BERA National Event Report Margaret Brown University of London, King’s College
The BERA national event relating to numeracy took place on Saturday February 26th, 2000 at the School of Education at the University of Exeter.
South Bank University
I will present some results from a teaching program in which a child scored poorly both on quantitative static tests and in a dynamic assessment procedure which indicated a low level of fluency. I will suggest that the developing buds of her ability did, however, become clearer in a video record. I will argue that the developing fruits of learning, and the child’s potential or readiness for further work, can be more fully assessed by means of a combination of dynamic and qualitative procedures.
Christine Hopkins and Sue Pope
Faculty of Education, University of Surrey Roehampton
Four year I classes in different schools watched a series of programmes from one of two television series designed to support numeracy needs. In each school another year I group was identified as a control. The control group had lessons with the same learning objectives and similar worksheets and resources but did not use the television .’Jrogrammes. Pre- and post- tasks were used to assess the children’s progress in numeracy skills. The average gain from pre- to post- test results was higher for the television groups than the control in two schools and lower in one school. For all the television groups it was possible to identify small groups of children with low pre-test scores who made substantial improvement. This feature was not present in the control groups. In the control groups gains were focused on one or two assessment items. In the television groups gains were more evenly spread across the test items for children of all achievement levels.
Centre for Teaching Mathematics, University of Plymouth
Associate Professor of Educational Foundations, Department of Education, Montana State University
“Very considerable sums of taxpayers , money are invested in educational research, some £50-£60 million pounds a year. Much of that money is not having any benefit at all. We should ask where the money is going. My task is to question the gobbledegook that is promoted by the academics”. So says Chris Woodhead in the Sunday Telegraph (Nov. 211999). In this session I will argue that much gobbledegook does exist in mathematics education research, that this gobbledegook is a legacy of the mathematics curriculum reform of the 1950’s/60’s, that the State supported and legitimised this legacy and is therefore in no position to criticise it. I shall also argue that the State is ‘merely’ using the ‘gobbledegook’ card to legitimise the notion that education research ought to be subordinate to government policy.
University of Bristol, Graduate School of Education
In this ESRC small grant project four teachers are working with their year 7 classes to develop algebraic activity. As one of the data collection activities I have interviewed 6 pupils in 3 of the classes (and, now, also the fourth class) and, in this session, presented data from these interviews for discussion of the pupils’ approaches to algebra. A mathematical activity was presented to the pupils and their work on it discussed with them. The same pupils were then re-interviewed about two months later and the same activity offered to them so that their developing strategies could be considered. This pattern wil/ be repeated each term during the year. Participants in the session were asked to consider what evidence of algebraic activity they could see in these interviews and samples of pupils’ work.
On 13 November a substantial number of members discussed the remit of a BSRLM workingg roup and agreed that priroty should be given to the development of better communication between researchers and practitioners.
Pat Drake and Hilary Povey
University of Sussex and Sheffield Hallam University
The purpose of the session was to begin the process of developing a critical, research¬based response to the government’s imposition of skills tests in numeracy on those seeking to attain qualified teacher status (QTS). We asked
- what are the key research questions we should be asking about this development?
- how might we set about answering them?
Convenor: Keith Jones
University of Southampton
A report based on the meeting at the University of Exeter, 26th February 2000 by Tandi Clausen-May, Association of Teachers of Mathematics Keith Jones, University of Southampton, Alan McLean, Rolle School of Education, University of Plymouth Stuart Rowlands, University of Plymouth and Robert Carson, Montana State University.
The question of how to construct an appropriate geometry curriculum is a long-standing one. A recent estimate suggests that there are more than 50 geometries. This creates afundamental problem in devising a geometry curriculum: there are just too many interesting things to include so some decision has to be made as to what to include and what to exclude. This reportftatures three perspectives on the issue of the design of the school geometry curriculum.
Kings College London
Lesson evaluation can imply an assumed general model for good teaching, pre-specified for all teachers, classes and lessons, and an assumed authority by the observer to make judgements. This is often challenged by reference to the specific conditions of the class and the teacher. An alternative mode of evaluation can simply be a ‘second opinion’ by a peer, based on an agreed desirable model for the given lesson and class. This would also take into account the professional development trajectory of the teacher ..
An example of a model of observation notes on a trial of a Thinking Maths lesson is discussed to disentangle some of the issues involved They point to Formative Interactive Feedback being the main aspect of the peer-tuition in evaluation.
Julie Anderson and Mark Boylan
Sheffield Hallam University
The Numeracy Strategy documentation and training materials encourage an increase in whole class questioning with an emphasis on directing questions at individual children. From classroom observations and interviews with children, we report on how such questioning strategies may be experienced by pupils. Initial findings lead to the contention that questioning of this type may lead to an increase in anxiety that could adversely affect attainment. In this report we focus on one aspect of teacher and pupil interaction; we do not have the space to discuss the importance of how these interactions are embedded in a whole variety of complex social behaviours.
University of Bristol
This paper introduces the discursive psychology of Edwards, Potter, WethereIl and others and sets out haw it addresses some of the difficulties I have encountered in interpreting interaction in multilingual classrooms. Discursive psychology rejects the possibility of analysing discourse as a way of gaining access to participants’ psychological states, such as what they know. Instead it seeks to understand haw states like knawing are rhetorically managed in discourse as a form of social action. In order to develop my understanding of this approach to discourse analysis. I have used it to examine a transcript of a primary school teacher working on an example of a hypothesis with her Year 4 class. The analysis reveals different ways in which she rhetoricaIly ‘underwrites’ her actions.
EdD student, Open University
The purpose is to present a short anecdotal account of the authors experience using a resource recommended by the National Numeracy Strategy (NNS). The aim is to encourage research into the effects of particular resources on children’s learning of mathematics. In primary classrooms, resources usually provide practical experience, along with language, that develops a concrete understanding in the early stages. Over time, through a range of activities children develop a more abstract understanding. The difficulty for the teacher lies in knowing the perceptions children have of practical situations, the mental images they might form and how these become translated into abstract mathematical concepts.
Rona Catterall and Margaret Sangster
Sheffield Hallam University
There is an assumption that early number knowledge will directly support the learning of money. Here we consider one situation Key Stage One children experience, that of paired number bonds and its value in dealing with simple money equivalence and addition. An analysis of this situation will illustrate where positive and negative transfer might be taking place.
Soo D. Chae and David Tall
Mathematics Education Research Centre
University of Warwick
This research was conducted using computers and oscillators at the University of Warwick, UK. Several kinds of concept images are found, including those related to: J. supervision, 2. an experiment using computers, 3. an experiment using oscillators, 4. past learning. Empirical evidence is presented to support the hypothesis that graphic representations play an important role in conceptualising the notion of period doubling in chaos theory. That is, graphic representations generated by computers and oscillators are not only visual but also conceptual.
Penny Coltman, Dinara Petyaeva and Julia Anghileri
Homerton College, Cambridge
With the current focus on the teaching and learning of number skills aspects of mathematics relating to shape and space have recently received rather less attention. This paper reports research into the role of a supporting adult in promoting effective learning relating to aspects of 3D shape in young children, using wooden blocks, in this case Poleidoblocs. Children in the study carried out problem solving tasks embedded within playful contexts. The study showed that under these conditions, structured adult intervention increased the effectiveness of learning and led to an enhanced development of secure and transferable concepts.
Ray Godfrey and Carol Aubrey
Canterbury Christ Church University College
Marija Kavk1er, Simone Tancig and Lidija Magajna
University of Ljubljana
The work discussed here is part of an international study involving Dutch, Belgian, German, Greek, Finnish, Slovenian and English children. The project, co-ordinated by the University of Utrecht, employs the Utrecht Early Mathematical Competence Test. This paper looks at comparisons of performance between England, where children were in formal schooling throughout, and Slovenia, where they had not startedformal schooling at the end of the year. Major contrasts include the following. English rather than Siovenian younger and older children within a cohort are more drawn towards the cohort’s mean performance at anyone time. English schools differ more than Siovenian nursery classes; but there is less variation within English groups than Siovenian groups. Children are more fIXed in position within a cohort in England than they are in Slovenia. The relative emphasis on Piagetian developmental tasks compared with more arithmetical tasks differs between the two countries.
Centre for Mathematics Education, Open University
The work reported below is based on participant observation research carried out with a Year 5 bottom mathematics set. The focus is on a group of children who respond positively in class discussion but do less well on apparently easier written tasks. This raises the question of why the tasks were not completed correctly. It is argued that for some children with non-mathematical difficulties, making the mathematics easy does not help. It isfurther argued thatfor some children, being asked to do work which is too easy may actually have a negative effect on performance. This raises questions about assessment and about setting.
University of Oxford
This paper is about relationships betweell teaching and research ill mathematics classrooms. Its main focus is research in whicll teacllers participate in some way. This research is contrasted with established forms of researcll, and judged agaillst its purposes ill contributing to developing teaching.
Adriana C.M. Marafon
School of Education, University of Birmingham
In my PhD I am looking at how is operated the recognition that constitutes the ‘individual’ while ‘working mathematician’. Seven working mathematicians were interviewed who belong to the Brazilian and the Sao Paulo Academies of Science, as the professional life of these working mathematicians carry also prestige which make them mathematicians above any suspicion.
School of Education, University of East Anglia
In their first encounter with the subtle concepts of supremum/infimum, mathematics undergraduates often construct perceptions such as: a set contains its infimum; the Approximation Lemma, the second condition of the concept definition, is redundant; any number smaller than the supremum of a set, must necessarily be in the set. Furthermore the students are perplexed with the alternation of the terms ‘greatest’, ‘least’. ‘upper’ and ‘lower’ in the concept definition. Given the epistemological relevance of supremum/infimum to the notion of limit and that, in finding suprema and infima, set-theoretical perceptions become implicated as do strategies for manipulating algebraic inequalities. these concepts provide a rich pedagogical milieu. Here I exemplify the above with a characteristic learning episode.
Homerton College, University of Cambridge
From 1994 to 1997 schools could choose between two GCSE syllabus optionsfor assessing Using and Applying Mathematics: coursework tasks or written Mal papers. This paper sets out to examine the effict of this choice on the nature of the assessment. In attempting to establish methods of comparing assessment instruments without reftrence to candidates’ performance, I trace the origins of these modes in ‘authentic’ and ‘competence~based’ assessment. Scrutiny of the papers and examiners’ reports suggests that the original purposes underlying the choice of mode have been subjugated to the examiners’ requirement for reliability, and that the combination of new assessment instruments with traditional examining processes can lead to less valid assessment.
University of North London
The recent publication of the guidelines for homework and the development of initiatives such as out of school learning show the government’s interest in the area ofhomework. How do teachers view homework and the role of parents. This paper reports on data gatheredfrom interviews with teachers and discusses the implications.
University of Leeds
The National Curriculum for England and Wales introduced in 1989 brought probability into the mainstream primary curriculum for the first time, but just over ten years later in the curriculum review 2000 it has to a large extent been taken out again. This paper examines some evidence from the analysis of children’s performance in national assessments to try to decide what children have learned from extensive teaching of probability in primary schools in the intervening years, but concludes that the assessment of probability in the primary school is unavoidably ambiguous.
Pat Drake and Hilary Povey
University of Sussex and Sheffield Hallam University
At the first meeting of the working group, a variety of suggestions was made for producing a critical research-based response to the Government’s imposition of the skills tests in numeracy on those seeking to attain Qualified Teacher Status. At Loughborough, we met to review those suggestions, to report on progress to date and to discuss ways forward either jointly or separately.
24 “An outrageous requirement”? Some reponses from initial teacher training education students to the imposition of teh Numeracy Skills Test
Mark Boylan, Sue Elliott, Hilary Povey and Kathy Stephenson
Sheffield Hallam University
The aim of our project was to catalogue our trainees’ initial feelings with respect to the imposition of the Numeracy Skills Test and their perceptions of its impact on their sense of professionalism and of what it means to be a teacher.