Advisory Committee on Mathematics Education (ACME)

Case studies - professional learning for all teachers of mathematics

In spring 2016 the Expert Panel undertook a survey seeking to gain an insight into what teachers described as critical incidents in their mathematics professional learning and how this changed their practice.

The case studies below are not seeking to provide examples of best practice, but instead highlight some key themes highlighted by teachers across phases and how they described the learning in their own words. They also show the very different entry points and professional opportunities undertaken.

Each teacher and senior leader reflecting on the mathematics-specific knowledge will have their own journey and may wish to reflect on what they describe as critical learning opportunities and how this affected their practice. They may also identify gaps that they might like to address.


Case Study 1

CURRENT ROLE: This teacher is a full time teacher who is part of the senior leadership team, working in a state junior school, who has only ever worked in this setting and only has taught Key Stage 2. The role involves teaching Year 4 children for four days. The final day a week is split into half a day for Planning, preparation and assessment (PPA) and half a day release for mathematics subject leadership and year group learning.

ENTRY INTO MATHEMATICS TEACHING: This teacher followed a postgraduate route into teaching, (a PGCE) and also undertook a school-based Graduate Teacher and a Masters in Teaching and Learning.

FURTHER STUDY: The master's level study was described as a critical incident in the development of the teacher noting that 'as part of the course I undertook a project in school looking at language issues and optional SATs papers. I asked a Year 5 child to answer a question involving finding the difference between a positive integer and a negative number. She said "we haven't done fridges yet!". The question was in a context with a fridge and freezer. Often children do not have the opportunity to link learning in different areas so non-contextual learning is not applied to a word problem in a particular context.' She noted that as a result 'I try to relate maths learning to real life and encourage children to create their own problems based on a particular area of maths, I present problems as part of a lesson to link different areas of maths together'.

MATHEMATICS PEDAGOGY: This teacher reflected on the learners' practice in the light of their own experience saying that 'I am aware of frustration and share experiences where I have been frustrated as a learner. I encourage the children to develop resilience so that they can achieve their best. I teach children to learn together and support each other to avoid frustration'.

PROFESSIONAL OPPORTUNTIES: The teacher recognised the variety of professional development opportunities required noting that 'at times in-house activities are best. As a maths subject leader I know what needs to improve and how. At other times, going a maths course can be interesting as there are other people who can present the knowledge in different ways and get colleagues talking about their practice and how they will adapt it as a cause of attending the CPD'.

Case Study 2

CURRENT ROLE: This primary teacher is a full time assistant head teacher and mathematics subject leader who teaches Year 6 at a community primary school. The role involves teaching 4 days a week and 1 day a week is spent for leadership duties.

ENTRY INTO MATHEMATICS TEACHING: This teacher was a graduate in English and undertook a post graduate qualification in Teaching English as a Foreign Language. The teacher has also taught Early Years, primary and Key Stage 3. The teacher described an interest in mathematics that led to participation in the MaST programme. Following MaST, the teacher gained accreditation as a Maths PD Lead from NCETM.

ENGAGING WITH RESEARCH: The teacher noted the importance of reading academic literature about pedagogy in order to understand learning in classroom practice that the teacher was leading. This reflection led to the teacher noting how important it was for learners to understand why something is happening and explain why it happened. This has led to the teacher emphasising reasoning and communication in teaching and learning. This teacher observed that 'unfortunately, not many teachers engage in CPD through reading meaningful research' and led the teacher to introduce compulsory reading which led to changed mindsets of teachers.

SCHOOL LEARNING CULTURE: The teacher noted the importance of a school culture of learning noting that 'although it took me time to convince the Senior Leadership Team so many years ago when I wanted to try out new ways, it helped me enormously when I was given the trust to carry out my plans as a subject leader. School culture can be changed as long as there is respect and trust amongst colleagues.'

Case Study 3

CURRENT ROLE: This further education teacher teaches full time in a further education college with an attached sixth form. As well as teaching GCSE Mathematics for the past 18 months (9 hours contact time), the teacher also teaches health and social care.

ENTRY INTO MATHEMATICS TEACHING: This teacher has taught in a variety of settings, including pre-school, nursery, infant and junior schools. The teacher explained their recent journey to become a teacher of mathematics. The teacher explained how the teaching of mathematics followed after a request to teach Functional Skills mathematics at Entry Level and Level 1 four years ago to 16-19 year olds.

TEACHER AS LEARNER: The teacher noted 'I was really nervous and worried as I only have a C in my GCSE. After taking the challenge I found that not only did the students have a very low starting point, but I was also able to learn some things I had forgotten along with them. It was a really good experience for me as I was previously very confident in my vocational subject and this reminded me what it was like to (re)learn something and be exposed as a learner as much as a teacher. What it taught me was that if we talked through problems and persevered, we could find the answer.' The teacher is keen to continue the journey, saying 'I know I still have a long way to go, but I love it and I'm thirsty to learn more maths and develop my pedagogy in maths teaching'.

BUILDING KNOWLEDGE OF MATHEMATICS: The teacher highlighted the importance of developing subject knowledge through a subject knowledge enhancement (SKE) course that was organised over one year. The teacher noted that 'The first session was really scary as I knew my maths skills were still poor and I would be among people who were already teaching GCSE…Despite being the least able in the group I was supported so well by the tutor and the other members […] key points would be: to make learning active, to involve learners in problems they want to solve, to use a variety of methods and pull on the learner's own knowledge to develop discussion and answers and not be afraid to get things wrong - that's how we learn'.

EXTERNAL CHALLENGE AND REFLECTION: A critical moment for this teacher was being observed teaching mathematics noting that observation from the SKE course tutor 'without grading is one of the best things that can happen. I had never had such informative feedback on a lesson. Techniques and approaches to presenting information were invaluable'.

Case Study 4

CURRENT ROLE: This secondary teacher is a senior leader and Advanced Skills Teacher in a 14-19 school. The teacher has 36 hours contact time with students per fortnight with Key Stage 4 and 16-18 students.

ENTRY INTO MATHEMATICS TEACHING: The teacher took a PGCE route into teaching.

CRITICAL EVALUATION SKILLS: The teacher noted the importance of critical evaluation skills stating: 'It's important for all maths teachers to engage with current research projects to help to shape and develop them as a good subject specialist and classroom practitioner.' The teacher also noted having explored a student-led inquiry research approach within and across schools and consdering how to use things around them to engage students in lessons. The teacher also described the benefits of having been involved in a lesson study project working with partner schools.

UNIVERSITY-SCHOOL PARTNERSHIPS: The importance of school and university partnership was underlined by this teacher who relayed that they had 'explored relevant ways of engaging students in maths, [the] opportunity to be a creative teacher and develop creative resources' meaning that 'I am more passionate and engaging in delivering lessons and draw widely on a range of approaches and resources to motivate and challenge students'.


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