University of Oxford
Is what is addressed in lessons through classwork likely to be mathematically different to what is addressed through seatwork? And if so, is this a planning issue to which mathematics teachers might usefully attend? This paper will address the above questions, which arose from an explorative study in which four series of lessons were analysed by treating each as a sequence of episodes. Focusing on the mathematics, a finding of this study was indeed that across each of the four lesson series what was addressed through classwork episodes was different to what was addressed through seatwork.
Caldicot School, Wales
A frequent complaint of mathematics teachers is that students cannot recall their prior learning, thus hindering efforts to build on this, to make further progress. This session reports on an action research project that aims to improve Year 7 students’ retention of mathematical learning and memory through recall and application of knowledge and skills. The research draws on the work of pioneering psychologist, Ebbinghaus whose work included the discovery of the forgetting curve, demonstrating how newly gained information is lost from memory over time when no attempt is made to retain it. Initial findings indicate that it is not only the act of retrieval that is important but also the associated feedback.
Ysgol Bryn Elian
This strand of design research is part of an on-going study that aims to evaluate the impact of domain specific self-questioning prompts and regular exposure to common mathematical methods and formulae in the form of ‘Numeracy Mats’. The concept of the mats is based on the theory of metacognition and its influence on problem solving. Important mathematical information was connected on the mats by questions that model a self-regulatory approach to arriving at the methods or formulae needed to calculate solutions.
Giorgio Bolondi1, Clelia Cascella2, Chiara Giberti1
1Free University of Bolzano-Bozen, 2University of Manchester
Different words, numeric values or semiotic registers, figures, graphs or tables, namely elements of item formulation, affect students’ probability of encountering an item correctly. An experimental study was carried out to compare different formulations and their effect for validating a comparative technique. Four anchored math achievement tests were administered to a sample of 1647 students attending grade 8 to explore students’ misconception about the relationship between perimeter and area. Results confirmed that item formulation channels students’ solving strategy and thus modifies the probability of a correct answer more than item content.
George A. Constantinides1 and Charlotte Neale2
1Imperial College London, 2Langham Primary School
Drawing on the theory of formal mathematical logic, it is shown that precisely defined syntaxes and semantics can be introduced for Cuisenaire rods and part-whole bar models. By interpreting sentences expressed in these representations as sentences in the first-order theory of arithmetic, it is possible to rigorously study the potential and limits of these representations. It is shown that different approaches to bar modelling vary depending on the semantic content given to geometric bar length, and the implications of this observation are studied to reveal the relative power of these representations for expression of word problems and their subsequent solution within the representation.
St Joseph’s Cathedral Primary School
The current research concerns a possible professional development intervention to reduce anxiety felt by teachers when teaching mathematics, in turn aiming to reduce the anxiety passed on by teachers to their pupils. Four teachers in primary schools videoed their own lessons and in pairs discussed critical incidents captured, linking to the 20 codes of the Knowledge Quartet. Findings suggest that mathematics anxiety may be reduced and teacher learning promoted.
Gower College, Swansea
This paper will explore the changes in students’ experience through the use of structured discussion in mathematics, looking at the issues of creating an environment to catalyse dialogic teaching. The student response to this initiative is considered, comparing it to more traditional forms of teaching and this intervention is recommended as a valuable, straightforward, teaching tool for discursive learning.
Holly Heshmati, Sue Johnston-Wilder, Ben Sinclair
University of Warwick
This paper will report on action research aimed at improving pupils’ self-efficacy in mathematics. There are four factors influencing learners’ appraisal of their self-efficacy: learner’ past attainment, their vicarious experiences, their experiences of being ‘persuaded’, and their physiological reactions. The results will confirm that pupils’ engagement in creating VLE resources exposed pupils to various sources of experience in developing self-efficacy. Pupils’ collaboration and teachers’ feedback improved pupils’ subject mastery along with their experiences of vicarious success and persuasion, and positive physiological reactions.
Jenni Ingram and Nick Andrews
University of Oxford
In this paper we will explore the tensions and opportunities that arose during a collaboration between mathematics teachers and researchers which took the form of both a research project and a professional learning opportunity for all involved. Throughout the process there are choices and decisions that needed to be made and the relationship between the research and professional practice can bring complexities to these choices that can both open up new possibilities and raise tensions between the two roles within the collaboration. This exploration includes considering the goals, processes and participants and the different roles each plays as the project evolves.
University of Bristol
In this paper I will review the existing definitions of rigour in the literature within the realm of mathematics education. From the review, I suggest that there are four categories of discussion of rigour: mathematical definition of rigour, rigour in curriculum, rigour in teaching, and learner’s rigour. I will attempt to form a definition of learner’s rigour, with the thought that different views of rigour may be at the heart of cultural differences in mathematics teaching and learning (e.g. between China and England).
Rachel Marks, Nancy Barclay, Alison Barnes, Páraic Treacy
University of Brighton
This paper will provide an overview of work on a commissioned review offering a critical reflection of BSRLM conference proceedings from the last 15 years (2003-2017). We give a statistical overview of the 773 Informal Proceedings papers published during this period, examining trends in research, highlighting strengths and identifying gaps. We will present our coding system, methodology and rigorous approach to inter-coder reliability. We find a heavy focus on empirical studies, early support for seminal projects and a strong interest in specific topics such as geometry and teacher development. There are limited papers addressing the Early Years Foundation Stage (EYFS) and students with Special Educational Needs and Disabilities (SEND). We contrast these findings with the previous BSRLM proceedings review (1995-2002).
Nejla Tugcem Sahin
University of Aberdeen, UK
Almost one in six children in England has special educational needs (SEN), and considering the large proportion of children with SEN in general education classrooms, teachers’ preparedness to teach in inclusive settings has become an important issue. This study will examine the attitudes of in-service and pre-service secondary school mathematics teachers towards children with SEN in a comparative way, considering years of experience in teaching. The results indicated that teachers’ attitudes were generally positive towards children with SEN. Additionally, the findings suggested that teachers’ prior experience with individuals with SEN affected their attitude positively.
University of Brighton
This theoretical paper will discuss the value of integrating mathematics and science in the secondary classroom, understanding gained from previous studies in this field, and the means by which lessons of this nature can be effectively designed. Attempts to integrate mathematics and science in the classroom often encounter barriers such as the rigid nature of the school timetable, deficiencies in teacher knowledge of their non-specialist subject, and lack of instructional materials, amongst other issues. A model for integrating mathematics and science in the secondary classroom is presented here which aims to account for these barriers and allows for the development of students’ problem-solving skills and the facilitation of meaningful applications of mathematics to other disciplines.
Eleni Tsikalaki and Christina Misailidou
Department of Primary Education, National and Kapodistrian University of Athens
We will present selected results from a study on Greek primary school teachers’ attitudes and beliefs about mathematics. Contrary to previous findings, most of the teachers of our sample exhibited a positive attitude towards mathematics. This is an encouraging result since primary school teachers in Greece do not usually have a strong mathematical background from their secondary school years.
Gelliswick Church in Wales Voluntary Controlled Primary School
Concrete mathematical resources are generally much less common in upper Key Stage Two classes than in lower years. However, I believe they still have an important role and in this action research project within my own classroom, I report on an intervention to promote the use of concrete resources focusing on developing understanding of key concepts as opposed to mathematical processes. After spending time experimenting with manipulatives such as Cuisenaire rods, number counters, bead bars and numicon, learners are moved towards a pictorial representation, commonly the bar model. Although the approach has been adopted with all children, the research has focused upon the progress of four children.