given an area of maths, such as shape, they struggled to link it to many real life contexts. Most identified aspects of maths that they enjoy were; using equipment, games and discussions with a partner and practical activities and which they can ‘get on with’. Many linked real life maths to being given real life word problems to solve. As Jo Boaler says (Boaler, 2009, p6) With development of technology to help with calculations – ‘ We all need to be able to reason mathematically in order to work and live in today’s society.’ For my project, I chose to investigate how you could incorporate real life maths into different areas of the subject. Could a real life context always be applied to the maths lesson? What different strategies could be used to bring the child’s attention to a real life link? Most importantly, what are the most effective ways of making maths relevant and also enjoyable? My research explores many strategies in the hope of engaging children in their learning and motivating them by providing a ‘reason’ to learn. These strategies include a week long project, short projects, oral mental starters and conclusive plenaries. As I was trying to gauge a change in attitude, enthusiasm and motivation, I decided to use pupil interviews and a scoring system to collect my information. At the beginning of this project, all of the children in group A gauged their enjoyment of maths at 5 or 6 out of 10 and their confidence in their ability between 3 and 6. The quality improvement agency state that (QIA,2008,p17); ‘Many of us learned our Mathematics at school or college by traditional ‘transmission’ methods. This is where the teacher explains the method, shows some examples and learners then complete an exercise which often mimics what the teacher has just

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demonstrated. This method does not promote a deeper understanding of the underlying concepts. I anticipate that this research will impact my teaching as it will force me to avoid this ‘traditional transmission method’ and focus a part of each lesson on the relevance of the concept within a wider context. Within my planning, I will be considering and then sharing the purpose of each lesson with the children. Through exploring different strategies, I hope to be able to decide on a practical approach for future teaching that can be realistically sustained. Whilst using my creativity to make maths more interactive and motivating, I hope to investigate methods where children are also encouraged to use own imagination and be creative within maths. I anticipate that by involving children in the planning of the projects and by giving clear and motivating aims in their work, the children will gain more ownership of their learning. I aim to involve children’s interests in the subject and provide stimulating opportunities where the children can apply their knowledge. By working towards an ‘end result’ through project work or investigations, I will be able to create more opportunities for self and peer assessment. Review Ofsted stated in their 2011 summary (Ofsted, 2001, p1) on good teaching of mathematics that ‘skills in calculation are strengthened through solving a wide range of problems, exploiting links with work on measures and data handling, and meaningful application to cross-curricular themes and work in other subjects.’ The summary praises schools that take time to create situations that are ‘out of the ordinary’ for a maths lesson. Yet some of the ideas are as simple as using items in the playground to work with on their problems (for example; measuring for new equipment.) If worksheets need to be given, there are real life contexts that the children have most likely come across, for example; which offer on drinks is the best value. In these schools, the report explains that ‘problem-solving and cross-curricular use of mathematics were

regular and integral to pupils’ learning of mathematics, and diverse in nature.’ The context that were created were not based on word problems but problems arising from exploring situations; how much tarmac is needed to resurface the playground. As I also believe, ‘mathematics is all around us; it underpins much of our daily lives and our futures as individuals and collectively.’(Ofsted, 2011, p4)

The National center for research on teacher learning (NCRTL, 1993) supports Ofsted’s report by explaining that it is the teaching of reasoning and problem solving that empowers students as they learn to offer solutions, clarify and expand on their ideas. It is about providing a context for the children which enables them to be reflective upon their learning. These contexts, should be ‘experiences that are likely to help students develop the understanding of maths.’

It is interesting that these ‘experiences’ are viewed differently by researchers. Angela Youngman (Youngman, 2012) believes that ‘children will remember the innovative and interesting ways in which a subject is presented. If it is interesting, they are more likely to understand it.’ She agrees that a child is most likely to learn when maths is shown ‘in action’ and when relevant, but goes on to suggest tick tock books. These books place pupils in role play situations using exciting concepts such as flying a jumbo jet, design a roller coaster, be a vet. These situations are engaging to children and require imagination, but are not technically providing contexts in which the children would have ever had previous personal experience of before. She argues that teaching children to think laterally about the application of maths to ordinary life, encourages them to begin to consider different ideas and find new ways of applying a concept. What I find most interesting about her views is that she contributes other areas of learning, such as; assessment for learning, development of conversations and the relating of theory and practice to these ‘active and real’ opportunities given to children. Jo Boaler (Boaler, 1993,p13) has very strong opinions which challenge some of the views previously stated. Boaler again identifies that real world contexts help to motivate and engage children as well as giving them a means in which to understand reality. The contexts however, she claims ‘often relates to experiences that are more relevant to the adult than the child.’ I believe that where this can be true, children are often discussing what they notice about life as an adult and enjoy imagining their futures. Boaler (Boaler, 2009, p14) shows concerns about the Narnia world that is created in maths where the children can solve the problem but do not transfer their learning to another. They do not need their world knowledge or common sense and students begin to ignore the context and not answer the problem correctly. (Boaler, 2009, 47)

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Pilot study and findings (main section) Short term projects – I began my research with Unit C, Handling data. Ofsted and Jo Boaler both suggest that this is an area which lends itself to real life contexts. Through discussions with the children, I found that children associated collecting data with ‘favourite colours, shoe size and number of pets that people have.’ They were not able to tell me when they would use this information after collecting the data; they did not provide me with a reason for data handling. Over a three day project, I created a scenario to provide a real life purpose to their data collection (see appendices). On the first day, I created an advert, recruiting children to help Kaylogs with market research. Kaylogs were having problems selling their goods and needed help in discovering why. The children were given different charts to analyze and identify reasons for the company’s data; for example, two charts had been compared without taking into consideration the different scales. The children were very engaged with this activity as it gave them the opportunity to use their experiences of being a customer. They also became excited at the idea of having a role, an ‘aim’ beyond completing a task for the teacher in their books. Two children from group A became so involved with this project that they spent their lunch break collecting information from other children in the school. On the second day, the children were asked to create new names and slogans and collect data to show which was the most popular. The children were comfortable with collecting data as they had done in previous years but this time, they were going to use the results effectively – to feedback to Kaylogs. I felt that this creative aspect to the project again drew the children’s attention to the task and took the focus away from their traditional view of maths. When asked, one child from group A said they felt they had ‘lots to do but felt free to work it out on their own with their group.’ They felt that they had more ‘freedom’ as it was ‘talking and problem solving rather than working.’ The recording of their data gave the children a chance to assess their own approaches and identify any faults that may have made in their approach. They had a purpose to their self-assessment as they wanted to be sure of their work before reporting to Kaylogs. Groups took turns to feedback to the class. I was surprised to see that one child from group A was very disappointed that Kaylogs were not coming to school to hear their reports. Over the three days, the child had become so absorbed in the context of the task and worked hard at having ‘the best’ data. The effort and engagement of all of the children in group A was significantly greater. The children scored their engagement and enjoyment of the project an average of 8 compared to an average of 6 in the previous half term. All children scored higher after project work. ‘There were lots of different activities to get to the results at the end of the project.’ ‘It doesn’t feel like boring maths, even though we were still looking at some sheets… they were not worksheets.’ ‘Instead of what is your favourite food, it was like a real shop.’ Reuben Hersh said that ‘Maths is learned by computing, by solving problems and by conversing, more than reading and listening (Hersh, 1997, p27) This was certainly the case here and I was reticent to return to a way of teaching where children waited to be active. I was however cautious of being able to maintain project work as it was demanding on planning time, creativity and preparation. I also felt that I was in danger of it becoming repetitive for the children. I decided to try a one day focus where the learning was put into a context of the children’s choice. I wanted to investigate how more ‘teaching’ could be done within a context. I was finding some objectives hard to put into a real life context. The children wanted maths to be about football and so I created a football scenario around finding averages. As Jo Boaler (Boaler, 2009, p13) says, it was using the children’s knowledge of the world and interests to engage the children. I presented a newspaper article which argued whether it was fair to have football teams where the average age of the players were different in each team. The boys especially wanted to have a debate about whether it was right to have a team with many young, fit players or a team with many senior professionals. There was a recognizable difference in the participation from the class and varying opinions meant that when we came to the activity, children had focused on the learning, ‘how to work out an average’ and had an interest in completing the task. The context was not necessarily one that the children would find themselves in as an adult but provided a way of exciting them and motivating them to find the answer.

Jo Boaler (Boaler, 2009, p13) claims that scenarios that are not realistic do not help with the procedures and performance. In this case, many children worked harder during lesson time to understand the concept as they

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wanted to take part in the activity. They would not use averages in this context again but the lesson definitely did engage and motivate the children. Boaler (Boaler, 2009, 45) noticed that with ‘make believe maths’, the children became good at engaging with it but not good at transferring skills.’ I was aware of this problem so looked to using a plenary which could explore real life themes. Conclusive Plenaries – During another day project, the children had carried out an investigation on the area and perimeter possibilities of different fields. Their work was based within one context for the lesson but during the plenary, the children were asked to identify other times when these maths concepts would be used. The children had been engaged by the open ended investigation, but had considered the context and were able to find many other situations. A discussion during the plenary worked particularly well in highlighting real life links. As I progressed into units A and B I found it increasingly difficult to create real life contexts for the objectives in each lesson. The contexts were becoming forced and distracting too much from the learning that needed to take place. Planning a 5 minute discussion during the plenary meant that the children were reminded regularly of the importance of finding the relevance in their work. The focus of my lesson returned to the objectives being met and I felt more freedom to plan the lesson how I wanted. I was not being restricted by the real life context in lessons where a project focus did not naturally fit. Plenaries which discussed real contexts were most effective after an investigative lesson or a lesson that required a calculation strategy to be learned.

I began to notice that it was not the real life context necessarily that made the children initially engaged, but the interaction and involvement that I had created at the beginning of the lessons. Group A needed to be distracted away from their idea of doing ‘boring maths’ and grasp their attention through discussions, debates, partner activity or active game. One child explained that they enjoy getting involved in fun, active activities as otherwise they found it hard to concentrate and left the answers to the others. ‘When I do it, I understand it more.’ Real life skills were being practiced; talking, vocalizing ideas, problem solving, investigating of statements and conclusions. Oral Mental Starters/ Short, active learning activities

For one week I reverted to ‘traditional’ way of teaching; highlighted by Boaler as being lessons where children listened, practiced a concept and recorded work independently (Boaler,2009,p4). All of my lessons were without a scenario, project focus or mention of the relevance to real life. I soon felt that the children’s enthusiasm immediately plummeted and at the end of the week, the children of group A rated their enjoyment and understanding down (average of 4). They had had an intense focus on project/ scenario work for a term and a sense of ownership of their own learning. One girl out of group A began to show disengagement as soon as she saw maths on the timetable. ‘It is just numbers at the moment.’ ‘I know I won’t understand it, I am not good with numbers’. This was the same child who had rated her understanding of the averages level higher than her peers.

As I had found with my research in the previous term, motivation at the beginning of the lesson (scenario, explaining project focus) was vital to keeping the enthusiasm going throughout the lesson. The aim was now to create a fun, engaging and practical oral mental starter that involved all children ( If this is the answer, what was the question? Guess my number, if I know that 10 cubes measure ….. what else do I know? Find different angles in an Escher picture.) I was also keen to provide more opportunity for children to develop the ‘life skills’ mentioned above

This took the focus away from ‘listening’ to the teacher and more focus on the discussion time that they had had and benefited the children in previous units. Children who were unsure of their ability in maths, I found, if partnered with a supportive and more confident peer, were encouraged to discuss and access the task at their level. Mixed ability partners had a positive effect on the higher ability children. They remained engaged and challenged by the activity as they were encouraged to learn to explain concepts and teach others. ‘Active engagement requires students to reflect upon their own thinking, questioning, negotiating and problem solving strategies.’ The teacher’s role in discussion becomes minimal, but the learning is there. The teachers can ask questions to move discussion on or give extra information to ‘spark further thinking.’ (NCRTL, 1993,p6)

Before a lesson on inverse calculations, I presented an activity to the children. If 10 multilink blocks measure 20cm, what else do I know? Group A stated that they enjoyed the activity as they had ‘freedom’ again to explore and discuss. There was not just one answer, an approach that appealed to the children who waited

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for the child that ‘knew the answer’ in order to take part. The children in group A were more eager to participate during the ‘teaching’ part of the lesson as they used the relevance of their mental starter.

I began to try and maintain the control over their learning in maths they had felt they had with project work. Self-differentiation was used where recorded or independent activities had to be done. The children of group A began by choosing the ‘Tricky’ sheet (simplest level) and only 2 out of the 6 children would move onto a different sheet. If time was given for discussion and a practice of the skills required, embedded into the lesson, the children became more adventurous. 5 out of 6 in the ‘inverse’ lesson moved to ‘Tricky Tricky’ or ‘Tricky, Tricky, Tricky.’ The children had not been able to ‘switch off’ as the lesson required interaction between the children; more learning had been done.

Long term projectsAfter exploring different strategies for contextualising learning, I returned to the project based approach for block D. My intentions were to give a long term aim of designing and budgeting for a bedroom. Group A were allowed to take control of their learning by brainstorming what we might have to cover before starting the task (for example, money, area, measuring skills.) It was important that the children were taught methods they need, as well as use them in solving of problems. (Boaler, 2009,p27) The children were able to break the two week unit down into sensible steps of learning. This highlighted the fact that doing Mathematics helps people to reason and organise complicated situations or problems into clear and logical steps. (QIA, 2008, P5)

The feedback from the project was very positive from the children, especially Group A. One child said he liked the week project as he knew what to expect in maths from the week. Another, who struggles to record much in lessons said that he felt he had produced so much work compared to working ie: with worksheets.

As a teacher, I enjoyed the creativity of the project and the focus it provided for the class. The skills were put into practice that they had learned, but I felt that the opportunity for extending the learning was not always there. There was some scope to extend the higher ability, but it was difficult to access a deeper level of learning. The context, I felt at times, dominated and swamped the learning. It is the teacher’s role to provide students with the opportunity to discuss problems with others in ways that illuminates the key points for understanding at an in depth level. (NCRTL,1993) The class became absorbed in context and once they had a suitable method, did not naturally explore the project as much as in an open ended investigation. Jo Boaler explains herself that contexts often used in an attempt to motivate and stimulate students while often they only act as distracters or even barriers to understanding. (Boaler,1993,p14)

I became to realize that the children’s motivation and learning was at its best during investigations. The project needed to be more open ended. Boaler suggests starting with a context open enough for students then to follow their own directions. They will attain personal meaning from their own development and methods of application. ((Boaler,1993,p14)

Next time I want to teach the objectives away from the task – using games, investigations, problem, puzzles to teach the skills and allow the children to develop their understanding at a deeper level. By using it as an end of unit assessment, I could assess how the children approached the task, reflected on the work and found their way to a solution. An end of unit assessment would act as a practice for how to choose and apply maths skills, learned at school, in a context beyond the classroom.

Using a contextualized project as an opportunity was very beneficial to me. I could observe and listen to conversations – judge where learning had developed and where the learning needed to go. The children explained that they enjoy it a lot more when they were sent off on a project and support was there if needed. Thinking about maths and talking about it to someone else is what is essential to an active approach (Flannery,2002,p38) To know whether they are understanding methods…they need to be talking through and explaining different methods. (Boaler,2009, p45) After block C and D I asked the children for feedback. These are the main points given; ‘It gave us freedom, there was more to do, we had fun and said they ‘understood the maths better. Many enjoyed it and wanted to take it even further.

Some children would have preferred to do the project independently instead of with partner. All 30 children said that they enjoyed the task. 13 children said that they would like to do that more regularly. The class agreed that it was suitable for once every term. 17 said that they preferred one/two day focus more as it felt that they covered more and allowed us to have lots of projects. For those who weren’t as interested in decorating a bedroom, 10 days was a long focus. During one day focusses, I could try to interest all children

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by choosing topics that interested each of them. The children agreed that they would like big projects every half term to a term. 1/ 2 day projects were recommended to be every fortnight. Reflection, evaluation and interpretation of the outcomes I have found pros and cons to the projects that I have used during this research. I found that the longer projects didn’t allow for a deep level of learning to take place, as too much time was given to one focus. The children however responded very well and marked their level of enjoyment and motivation at its highest (average 8) during this project. The shorter projects that used scenarios captured the children’s imagination and they enjoyed the creativity and personalization of the approach. There are some doubts as to whether the children would be able to apply their learning to another context. Youngman (Youngman, 2012) had praised ordinary life situations in maths lessons but had only explored measures, shape and space which naturally lend themselves to the work with contexts. For some objectives, it was unrealistic and unnecessary to try and create a real life context. I began to focus too heavily on real life links and found that this could become forced and unproductive; distracting me from the teaching that needed to be done.

I believe that variation is key to sustaining children’s engagement and motivation in maths. Whether short/long projects, use of scenarios, interactive mental starters or plenaries; there was a motivating ‘aim’ for the lesson and an ongoing reminder of the relevance of maths. It is allowing children to be ‘reflective on their learning’ through working towards an aim, set by project, activity or teacher. (NCRTL,1993,P2) I developed an expectation for all children to reflect on their learning. Through assessment for learning (lollipop sticks, paired discussion, recording on whiteboards), I could involve every child in the activities and focus the children on the lesson. Contexts encourage students to ‘explore’, ‘negotiate’, ‘discover’, ‘discuss’, ‘understand’ and ‘use’ maths (Boaler,1993,p15)

Group A began to show that they no longer had preconceptions about the math’s lessons. They were far more inquisitive and would ask what we would be covering next. A child explained that they were looking forwards to ‘games, fun equipment and talking with my friend.’ Children will remember the innovative and interesting ways in which a subject is presented. If it is interesting, they are more likely to understand it. (Youngman,2012) It is vital for children to see the purpose of maths. I am suggesting that projects are planned carefully around objectives that lend themselves to a real life context. I advise the use of projects for assessment opportunity and a time of reflection for the children. For the other lessons, fast paced, interactive activities need to be maintained with a strong emphasis on paired discussion. Mental starters and plenaries should provide opportunities to discuss and explore real life links where contexts cannot be used in the main body of the lesson. At the end of this research project, Group A marked their enjoyment level at a 8 (previously 5) and their level of understanding as a 6 (previously 4). I am surprised by how big an impact these changes have made to group A and the enjoyment and motivation that they now show for the active learning approach. I have become more aware of the needs of the children in my class and have enjoyed the creativity of personalizing their learning. I am wanting to pursue this new approach to teaching and learning and particularly share the ideas for assessment opportunity with the staff (as is a focus for our school development plan). Reference List Boaler,J (2009)The elephant in the classroom – helping children to learn and love maths, London: Souvenir Press Boaler,J( 1993)For the learning of mathematics- The role of context in the Mathematics classroom: Do they make mathematics more real?, FLM Publishing association, Vancouver Flannery, S (2002) In code: A mathematical Journey, Chapel Hill: Algonquin Books. Hersh, R (1997) What is mathematics really? New York: OUP Ofsted(2011) Good practice in primary mathematics: evidence from 20 successful schools: London: Ofsted NCRTL (1993)How teachers learn to engage students in active learning:Michigan: NCRTL publications. QIA( 2008)Improving teaching and learning in mathematics. Learning mathematics in context: London, Excellence gateway. Youngman (2011)Be creative with maths. http://www.teachingexpertise.com/articles/be-creative-with-maths-2720 Appendices Handling data activity taken from Primary Resources www.primaryresources.co.uk