The Teaching of Number in Three Inner-Urban LEAs

OFSTED 1997 115/97/DS purple A4 booklet

What was it that these teachers were doing or not doing which made the difference?

These research findings reinforce the view that it is what schools and teachers do which makes a substantial difference to pupil performance rather than factors, such as home background which are outside their control.

Page 1

Features of good lessons identified: · planning "it was rare to find a well planned lesson taught badly" 3. · Assessment of pupils’ strengths and weaknesses · subject knowledge (calculators, methods, role of discussion) · leadership and management page 4

para 6 - whole class, group and individual work "In the best lessons there was a higher proportion of time spent teaching the class together ....." "The effect of this was an obvious common gain in core knowledge and skill which made it easier for pupils to help one another and progress together. For the teacher, too, this well-structures mix of whole-class, group and individual work not only made the lesson more manageable, it also established a climate and a common language for talking about mathematics which benefited more children for more of the time." Page 8

para 7 - too much individual work "dissipated rather than intensified the quality of teaching and reduced the opportunities for children to learn"

para 9 - Some of the important characteristics of the best lessons included: · clarity of teachers’ explanations and instructions · ability to ask appropriate questions and engage pupils in interactions which promoted familiarity with content ... · analysis of errors fed back to the pupils so that they knew what to improve · ability of teachers to relate work previously taught to new work

para 10 - importance of teacher’s subject knowledge outweighs expectations of pupils. "The pitch of the work and the pace of pupils’ progress depended far more on teachers’ understanding of number and their ability to make planned, incremental demands on the pupils than upon the teachers’ perceptions of the "innate ability" of the pupils. Often the teachers expected too little of the pupils not because they thought the pupils were incapable of higher standards but because they themselves were unsure about how to progress number work ..." page 9.

Para 12 - "Along with increasing teachers’ subject and curricular knowledge must go a better understanding of how to teach the class together and relate whole-class teaching to other forms of grouping." Page 10.

Para 33 - 3 phases described - beginning, middle , summary

para 34 - "The introduction to a lesson was crucial in setting expectations and teaching the children what they needed to know to be successful in the rest of the lesson" page 17. Brief recap, pupil participation

para 35 - sharpness of questioning

para 36 - "A frequent weakness in lesson structure was the poor management of the transitions between each part of the lesson."

Para 37 - "... no final drawing together of the class, only a request to put away resources, opportunities for consolidating pupils’ knowledge and understanding were lost." Page 19

para 40 - most significant factors were · timing and quality of interactions with pupils · management of the class · "in the most effective lessons, the teacher generally taught a group of pupils while the rest worked at carefully planned tasks which took account of pupils’ prior attainment." Page 20

para 44 - pupil grouping

para 49 - "well structured planning framework which clearly stated long and medium tern objectives. Progression was identified but achievable with demanding but targets set for the pupils in each year group." Page 23.

Para 50 - "It was rare to see a well planned lesson being poorly taught. On the other hand, inadequately prepared lessons were associated with very little pupil progress." Page 23

para 60 recording of pupils’ progress

para 61 marking

para 66 - blackboard, pace

para 67 - " The best teaching was well prepared and carefully structured" ample opportunities for pupils to explain.

Para 72 - low quality interactions - insufficiently probing, too far apart

Effective Teachers of Numeracy Askew, Brown, Rhodes, Johnson, William Kings College (commissioned by TTA) 1997 1 871 984 63 7 Red A4 paperback

"This project explores the knowledge, beliefs and practices of a sample of effective teachers of numeracy. It is one of a small number of projects where effectiveness is defined on the basis of learning gamins." Page 1

Found effective teachers had · coherent beliefs · able to identify connections · use efficient and effective teaching strategies · set appropriate challenges · stressed pupils discussion of mathematical ideas · moved quickly towards abstracts · high levels of subject knowledge · had undertaken substantial continued training · formed a snowball effect through good management

Sample of 90 teachers (which makes ours seem a bit silly) Before and after testing

Section 1.4 - How do we define effective teachers?

Definition couched in terms of pupils learning

based on evidence of · teacher behaviour · pupil behaviour · pupil learning outcomes

informed by · what teacher trainers, advisors and heads expect · what OFSTED recommends · what media and literature suggest are good practice

" in the absence of evidence about specific behaviours which promote learning, judgements about teachers’ behaviours are likely to be unsubstantiated and determined according to the belief system of the observers" page 7,8

discussion of how to identify effective teachers through pupil learning outcomes (useful for review of our methodology) page 8

page 15 initial selection failed to spot many effective teachers

Section 2, 3, 4 explores the interplay between beliefs, knowledge and classroom behaviour use the end of section summaries. Section 5: Professional development experience and effectiveness mainly about specific maths inset page 83 good argument that individual schools can, by skilful management of INSET, create a cluster of effective teachers. Summary on page 89-92 - highly relevant to our study includes comparison of amount of time English teachers spend discussion methods compared with foreign teachers Appendix 2.1: Teacher research instruments and outcome data use this in our write up Appendix A: 1.2.3 Research into effective teachers pp 114-115 use this in our write up - good literature references 1.2.5 Research into means of change and professional development pp115-117 use this in our write up Bibliography lots of good and up to date references Teaching for Effective Learning Scottish Consultative Council on the Curriculum 1995 Gardyne Road, Broughty Ferry, Dundee DD5 1NY Tel 01382 455053 Fax 01382 455046 A4 photocopy 33 pages good references A digest of research to enable Scottish schools to develop. Interesting formatting - simple statements , widely spaces, backed up by a column of quotes. The climate they describe is very much the same as we are aiming for in TQI, particularly chapter 4 - How teachers learn. Each page is described in a single sentence at the top. This is supported with examples. Section 1 - rationale "This paper is written in the belief that an understanding of the purposes and principles which underpin our everyday actions is crucial to the practice of everyday teaching." Paper is designed to encourage and enable teachers to: · re-examine their current practice · reflect on the purposes and principles which underpin their practice · develop strategies for personal and professional development

Section 2 - How We Learn Discusses three basic questions: · What do we understand about how people learn? · What implications does this have for how young people learn at school · What are the practical implications for teachers and schools?

Intelligence is not fixed. We all have much greater potential for learning than is commonly recognised (page 4). We are more likely to learn when we feel motivated to do so. Young people who feel good about themselves are much more likely to be highly motivated to learn. (Page 5) It is now argued that there is no such thing as a single gene intelligence, which we all possess to a greater or lesser degree. (Page 6) We learn most efficiently when we think things through for ourselves (page 7). Learning is messy. We rarely learn anything by proceeding along a single path to predetermined outcomes (page 8). Most learning involved other people (page 9). Learning involves emotions and feelings as well as thinking (page 10) There are differences in the ways that people prefer to learn. These are all equally valid. (Page 11)

Section 3 - Effective Teaching Discusses three basic questions: · How best can we clarify the importance of teaching the role of the teacher and what the basic aims of teaching are? · In the light of this, how can we talk and think about effective teaching? · What do teachers and young people themselves consider to be effective teaching?

Page 14. Teachers are important and make a difference. The quality of individual teachers is the single most crucial factor in promoting effective learning in schools.

Page 15. There is considerable agreement about what constitutes effective teaching, but it is practised by people who can be very different from one another.

Page 16. The ability to establish and maintain good quality relationships is central to effective teaching.

Page 17. Knowing what kind of people your learners are, and having some understanding of what they are thinking is essential for effective teaching.

Page 18. Effective teaching involves talking regularly with learners about their learning and listening to them.

Page 19. Teachers have both a right and a responsibility to develop a climate in the classroom which supports effective learning. This involves maintaining order without undermining learners’ self esteem.

Page 20. Effective teaching involves effective organisation and management, but no single style or approach to classroom management is best.

Page 21. Teachers’ own preferred ways of working tend to affect the ways in which they teach.

Page 22. Effective teaching involves being knowledgeable about what you are teaching but also looking for links across topics and subjects.

Section 4 - Teachers as Learners

· What strategies can teachers adopt to reflect on their practice and their thinking and to take responsibility for their own development? · What conditions and support do teachers need to help them to do this?

Page 24. Reflecting on what individuals truly want to achieve in our job is an important starting point for identifying personal and professional development needs. "Most people have a reason for being a teacher which goes beyond financial reward. They came into teaching to make a difference of some kind" see other quotes.

Page 25. As well as being clearer about what we want to achieve, it is also important to reflect on current practice and have a realistic view of that practice. This section contains much of the justification for TQI.

Page 26. Teaching should not be a lonely or isolated activity. Teachers need opportunities not only to talk to each other about their work, but to work together, and to use each other as resources. This section contains much of the justification for TQI.

Page 27. Successful school have a culture which encourages and supports teachers to reflect on their purposes and principles as well as their practices and helps them to work together to improve theses practices. This section contains much of the justification for TQI.

Page 28. Schools need to make the best use of all the resources at their disposal to support teachers’ personal and professional development. This section contains much of the justification for TQI. It deals with need for sustained time, extended Prof. dev programmes etc.

Taking positive action is an important aspect of personal and professional development. " Young people deserve teachers who have the confidence to learn and improve, and teachers deserve schools which help them to learn and improve."

Section 5 and 6 - Summary and useful bibliography about practical teaching. Some unusual sources. Effective Dissemination of Research Findings to Teachers Phillippa Cordingley 1997 Annex A A4 photocopy 12 pages good references, definitive recent bibliography?

Summary of messages from research findings

para 4 "The readily available body of material ... is not extensive. The material on how teachers learn is the most substantial, although a great deal of it is focused on initial teacher training rather than on disseminating research or policy to existing classroom teachers."

Para 12 "The core problem ...is that of linking practical knowledge and understanding to theoretical knowledge and understanding. Elliott (1991) goes so far as to suggest that teachers can’t improve their practice simply by assimilating abstract knowledge. ... they need to develop a personal theoretical approach which synthesises their experience and new information ....."

Para 14, 15 Desforges - need to unlearn before they can learn

Para 16 Hargreaves model of widening circles - teachers at different stages in their careers can take different aspects on board.

Para 22 Joyce and Showers link teachers’ professional development with pupil performance. Statistical chart comparing effects of different staff development activities with learning. Another key background text.

Para 25 "when the desired outcome is for teachers to exhibit full control of a new theory or skill in day to day classroom practice".....requires all four components (demonstration, practice, feedback, coaching) to be present. "...The pace of curriculum development in England and Wales in recent years has allowed little scope for the experimentation (required)"

Para 26 explores relationship between INSET and teacher behaviour by analysing the results of evaluations. Describes 11 characteristics of well- received INSET. These need to inform the TQI programme.

Para 30 - 38 how research is organised

para 39 Implications for informing classroom practice:

These are crucial to the work we plan. Using OFSTED criteria to develop classroom practice Gill Davidson 1997 from Teaching Geography January 1996 A4 photocopy 4 pages

Works through the OFSTED criteria, giving examples of observed practice.

Useful description of good teaching in Geography

Differentiation: Some definitions and examples

Peter Smith HMI

from Primary Geography January 1997

A4 photocopy 3 pages

Useful description of differentiation in Geography