Howard Tanner

Becoming a successful teacher of mathematics

Introduction 1.The Nature of the Mathematics Curriculum 11 to 18 2. What Makes a Good Maths Lesson? 3. Managing the Mathematics Classroom 4. Planning and Evaluating a Mathematics Lesson 5. Learning to Think Mathematically 6. misconceptions and Planning to Deal with Them 7. Effective Teaching Approaches 8. How do Children Learn to be numerate? 9. Calculators 10. Learning 11. Assessment and Learning 12. Evaluating and Developing Your Teaching

Using Peer and Self-Assessment to Develop Modeling Skills with Students Aged 11 to 16: A Socio-Constructive View.

Eight Welsh secondary schools participated in an action research project which developed approaches to teaching and assessing mathematical thinking skills involved in practical modelling situations. The development of the metacognitive and strategic skills necessary for successful modelling is discussed from a socio-constructivist perspective as a process of acculturation as well as cognitive construction. Learning to model involves socialization into the consensual realities of a wider mathematical culture and the teacher plays a pivotal role in the generation of this consensus through the legitimization of linguistically expressed subjectivities. Assessment is an integral part of this process. Participation in peer and self-assessment was found to involve the student in a recursive, self-referential learning process which supports the explicit development of metacognitive skills.

SCAFFOLDING FOR SUCCESS: REFLECTIVE DISCOURSE AND THE EFFECTIVE TEACHING OF MATHEMATICAL THINKING SKILLS

This paper describes a research study into the teaching of mathematical thinking skills. Nine classes of students (in total) who had followed a course emphasising metacognitive skills outperformed their control groups on assessments of those skills and were also more successful on measures of their mathematical development. However, participant observation data revealed that there were important variations in teaching style between teachers and the success of their classes varied considerably. Observational data was used to classify the teaching styles into four groups. The teaching styles of the two most successful groups, the ‘dynamic scaffolders’ and the ‘reflective scaffolders’, are analysed here.

How engagement with research changes the professional practice of teacher‐educators: a case study from the Welsh Education Research Network

Learning to teach well is a complex task. Teacher‐educators have a significant role to play in enabling students to reflect critically and analyse their own practice. However, there is a danger, as a result of funding pressures and other contrary factors, that many institutions that provide teacher education will become separated from their research base. The Welsh Education Research Network (WERN) is a pilot project funded by the Higher Education Funding Council in Wales and the Economic and Social Research Council with the aim of developing educational research capacity in Wales. This paper provides an analytical account of one research group of teacher‐educators funded by WERN. The case study describes the research activity of the group and the views of its members on its impact for their professional practice. Finally an analysis of the findings concludes that engagement with research has resulted in positive changes to the knowledge, skills and critical awareness of the teacher‐educators which has in turn brought benefits to the learning of their students.

Interactive whiteboards and all that jazz: the contribution of musical metaphors to the analysis of classroom activity with interactive technologies

The teacher’s role has often been described as one of ‘orchestration’, and this musical analogy is a powerful one in characterising the manipulation of features in the classroom setting in order to generate activity or ‘performance’ which leads to learning. However, a classical view of orchestration would fail to recognise the extent to which effective teaching and learning make use of serendipity and improvisation – characteristics more often associated with jazz. This paper uses the characteristics of various musical genres to characterise teaching approaches observed in the authors’ work in two research projects investigating the use of ICT in mathematics classrooms. In particular the authors demonstrate how jazz and other musical analogies can be useful when describing some of the more effective classrooms in which serendipitous events were exploited and performances were improvised by pupils as well as teachers. They discuss the ways in which teachers were able to use ICT to establish conditions under which more jazz‐like performances were likely to occur, offering opportunities for more creative, improvised teaching and learning. They also examine lessons that can be learned by examining differences between musical and pedagogical settings.

Using information and communications technology to support interactive teaching and learning on a secondary mathematics initial teacher training course

Abstract An open and distance learning version of the full-time mathematics Postgraduate Certificate of Education (PGCE) course has been developed and trialled at the University of Wales Swansea. This was a part of a larger collaborative project, ‘HATT, 2000’ between the constituent colleges of the University of Wales which aimed to use the affordances of information and communications technology to enhance PGCE programmes and to widen access to teacher training in Wales. The project made use of conferencing email, web-based bulletin boards and streaming video to provide an alternative to some of the usual college-based elements of the course. This article discusses the pedagogical principles underpinning the design of the PGCE mathematics course, and focuses on the changes in the learning discourse arising from the affordances of the technology.

An analysis of the changing shape of initial teacher education and training in Wales since devolution

After a sustained period of relative calm, initial teacher education and training (ITET) in Wales has seen much change in recent times since devolution and all the indications are that this change agenda is likely to escalate in both the short and long term. In order to understand what has been happening in the ITET field in Wales, our paper sets out to achieve three things: first, it has contextualised the changing ITET, political, social and economic climate within Wales. Second, it has presented ITET data for Wales from the onset of devolution to the present time. Thereafter, these data have been compared and contrasted. Third, we have attempted to project our findings forward, albeit in an era which is increasingly difficult to predict given both the financial climate and “cuts” agenda. These latter aspects may result in the longer term, at best, to ITET in Wales becoming even further fragmented or reduced in numbers to, at worst, being decimated or changed forever from the more traditional scene which was apparent in both Wales and the rest of the UK since the Robbins Report aftermath in the late 1960s.

A model for the study and design of teaching situations with ICT

Any situation in which activity takes place provides affordances for the activity. We use this idea first to characterise learning, and then to discuss the way in which the educational environment is manipulated by the effective teacher in order to foster learning. ICT provides some particular affordances which successful teachers exploit in their classroom practice, and the use of an affordance model helps us to analyse the pedagogy involved. We provide a number of practical illustrations and draw general conclusions concerning the effective use of ICT in teaching and learning.