The following blog is proof positive of how teachers as researchers in their classrooms are a force to be reckoned with. Three of our advisers, Gill Shearsby-Fox, Nicola Randall and Louisa Ingram worked with just such a group and we’re thrilled that research from 17 schools is now ready to read as case studies on the Herts for Learning site. Thanks to Jasleen Dhillon HfL researcher also for her support. The following blog by Gill shows how our advisers approached the project.
The Great Maths Con Action Research Project
On Friday 18th September 2015 the Herts for Learning maths team hosted a national conference with Jo Boaler, Professor of Mathematics at Stanford University, as the key note speaker. Many Hertfordshire teachers attended the conference to find out more about developing mathematical mindsets and be inspired to continue improving opportunities in mathematics for their pupils. The focus of the conference was to dispel the myth of innate mathematically ability and look at how mathematical mindsets can be fostered and grown. Jo Boaler’s research into mathematical mindsets builds upon the work of Dr Carol Dweck. It is in her book, Mindset – Updated edition: changing the way you think to change your potential (2006, Random House), that the idea of growth and fixed mindsets are described. She explains that a “growth mindset is based on the belief that your basic qualities are things that you can cultivate through your efforts. Although people may differ in every which way – in their initial talents and aptitudes, interests, or temperaments – everyone can change and grow through application and experience.” (page 6). Many people can have a growth mindset about most aspects of their lives but when it comes to mathematics it can be fixed. Many people have strong and often negative ideas about maths which stems from the general belief that in maths is all about getting the right answer and it is a subject that needs to be endured and is only enjoyed by the selective few.
Following on from the conference the maths team wanted to support teachers in cultivating a mathematical growth mindset to ensure that more pupils enjoy mathematics and are successful. A number of delegates who had attended the conference were invited to participate in a short action research project. The purpose of the project was to explore some of the themes covered by Jo Boaler and research different ways of developing mathematical mindsets. The project started in February 2016 and due to the time scale of the project, one and half terms, the teachers who took part completed the research within their own teaching groups focusing on changes to their own practice. The action research process followed four stages:
Stage 1: Clarifying vision and targets – What do I want to accomplish?
Stage 2: Articulating theory – What do I believe is the approach with the greatest potential for achievement?
Stage 3: Implementing action and collecting data – What do I do to implement my theory and how do I collect data to review impact?
Stage 4: Reflecting on the data and planning informed – Based on the data, how should I adjust my future actions?
(Adapted from pg 5-6: R Sagor (2005) The Action Research Guidebook – A four-step process for Educators and School teams, Corwin Press)
Throughout the project there were regular opportunities to meet in groups and discuss the projects. The initial meetings were used to review the main themes covered at the conference and identify visions and targets for individual schools. When the project started in February many of the participants had already made some changes to their practice in light of the conference and had clear ideas about what they wanted their desired outcomes to be. The outcome of all pupil’s having positive mathematical mindsets was of course the utopia everyone one was heading for but finding the first steps to getting there involved identifying a theme and a targeted group of pupils.
The main themes from Jo Boaler’s presentations covered across the group were:
- Fixed mind-sets especially within perceived ‘able’ mathematicians
- Girls’ achievement and attitudes to maths
- Maths anxiety
- Attitudes towards making mistakes
- Low entry/ high ceiling tasks
- Collaborative learning
- Visualising and pictorial representations.
Many of the teachers looked at a combination of themes, for example: girls and maths anxiety, low entry, high ceiling task and collaborative learning. In most cases focus groups of children were identified and their progress was tracked. As the research was taking place within the teacher’s classroom the impact of the changes made to practice did have positive impacts on all. For example where talking frames were introduced to support a group of anxious girls in collaborative learning all children used them and the quality of mathematically talk increased. However because they were introduced to the girls first this had an extra impact on their confidence as they felt empowered to model mathematical thinking, something they didn’t normally feel able to do.
Due to the length of the project it is difficult to conclude whether the research has had an impact on the attainment of the pupils involved. However the teachers involved successfully used a range of data collection techniques to ensure that qualitative data could be recorded, repeated and measured. Many carried out pupil questionnaires which included both scaled scores and pupil comments, collaborative and filmed lesson observations where analysed for specific use of language / questions and pupils pictures were also used as sources of evidence.
In those studies focusing on attitudes, anxiety and confidence overall many children’s mindsets have changed with many pupils stating that they feel more confident and teachers noticing, in both books and during classroom discussion, that they are more engaged in learning. In a number of research studies a specific focus was put on the use of vocabulary; in questioning, feedback and mathematical talk. Consistent use of subtle changes in language has had impact on the children involved. Where greater use was made of questions such as ‘What do you notice?’ and ‘What’s the same, what’s different?’ alongside the requirement to prove their reasoning, pupils who previously struggled with this have been able to articulate their thinking both verbally, pictorially and with equipment. When giving feedback some of the research has shown pupil’s now have a greater understanding that mathematics is a developmental subject where mistakes are needed to learn. In some studies pupils are recording their reflections on their learning highlighting areas of struggle and they are beginning to articulate what they can learn from this also mistakes we learn from are being celebrated. This feedback and the pupil’s reactions to it, shows that pupils are beginning to “love challenges, be intrigued by mistakes, enjoy effort, and keep on learning” rather than being concerned by the right answer. This is one of the greatest gifts we can give to children according to Carol Dweck (pg 176).
A number of the projects focused on providing opportunities to increase the use of Bruner’s CPA (Concrete to Pictorial to Abstract) approach mainly within ‘low entry, high ceiling’ activities. In these activities it is their openness that provided the opportunities. Jo Boaler says that they encourage the 5 C’s of mathematics engagement: curiosity, connection making, challenge, creativity and collaboration. (pg 57, Mathematical Mindsets, Jossey-Bass, 2016). Where these tasks were used within the project teachers noticed a number of challenges:
- pupils struggled to find starting points,
- the language of problem solving and reasoning was limited,
- pupils lacked the skills to develop their own thinking through the problem,
- staff were unsure how to facilitate this activities and develop mathematical reasoning.
There are many reasons for these challenges but as Debra Higginson from Nascot Wood Junior School observes, children’s attitudes towards maths can be like lions in the zoo who know they will be fed this is due to the curriculum they are used to receiving being procedural and formulaic but she hoped in her project to change them into great mathematical hunters curious and keen. She has begun to make the pupils at her school better hunters through specific teaching about mindsets within PHSE. This is beginning to have impact within mathematics but she recognises that this cultural change will take time and attitudes of all stakeholders need changing.
Other teachers within the research have also seen positive changes in children’s attitudes to towards mathematics through low entry, high ceiling tasks from feedback from pupil voice interviews we know this due to the difference of these lessons to more traditional ones, greater opportunities for children to work collaboratively and different ways of recording – pictures, large sheets of paper. The groups of children it seems to have had the greatest impact on within these projects are the lower and middle achievers. Traditionally higher achievers did not always enjoy these tasks and many of the teachers reported that these children have more fixed mindset, viewing mathematics as a subject in which lots of calculations need to be done correctly and independently to be successful. In a lot of the projects it is this group of children who have been hardest to have an impact upon but in some cases changes were beginning to show.
At St Thomas More Catholic School there focus group was four children in Y3 who had attained very highly at the end of KS1 but were resistant to using the CPA (concrete, pictorial, abstract) approach and didn’t enjoy investigative tasks, or reasoning. Pupil voice was used to benchmark and responses to questions about equipment and maths activities (investigations) got responses such as “I don’t enjoy it when doing / using equipment”; “I hate activities, I like doing sums”. Greater opportunities for talk, reasoning and problem solving skills were provided within maths lessons and then pupil voice was repeated. There had been some changes in mindset across the pupils but some still felt using manipulatives was ‘cheating’, however another one of the four strongly disagreed with this stating that they ‘show your brain is working and helps you with your maths’. The impact of a CPA approach and the use of manipulatives on pupil’s mindsets in their ability to explain their thinking is evident for other projects that had this as a focus mainly from pupil voice interviews and observations within the classroom. However at St Cuthbert Mayne School data showed increased attainment of pupils in Y3 who achieved particularly well in arithmetic questions. The class teacher felt that this was because of giving the pupils time to explore concepts and a variety of strategies with manipulatives.
The pedagogical approaches to mathematics teaching is currently in a period of great change, with an age related curriculum introduced in 2014, influences from countries such as Shanghai filtering into text books and lesson organisation and teachers being encouraged to ensure that pupil’s ‘master’ learning and move through the curriculum together. All of these are very different from teacher’s own experiences of maths learning when they were at school and the level driven nature of the previous curriculum. Therefore change in mindset towards the approaches to maths learning that Jo Boaler shared at the conference need to be made by the teachers before there can be an impact on pupils. Many of the participants in the research realised this through doing the project and therefore one of the biggest impacts of the project was that they, as practitioners, have had a shift in mindset.
At the final meeting of the teachers who took part in the project what was going to happen next was discussed. Many felt that what they had done was a drop in the ocean and changing the mindsets not only of the pupils, but of colleagues and parents was a huge job. Especially as we currently live in a society where it is socially acceptable to be ‘rubbish at maths’. However the small changes in: teaching, pupil’s attitudes and language used, that have been made by our teachers involved in the project have shown that growth mindsets can be developed and with consistent fostering and care all children do have the capacity to fulfill their maths potential.
We are very grateful to the teachers involved, to their hard work and dedication. They have produced thought provoking write ups of their projects which are available as case studies on the HfL…. .
Thank you to the schools involved – click schools to see their individual case studies:
Abbotts Langley School – Do talking frames reduce girls’ anxiety in maths?
Abbotts Langley School – How do we use our resources to help us reason?
Aboyn Lodge School – Do Low Entry High Ceiling tasks reduce anxiety in mathematics?
Chater Junior School – Do Low Entry High Ceiling activities reduce maths anxiety and positively impact upon progress?
Dundale Primary and Nursery School – Does mixed ability grouping and choice of tasks help to give children confidence when approaching new mathematical problems
Howe Dell Primary School – Increasing attainment and fostering a positive approach towards mathematics for White British pupils
Maple School – How valuable is the Concrete-Pictorial-Abstract model of teaching mathematics concepts across the primary school phase for all children, not just the Lower-Ability or SEN pupils?
Nascot Wood Junior School – How can the use of language influence children’s attitudes to maths?
Pope Paul Catholic Primary School – How do low entry high ceiling (openended) problems facilitate talk?
St Cuthbert Mayne Catholic Junior School – Providing pupils with opportunities to use concrete resources through ‘explore’ activities in order to develop the use of multiple representation when approaching maths work
St Margaret Clitherow RC Primary School – Can we ensure that home learning consistently supports a growth mindset in maths for all children?
St Paul’s CE VE Primary and Nursery School – Can Concrete-Pictorial-Abstract support pupils to securely reach age related expectations in 6 weeks?
St Thomas More Catholic Primary school Berkhampstead– Will developing the CPA approach for high attaining children with a fixed mindset increase resilience, accuracy, understanding and thinking?
St Thomas More Catholic Primary Letchworth – How can questioning be used to support and encourage children when they say they are ‘stuck’ in maths?
Wheatfields Infants’ and Nursey School – How does the use of concrete manipulatives and visual props support the development of number fluency and number talk?
Wormley C ofE Primary School (VE) – Why are girls who are working above age related expectations at the end of Key Stage 1 not achieving the same at Key Stage 2?
Yew Tree Primary school – Can the effective use questioning develop growth mindsets and deeper mathematical thinking?
Boaler, J (2016) Mathematical Mindsets, Jossey-Bass
Dewek, C (2006) Mindset – Updated edition: changing the way you think to change your potential, Random House
Sagor, R (2005) The Action Research Guidebook – A four-step process for Educators and School teams, Corwin Press