The aim of this project was to increase attainment in numeracy for a targeted group of Primary 4 pupils with a view to them successfully achieving First Level, Curriculum for Excellence by the end of session 2019/20. Scottish Government suggest in their 2012 publication ‘Raising Attainment’ that numeracy should be a key focus for those seeking to raise attainment in schools. The Scottish Attainment Challenge, launched in 2015, further emphasises that raising attainment in numeracy (as well as literacy and health and wellbeing) will significantly increase the prospects of Scottish children in future. Haylock and Cockburn (2008) suggest that, in order to establish deep understanding, learners must experience the new concept using concrete materials, pictures, symbols and language. Dweck (2008) suggests that attainment can be increased by developing a growth mindset. A growth mindset is the belief that challenge, effort and set backs are the most valuable components in a learner’s journey and that ability is not fixed. The numeracy interventions were planned to sit alongside group sessions where the focus was on developing a growth mindset to allow these pupils to view challenge more positively and thus increase their capacity for numeracy learning. Six children were initially identified to take part in the intervention which would serve as a small test of change. Whilst results from a sample of this size may not be generaliseable they will serve as a starting point for discussion.
Progress was made towards achieving the aim of the project: the children involved have a clearer understanding of some basic concepts than they did initially, they are demonstrating more resilience and perseverance and, are talking about maths more positively. However, based upon class teacher predictions, there has not been the degree of progress necessary to say confidently that these children are now well positioned to achieve First Level, CfE by the end of this academic year and so, in that respect, the project has failed to reach expectations. On reflection the aim was most probably too broad for a project of this size and scope. Focussing on one aspect of maths (such as numbers to 100) and aiming to improve this by building growth mindset may have had more demonstrable success. Nonetheless, it is important not to diminish the progress that was made and to build upon it going forward. Whilst the aim of the project was for the children taking part to achieve First Level, CfE by the end of Primary 4 Scottish Government (2004) state in the CfE guidance that this is an expectation of most children and not all. With continued support, such as that received during this intervention, there is confidence from class teachers that these children will achieve First Level, CfE during Primary 5.
The initial three weeks of the intervention ran according to schedule. However, it became apparent that removing several children from the same class for one to one sessions throughout the day was becoming disruptive to the teaching and learning going on in class. This was overcome by altering the format of the intervention. Children were removed from class to work in small groups rather than on a one to one basis. Working in small groups proved to be beneficial as there was more spontaneous dialogue and scope to work together during problem solving activities. During week 4 there was a change of timetable (for the teacher conducting the research) to accommodate a child who is not part of the intervention. This allowed less time to focus on the intervention. The impact of this was that growth mindset sessions had to be shortened and incorporated into the numeracy sessions. Throughout the course of the intervention some sessions have not taken place. Due to staff shortages the teacher conducting the research had to cover classes. Whilst this is not ideal, and some flexibility was built into the timetable, it was unavoidable and priority must be placed on the smooth running of the school. Valuable lessons have been learned from this and in future, fewer sessions would be planned with greater flexibility.
Undertaking action research as a ‘teacher researcher’ invariably carries the possibility of plans changing frequently. There were changes made throughout the project due to the changing needs of the school in which it took place. However, the aims of the project remained unchanged. One to one numeracy sessions were changed to small group sessions (three children and the researcher) to lessen the disruption to class teachers and children. Growth mindset sessions were initially planned as a separate session but had to be incorporated into the numeracy sessions due to lack of time. Gregson (2004) discusses the difficulties of conducting action research and the underlying internal conflict when situations are viewed from a ‘teacher’ or ‘researcher’ perspective when the ‘teacher’ and ‘researcher’ are one and the same person. From the perspective of a ‘researcher’, when the focus has been on finding a solution to an identified problem, changes to project plans can be frustrating and time consuming to redo. From the perspective of a ‘teacher’ the teaching and learning needs of the children are always the first priority and changes to plans are regularly accommodated.
Nottingham (2017) suggests that learning can be explained as a pit that we must first fall into and then climb out of in order to achieve deep learning. Early in the project the group discussed what it felt like to ‘be stuck’ when trying to figure out a maths problem. Worried, upset, stupid and dumb were some of the responses. When asked what they would do next most replied that they would ‘give up’. One child said they would ask for help. The group then spent some time looking at ‘The Learning Pit’ and discovered that they were falling into it and needed to learn some strategies to work their way out. The more sessions went by the more positively the group came to view falling into the pit; or ‘challenge’ as it came to be known. By the end of the project when children were asked how confident they were that they would be able to solve a tricky maths problem they all responded with increased confidence when compared to being asked the same question pre-intervention (see appendix 1). When asked what they would do if they got stuck they replied: · ‘keep trying’ · ‘not give up’ · ‘ask a friend’ · ‘ask the teacher’ · ‘use my Numicon’ · ‘use my number square’ · ‘take a break and try again’ · ‘look for another way’ They further demonstrated the change in their mindset when asked to choose from a selection of tasks in a ‘chilli challenge’. All of the children chose the ‘hot’ task (the most difficult) over the ‘medium’ and ‘mild’ tasks. Their more positive mindset towards challenge may have given them an increased sense of confidence to persevere when an attempt failed. By this point the children had developed their mathematical ability and had more strategies to use to help them solve challenging problems as well as a range of physical resources that they were proficient in using. The responses noted in appendix 1 may be due to a combination of these factors. There has been a positive impact on maths attainment due to the increased perseverance on task, willingness to try alternative strategies and to seek help when needed which has been exemplified during problem based learning. The project has also illustrated to the researcher the importance of modelling positive language both with children and adults (other school staff and parents). Whilst it is not a ‘cure all’ adding ‘yet’ to otherwise negative sentences is a powerful tool if used thoughtfully. It has also established the importance of appropriate praise and the continual identification of next steps to promote deep learning. Through their involvement with the project parents have also come to realise the important role their experiences and perceptions have on their children. Many had subconsciously given their children the message that it was acceptable not to ‘be good’ at maths because they were not either. Encouraging parents to recognise that our abilities, in maths or any other subject, are not fixed has motivated them to learn about the resources being used in school and to grow their own abilities alongside supporting their children.
The impact of the intervention was measured in several different ways including: evaluation of weekly notes; consultation with class teachers; comparison of pupil mindset questionnaires completed during week 1 and week 6; comparison of pre and post intervention attainment predictions; SNSA results and; consultation with parents pre and post intervention. By evaluating the weekly notes it was found that all children who took part had sought out challenging tasks and had spent longer persevering on challenging tasks than they had initially. Children persevered on the challenging task in week one for between one minute and thirty four seconds and three minutes and two seconds. This suggested to the researcher that the children may only be trying one strategy to solve the problem before abandoning their attempt. There was also an inference amongst the group that if the answer could not be found quickly there was no point doing the task. Just one child completed the task. After participating in the project the same children persevered on the (new) challenging task for between two minutes and fifty one seconds and four minutes and twenty seven seconds. All children completed the task and offered support and encouragement to others in the group. This suggested to the researcher that the children had learned a wider range of strategies to try and that they no longer saw completing a task quickly as their main motivation. They now wanted to complete the task for the pleasure of succeeding. Reviewing weekly notes also highlighted the shift in language from negative statements regarding challenge such as ‘this is too hard and ‘I can’t do this’ to a more positive view of the same degree of challenge. Statements including ‘I’ve managed most of this’ and ‘this is really tricky so I’m growing my brain’ revealed this shift. These statements became more common amongst the group the more success the children had after persevering with a task. They also became confident in asking for help from each other. At the beginning of the project some of the children appeared to view asking for help as a sign that they were not intelligent. They now seemed to believe that asking for help meant that they were intelligent enough to know that others may be able to provide them with a strategy they had not already tried. During consultation with class teachers it has been identified that most of the children who have participated in the project have shown increased positivity to challenge across the curriculum and are utilising the skills they have developed in using the manipulatives in maths. Whist attainment predictions have remained unchanged (the same class teachers made predictions in August 2019 and December 2019) they have stated that it is their professional judgement that with continuing intervention these children will achieve First Level, CfE during Primary 5. Early analysis of the SNSA results for these children appear to endorse this (see appendix 2). Comparison of mindset questionnaires carried out pre and post intervention specifically focussing on attitudes to learning are markedly different (see appendix 3). For example, when shown the statement: ‘when I don’t do well in a subject, I think I am not very good at it’ all children pre-intervention strongly agreed. Post-intervention one child agreed, two children disagreed and three children strongly disagreed. Similar patterns were evident in all ten questions. This suggests that there has been a shift in attitudes to learning due to taking part in the intervention. The children were particularly interested when the formation of new neural pathways was discussed and this knowledge appears to have given them the confidence to view themselves, and other, as ‘learners’ rather than being ‘stupid’ or ‘smart’. Through consultation with parents it has been gleaned that some of the children taking part in the project have been implementing their learning at home. Parents have reported fewer battles over homework (particularly maths), a more positive attitude to school and that their children have been sharing the strategies learned with others in their homes.
Appendix 1 Appendix 2 Appendix 3 References
Hattie and Timperley (2007) suggest that when seeking feedback it is important to be specific in which aspects of performance should be addressed. This in turn leads to precise feedback which can be used to close the gap between where performance currently stands and the end goal. Class teachers were asked two questions: 1. Have any of the children who participated in the intervention increased their attainment in maths based on their SNSA results or your professional judgement (e.g. have your predictions changed?) 2. Have any of the children who participated in the intervention demonstrated any changes to their mindset? Feedback from colleagues on the impact of the project has generally been very positive. Class teachers were eager to have additional input for children in their classes to potentially increase their attainment in maths. Although there were some issues around timetabling the class teachers were supportive and worked with the researcher to find solutions that worked for everyone. In response to question 1, predictions have not changed for any of the children who took part in the intervention. Although class teachers felt the intervention had been beneficial they also felt that longer term intervention would be required. In response to question 2, class teachers have reported a noticeable change in mindset from the majority of the children participating in the intervention. They have described children persevering for longer on tasks they find challenging than they would have pre-intervention; using more positive language to describe themselves as learners and; being more confident in the use of resources to support their learning.
The next step for this project is to roll out the intervention to groups of pupils in Primaries 5-7 who have also been predicted to achieve a level only with targeted support. At present there are around 25 children who fall into this category. Through discussion with class teachers, discussions with the children and baseline assessments they will be divided into small groups. Pupils will be grouped based upon who will work well together; who has similar maths learning needs and; to facilitate a mix of growth mindset perspectives. The researcher has recently undertaken training on how best to use Numicon to support learners at Second Level, Curriculum for Excellence and so this resource will continue to be utilised during the roll out of the intervention. This learning will be shared with class teachers to facilitate the wider use of Numicon throughout the school which will, hopefully, prevent the pupils forming any misconceptions that Numicon is solely for the use of younger pupils. Developing a growth mindset will remain part of the sessions with the expectation that this will filter back into classes. The researcher also plans to use what they have learned about growth mindset as the basis for developing emotional literacy in their own class.