Statements about Effective ITE
Effective Initial Teacher Education engages each trainee in beginning a life-long learning journey as a teacher of mathematics through working:
Please click on to the + this provides further information in a dropdown.
- individually and collaboratively
- innovatively, creatively and critically
- with research and evidence
- with tools such as digital technologies
- using the skills of evaluation and reflection
- with the emotional and social aspects of learning experiences
- and through the processes of….
ITE1 Developing their own passion for mathematics through profound and connected understandings of the subject
Effective ITE engages trainees through developing their own passion for mathematics through profound and connected understandings of the subject
- In the primary sector the emphasis is on building confidence alongside secure and appropriate mathematical understanding.
- Appropriate subject knowledge for mathematics teachers includes the following: applications, visual imagery, language, context, problem solving and problem posing, considering multiple representations, and ‘new’ knowledge or understanding that can be accessed through the use of digital technologies.
- Whilst secondary and college specialists need to have mathematics knowledge and understanding at a higher level than they generally teach, all those who teach mathematics need an appropriate profound understanding of fundamental mathematics (Ma 1999;and Nunes et al 2009).
- There is a need for ITE trainees to develop a view of mathematics that sees the subject from a broad range of perspectives and challenges narrow procedural views of the subject.
- There is also a need for ITE trainees to recognise and develop an understanding of their own mathematics both relationally and instrumentally.
- Those learning to be mathematics specialists need an extensive and structural understanding of mathematics that identifies the fundamental underlying structures of mathematics.
- Understanding the impact of digital technologies on what is learnt, when and how.
Examples of practice
- The process of creating a diagram or object using Dynamic Geometry Software exposes the underlying mathematics behind the created image.
- ITE trainees doing mathematics and considering what the experience was like, what they brought to it, how they are able to do these sorts of things and what sorts of difficulties they had.
- Recognising, for example, that much of geometry is based on key ideas about ratio, proportionality and similarity.
- Having the confidence in their own subject knowledge to choose an open-ended activity knowing that a variety of mathematics might be accessed by learners.
- Using resources such as the NCETM mathemapedia, self evaluation tools and the Maths Café to give ITE trainees opportunities to reflect on, challenge, and develop their own subject knowledge.
ITE2 Utilising effective mathematical pedagogical knowledge, judgement and practice developed through informed understandings of relationships between procedural and conceptual knowledge
Effective ITE engages trainees through utilising effective mathematical pedagogical knowledge, judgement and practice developed through informed understandings of relationships between procedural and conceptual knowledge
- Having a focus on learners and meeting the needs of learners.
- This includes considering different theories of mathematics pedagogy and learning and identifying effective tasks for learners that support the development of mathematics.
- Understanding how a teacher can mediate the learning of mathematics and mediate the experiences of learners.
- Focusing on both more general mathematics pedagogy and the specific mathematics pedagogy related to individual mathematical topics.
- Understanding when and when not to use digital technologies to develop learning in mathematics. Being able to evaluate the impact of specific uses of digital technologies on mathematics learning and to restructure learning sequences taking into account the affordances of new technologies.
- Developing an awareness of themselves as learners before moving on to consider the experiences of the learners they work with.
- Developing an understanding of how to make decisions about what, when and how to teach for conceptual understanding and fluency; procedural understanding and fluency; application and flexibility; and reasoning.
Examples of practice
- An understanding of the differences between relational and instrumental understanding allows ITE trainees to understand why mental calculations are learnt before written methods.
- An approach to planning where the first task is to create a mathematical ‘map’ by looking at both the interrelationships between topics and at structural aspects of the topic. This is followed by deciding on a narrative, or teaching stories, for the topic and finally by an orientation phase where classroom activity is developed in order to engage learners with each of the elements of the narrative.
- Sharing a piece of mathematics from the curriculum and demonstrating different ways of approaching it. Discussing the issues learners might have with the topic, the relative merit of the different approaches, where the mathematics is exposed and where difficulties might arise.
- Through tutors and mentors modelling a variety of different approaches including those ideas less commonly seen in schools and those that make innovative use of digital technologies.
- Examining learners’ work, examples of materials from school, or materials designed by the ITE trainees themselves and discussing what makes a good question for learners and what conceptual learning the materials support.
ITE3 Developing their capabilities in reflecting on their own learning and practice, and the practice of others
Effective ITE engages trainees through developing their capabilities in reflecting on their own learning and practice, and the practice of others
- Taking time to pause, to critically evaluate, to reflect and consider, to consolidate and accommodate what they have been learning.
- Developing reflection as a strategy for supporting their own professional development.
- Shared reflection with peers and others.
- Embedded approaches to reflection and reflective practice throughout their professional life.
- Reflection playing a part in the process of reconceptualising and reconstructing their mathematical knowledge and developing teacher identity.
- ITE trainees being able to take notice of what they’ve observed and implementing it so that it has an impact on their practice.
Examples of practice
- Using the ‘Knowledge quartet’ (Rowland et al. 2009) as a reflective tool.
- Setting unfamiliar mathematics tasks so that ITE trainees are working outside their comfort zone as a stimulus to shared reflection about what they were doing, the experiences they had, what the learning was, what learning opportunities the task offered and how the task could be used in the classroom.
- Days during teaching practice when ITE trainees return to their institution to support one another, develop strategies for problems and develop their practice collaboratively.
- Having a reflective element in assignments.
- Sharing the theoretical underpinnings of reflective practice and modelling the reflective process. Engaging ITE trainees with reflective practice at a point where they see the value in doing it.
- Paired teaching placements with one ITE trainee teaching and the other evaluating, reflecting and feeding back.
- Using reflective cycles that involve school-based mentors as well as ITE tutors in modelling the reflective process in post-lesson observation discussion, with a focus on the learner and the learning taking place as well as the ITE trainee’s personal learning.
- ITE trainees learning to pay attention to what they’re noticing and working on why they’re noticing it.
- Structured reflective practices such as keeping a diary, journal or blog with a series of headings or areas to consider when reflecting.
ITE4 Accessing, critically synthesising and using research and evidence on the learning and teaching of mathematics
Effective ITE engages trainees through accessing, critically synthesising and using research and evidence on the learning and teaching of mathematics
- Being able to communicate about learning and teaching mathematics with suitable academic rigour and using the skills of critiquing, summarising and synthesising sources.
- Building up an expectation that they will engage with research and evidence about learning and teaching mathematics.
- Being able to read, reflect upon and use research and evidence to support and challenge views about learning and teaching mathematics.
Examples of practice
- Taking an academic focus from the start of a course so sessions have academic reading as pre-reading or a follow up task; sessions include reference to research and evidence, including key research findings, and ITE trainees are pointed towards relevant resources.
- Setting tasks that lead ITE trainees to explore research for a particular purpose.
- The undertaking of Master’s level assignments on postgraduate courses and the academic requirements of undergraduate credit-awarding courses.
- Using research-active staff to teach on Initial Teacher Education courses.
- Responding to identified individual development needs by giving the ITE trainee some sources of helpful research and evidence.
ITE5 Making connections within and between: mathematics, cross-curricular opportunities, aspects of their practice, and reflective learning
Effective ITE engages trainees through making connections within and between: mathematics, cross-curricular opportunities, aspects of their practice, and reflective learning
- Developing the connectedness of ITE trainees’ own mathematical knowledge, connectedness in the way they teach mathematics, and being able to help learners make their own connections in mathematics.
- Being able to see how mathematical ideas are developed through the curriculum and how some topics provide prerequisite knowledge and understanding for other topics.
- Seeing connections across the curriculum, between mathematics and other subjects, including vocational and work-based learning.
- Understanding how digital technologies can be used to help develop insights in learners that are not possible in other ways.
- Exploring the connections between ITE trainees’ own subject knowledge, pedagogical knowledge and practice through the use of reflection.
- Connecting ITE trainees’ own mathematics and what happens when they do mathematics themselves with what their learners do with mathematics.
Examples of practice
- Using the planning of sequences of lessons, rather than individual lessons, as the dominant planning tool; understanding what images, language and models connect key ideas in mathematics, and what images, languages and models limit learners’ future understanding.
- Using digital technologies to make connections, for example between multiple representations of the same function.
- Making connections between the ways different tools handle pieces of mathematics, for example a calculator and a computer.
- Exploring the use of data, statistics and financial aspects of mathematics in Citizenship.
ITE6 Knowledgeable and critical professional learning about statutory and non-statutory curricular and assessment advice recognising inclusive practices for all across the curriculum
Effective ITE engages trainees through knowledgeable and critical professional learning about statutory and non-statutory curricular and assessment advice recognising inclusive practices for all across the curriculum
- Having a clear underlying philosophy and approach that goes beyond the immediate short-term concerns of current policy in order to see the big picture.
- Understanding the roles of both statutory and non-statutory guidance in informing practice.
- Developing an informed and critical approach to national guidance and policy.
Examples of practice
- Using examples of innovative practice from schools.
- Using the expertise of schools and school-based mentors to develop ITE trainees’ detailed knowledge of current assessment and monitoring practice, examination requirements, inclusion, national initiatives, etc.
- Giving ITE trainees a sense of how the current curriculum developed and key influential documents such as the Cockcroft Report, Better Mathematics, etc.
Developing an understanding of how mathematics is located within the curriculum and its potential to provide links across the curriculum.
ITE7 Developing pedagogical attributes so that they are able to enthusiastically engage and motivate learners in mathematical thinking and reasoning
Effective ITE engages trainees through developing pedagogical attributes so that they are able to enthusiastically engage and motivate learners in mathematical thinking and reasoning
- ITE trainees being enthusiastic about mathematics themselves.
- ITE trainees reconnecting with and developing their own motivation for learning and teaching mathematics.
- Understanding that teaching mathematics is a complex and multilayered process.
- Understanding what it is to think and reason in mathematics and the differences between mathematical thinking and other types of thinking.
- Recognising the motivational value of learners’ use of digital technologies for mathematical thinking.
Examples of practice
- Helping ITE trainees to learn how to communicate their enthusiasm through modelling by tutors and mentors and by learning how to use techniques from drama to look at themselves as performers.
- ITE trainees doing mathematics, enjoying mathematics themselves and thinking about what is involved in learning mathematics.
Gaining technological skills to improve confidence in their personal and pedagogical use of digital technologies and promote effective use by learners
ITE8 Developing pedagogical attributes so that they promote learners’ personal confidence and positive attitudes through enjoyment of mathematics
Effective ITE engages trainees through developing pedagogical attributes so that they promote learners’ personal confidence and positive attitudes through enjoyment of mathematics
- Developing the skills to make effective use of a range of approaches to teaching and a variety of tools for teaching including digital technologies.
- Building confidence in learners so that they want to continue studying mathematics.
- Understanding the creative opportunities provided by use of digital technologies.
- Having the confidence to allow learners to take the lead.
- Acknowledging that learners may have skills in some areas that their class teacher does not.
Examples of practice
- ITE tutors participating in learning experiences alongside ITE trainees.
- Taking risks teaching with digital technologies where learners may have more advanced facility and familiarity with the technology than those teaching them.
- Allowing high attaining learners to explore, conjecture and reason at their own level on problems they are interested in.
ITE9 Critically examining and reflecting on their own attitudes and beliefs about mathematics and mathematics pedagogy and the impact these have on their own learning and their teaching
Effective ITE engages trainees through critically examining and reflecting on their own attitudes and beliefs about mathematics and mathematics pedagogy and the impact these have on their own learning and their teaching
- ITE trainees considering their own beliefs and challenging the beliefs of others in appropriate ways.
- Recognising, exploring and exposing what practice suggests about actual beliefs rather than professed beliefs.
- ITE trainees making a shift in their sense of identity and perspective from being a trainee of mathematics to being a teacher of mathematics.
- Exploring assumptions about the nature of mathematics and what constitutes mathematical knowledge and understanding.
- Developing curiosity and an interest in learning as a route for further development and as having intrinsic value, rather than seeing learning only as a means to a goal.
- Recognising that attitudes and beliefs have an impact on the use of digital technologies.
- Making explicit and challenging their own preconceived notions about the value of digital technologies to support learning.
Examples of practice
- Through open discussion about choices, decisions and methods of teaching.
- Use of tasks and assignments to challenge preconceptions and promote change in practice.
- Use of pre-course reading to ‘set the scene’ and make explicit the course philosophy.
- Providing structure for thinking about teaching more broadly than from the ITE trainees’ personal experience.
- Using tasks that encourage ITE trainees to think about what they are learning, how they learn, how they were taught and the aspects of good mathematics teaching.
- Using role play and having ITE trainees argue from different standpoints.
- Exploring ITE trainees’ own mathematical history, writing something about their beliefs at the beginning of the course and returning to this at a later date.
Exploring understanding and beliefs about mathematics by not allowing ITE trainees to say: ‘simple’, ‘simply’ or ‘just’.
ITE10 Demonstrating understanding of the importance of historical, cultural, social, personal and societal aspects of learning, teaching and assessment in mathematics
Effective ITE engages trainees through demonstrating understanding of the importance of historical, cultural, social, personal and societal aspects of learning, teaching and assessment in mathematics
- Flexibility in recognising techniques and methods from a range of cultures, being able to understand how these methods work and the limits of their applicability.
- Recognising how cultural and societal factors impact on mathematics learning.
- Developing an understanding of some of the specific factors affecting learners’ development in mathematics.
- Considering developments in digital technologies and how they might impact on mathematics classrooms of the future.
Examples of practice
- Undergraduate route includes a module on the history of mathematics.
- Looking at the history of mathematics and at different societies, specifically Chinese mathematics and Egyptian mathematics.
- Considering activities for learners that use historical aspects of mathematics.
- Session on cultural and social origins of mathematics that looks at the non-European roots of mathematics.
- Session on the development of the statutory curriculum and curriculum development over the past 50 years.
- Recognising the importance of having things in a historical context and pointing ITE trainees to the huge number of good resources in this area on the Internet.
- Aspects of historical and cultural approaches to mathematics may form part of specialist primary, Subject Knowledge Enhancement and research-based courses.
- School or college-based practice relating to gender, personalisation and inclusion offers opportunities for reflection on theoretical perspectives provided by institutions.
Using case studies to develop ITE trainees’ understanding of the needs of individual learners.
ITE11 Understanding teaching mathematics as a life-long learning journey by committing to developing practice through continuing professional development, and by responding to new developments, technologies and research
Effective ITE engages trainees through understanding teaching mathematics as a life-long learning journey by committing to developing practice through continuing professional development, and by responding to new developments, technologies and research
- Recognising that as teachers ITE trainees continue to develop throughout their career.
- Becoming involved and contributing to collaborative learning communities.
- Developing the skills to become the subject leaders, leading practitioners and innovators of the future.
- Recognising that becoming a teacher is a lifelong commitment to their own learning.
- Becoming resilient in the face of change, able to acquire new skills, evaluate and innovate in response to new technologies.
- Keeping informed of new developments and research.
Examples of practice
- Examining how emerging digital technologies, such as podcasts and animations created by learners and teachers, can change practice.
- Encouraging participation in NCETM Regional meetings.
- Studying for further academic and professional qualifications.
- Joining subject associations, attending conferences and participating in other networks.
- Encouraging ITE trainees to return and study for a Master’s qualification.
- Assignments are tailored to help ITE trainees develop the skills needed to develop their own practice over the longer term.
- CPD is offered as part of mentor training.
- Many ex-trainees continue their relationship with a particular institution by mentoring for them.
- Providing NQT accreditation scheme and links to other CPD from ITE provider.