Proceedings of the Day Conference held at Manchester Metropolitan University, Manchester, Saturday 27th February 2016
01 Bangladeshi rural secondary school children’ s attitudes towards mathematics: Do attitudes vary by gender, school type or status of higher maths study?
K. M. Nabiul Alam
UCL Institute of Education, University of London
It is recognized that an increasing number of students are deciding not to study mathematics beyond minimum secondary school requirements and that many more girls than boys make this decision. A set of variables not only affects the amount of effort one is willing to employ to learn mathematics, but also influence the election of additional mathematics courses beyond the basic requirements. This paper reports the results of the analysis of pilot study data gained from a survey using a Bangla translated version of the Fennema-Sherman Mathematics Attitude Scales (FSMAS). The main purpose of the survey was to check the reliability of using Bangla translated version of FSMAS in the rural Bangladeshi context and analyze the preliminary data to observe the pattern of differences in attitudes to mathematics among different groups.
Nick Andrews, Jenni Ingram and Andrea Pitt
University of Oxford
In this paper we report on part of a two-year collaborative project seeking to develop the explanations students give during mathematics lessons. One cycle of the project explored teachers’ use of pauses during whole class teaching. A key contribution of this exploration is the exemplification of choices about pausing along three dimensions of possible variation: when within the context of the lesson to pause, where within a sequence of interaction to pause, and why to pause in terms of intended learning outcomes. We focus particularly on the experience of one teacher as he introduced using pauses during whole class teaching. This identifies issues associated with implementing changes in practice, which orientate around social and emotional implications of pausing, and additional planning demands placed on the teacher.
03 Lesson study in initial teacher education: students’ positioning analysed through the lens of Figured Worlds
The University of Manchester
This paper considers how lesson study (LS) can be used to support professional development in initial teacher education (ITE). The concept of Figured Worlds is used to analyse the student teachers’ positioning in relation to various ‘figures’ e.g. the school-mentor and university tutor involved in the lesson study process. Findings will aid reflection on how best to employ lesson study in initial teacher education. I argue that 2 teachers who have trained through lesson study might be able to challenge accepted practice. In this particular case the experience seems to allow student teachers to position themselves as teacher-researchers who are able to develop practice through reflection.
University of Chester
Year 11 students throughout England are currently attending ‘’intervention’’ classes designed to raise their mathematics attainment ahead of their GCSE examinations, using methods of instruction that seem to have proven unsuccessful the first time they were taught concepts, and then again, unsuccessfully, in subsequent lessons. This paper reports on a study of one class of lower to middle attaining Year 11 GCSE students who have been taught algebraic concepts using multiple representations and using teaching designed to allow them to reason from key known facts. Qualitative data from lesson observation, student and teacher interviews and students’ work is analysed to begin to construct a narrative interpretation of this small-scale classroom enquiry. This analysis demonstrates some promising outcomes in terms of pupils’ perceptions of learning mathematics and their use of iconic representations of concepts.
Abraham de la Fuente1, Tim Rowland2 and Jordi Deulofeu1
1Universitat Autònoma de Barcelona, Spain; 2University of East Anglia, UK
This paper describes a teaching sequence designed by a team of three teachers in Spain to enable a group of 13 to 14-year-old students to develop algebraic language through problem solving. Problems are introduced which provoke the thinking needed to solve systems of linear equations, without formal instruction in standard methods. We consider the mathematics-related knowledge that the teachers used while implementing these tasks, using the Knowledge Quartet (KQ) model to analyse this knowledge. In particular, we show how the connections that the teachers make between different representations of the same concept are key for the students to acquire algebraic language as one way to solve certain problems.
Özkan Ergene1 and Ali Delice2
1Sakarya University, Turkey; 2Marmara University, Turkey
In this research, the processes university students used to solve integral volume problems were analyzed using Polya’s problem solving stages, especially focused on the ‘look back’ stage. An integral volume test and a semi-structured interview form were administered to the participants. Qualitative data were analysed by descriptive analysis and content analysis. Interestingly, at the end of their integral volume problems’ solutions, even though almost all the students performed the ‘look back’stage, almost a quarter of the students modified or corrected some parts of their solutions. Discussions reveals that of Polya’s stages of problem solving, the ‘look back’ stage was performed with less care than other stages. Consequently, the participants’ movements in the ‘look back’stage occurred in three phases, one is from the beginning of solution to the end of the solution or vice versa or among the stages of the solution irregularly.
Jenni Ingram, Nick Andrews and Andrea Pitt
University of Oxford
In this paper, we identify three different interactional structures that lead to students offering explanations or reasoning in their responses to a teacher. Students explaining their mathematics is a key part of the teaching and learning of mathematics yet there is little research into how to enable and support students in giving these explanations. All whole class interactions from 22 lessons with 7 different teachers were analysed. Using conversation analysis, we look at situations where students gave explanations of some form in order to identify features of the preceding interaction that provoked the student into offering their explanation.
Güney Haciömeroglu1, Ali Delice 2 and Büs ra Sür2
1Canakkale Onsekiz Mart University, Turkey; 2Marmara University, Turkey
This study aimed to examine elementary pre-service teachers’ perceptions of STEM education through two open-ended questions. Fifty pre-service teachers volunteered to participate in this study. Results revealed that most of them thought STEM education would allow elementary students to acquire knowledge through discovery learning. This way, a STEM approach would let students to be creative about their own learning. This approach would also have a positive impact on students’ self-confidence. However, some participants were concerned that STEM education could be confusing for students that are not interested in these fields. Findings of the study revealed that pre-service teachers’ perceptions of STEM education was shaped by their experiences gained in science and mathematics education method courses as well as the courses they completed prior to entering a teacher education program. As a result, pre-service teachers’ perceptions of STEM education should be acknowledged by teacher educators when integrative STEM approaches are used.
Abate L Kenna
Manchester Institute of Education, The University of Manchester
Problem solving is an important skill children need to learn. It helps them to adapt to the ever-accelerating changes of the twenty first century. Advancements in technology have changed our world, how we teach and learn. Almost all of UK children play video games. However, teachers do not use interactive maths games to teach problem solving skills since the role of games is a source of controversy. This paper reports on a PhD pilot study carried out on problem solving and interactive games with seven Year six children from Greater Manchester. This qualitative case study explores how interactive maths games can be used in a small group setting to support children’s problem solving skills. Children completed various maths challenges on five games over a five-day period. Multiple data collection methods were used: interviews, direct observations and documents. The data shows how children used problem solving skills whilst playing games.
Education Office, Greek Embassy, London
This study explores the effects of two teaching interventions that focus on workplace and inquiry learning in problem solving. This research is part of the European Project MASCIL and refers to the solution of the Solar panel problem, which was assigned to 11 heterogeneous groups of high school students in Greece (year ten). In particular, by using audio and video recordings and qualitative content analysis, we discuss the ways in which collaborative inquiry learning and authentic workplace can be used to bring out and enhance the students’ mathematical argumentation. The results of the experimental teachings show that the workplace context and the inquiry activity favored the involvement of students in solving the problem. It is important to note the negotiations to cover the surface with a maximum number of photovoltaic panels that can be placed on the roof of a house and the students’ difficulties in trigonometry and three-dimensional space.
The University of Winchester
Teachers face persistent demand to achieve ‘excellence’ in teaching. These same teachers encounter paradoxes as they endeavour to reconcile their personal and professionalism identity, with the political agenda. For this research, the question was ‘How is excellence in primary mathematics teaching perceived by primary mathematics teachers?’ Four different teacher groups in the south of England were drawn through a purposive, specialist sampling method and interviewed producing narrative and mind-maps. An interpretative, thematic approach to analysis was adopted. One unexpected outcome was that ‘good enough’ teaching would suffice; targets in primary school can be met by less than excellent teaching. It might be questioned whether better than good teaching is essential, necessary or achievable by all teachers. However, the research also revealed reservations in the acceptance of a standard that is sufficient, citing enduring long-term gains and encompassing both aspirational and functional principles, such as societal gains, aesthetic and intrinsic value.
12 ‘ When Mamta met Nancy and Emily to do some mathematics’ – what intellectual and personal resources do primary student teachers draw on when doing and considering the teaching of mathematics?
Manchester Metropolitan University
For a primary student teacher, developing secure content and pedagogical subject knowledge within mathematics is of paramount importance and sometimes a cause of anxiety. As a teacher educator I was keen to explore the intellectual and personal resources students on a BA (Hons) primary initial teacher education (ITE) programme draw upon, to enact their mathematical self (‘I’) and mathematical teacher identity. Two students participated and the domain of fractions was chosen due to its reputation as being difficult to learn and to teach. The study employed an interpretivist approach, fulfilling an intention to watch and observe rather than to ‘intervene’. The four dimensions of Rowland’s knowledge were used to review key literature and as the theoretical framework to interrogate findings. The students had very different relationships with mathematics. Both had strong levels of self-concept and self-efficacy in relation to teaching mathematics, with clear strategies arising from high levels of self-regulation.
13 Implementing multi-touch tables into the classroom: In what ways are students engaged in an interactive mathematical activity ‘ around the table’ ?
Cyprus University of Technology
This exploratory study is about the design, development and evaluation of an interactive application on multi-touch table, in order to enhance students’ learning of algebraic generalization in a collaborative learning environment. Multi-touch table technology allows users to work together on a task displayed on its screen, supporting rich forms of interaction amongst them. In order to investigate the context of the educational application, a paper prototype was designed and implemented into two classrooms of 26 students, aged 12-13, in an experimental school of Athens, Greece (pilot fieldwork). Data was analysed with the SOLO (Structure of Observed Learning Outcome) taxonomy. Outcomes obtained from fieldwork fed into the design requirements that the final interactive prototype must meet. Thereafter, the final prototype was evaluated in the laboratory by two focus groups of users. Results show that students engaged in verbal interactions, affecting the understanding of the subsequent algebraic concepts introduced, encouraging further research.
Pauline Palmer, Sue Hough, Jo Kennedy and Sue Pope
Manchester Metropolitan University
Nationally there is an acute shortage of mathematics teachers. In central Manchester, performance in mathematics is close to national average in primary, but lower at GCSE. There is a shortage of teachers of mathematics and high turnover amongst those teachers that schools do manage to recruit. One large sixth form college with 1000 A level mathematicians wanted to develop an intervention that would help to raise the profile of mathematics in local schools. Students were invited to apply to be part of the intervention and out of 120 applicants, sixty were selected following an interview. The college timetabled a regular slot to facilitate the participation of students in both preparatory tasks and the intervention. As tutors, we were asked to prepare the students. We describe the intervention and the students’ responses.
Pauline Palmer and Sarah Lister
Manchester Metropolitan University
Mathematical reasoning and conceptual understanding are central to the national curriculum. We argue that a Content and Language Integrated Learning (CLIL) approach can support both aims, providing a meaningful context for subject content and language learning. Our research examines the role of communication within a second language, to develop and consolidate conceptual understanding. We describe a small-scale intervention project in which a group of teachers attended workshops, exploring the potential of CLIL pedagogy within primary mathematics, using the medium of French. Data collected consisted of tutor observation notes, supported by video recordings and semi-structured interviews. Data was analysed using a cognitive discourse framework. Articulating their own ideas and understanding in a second language enabled the teachers to focus on the key elements of their explanations to others. They developed a deeper understanding of the relationship between conceptual understanding and communication and saw that communicating ideas can contribute to conceptual development.
16 “It was all led by them”: opening up opportunities for making mathematics through a children’ s exhibition
Hilary Povey, Gill Adams and Colin Jackson
Sheffield Hallam University
The Mathematics in the Making (MiMa) project drew on Pestalozzi’s model of learning – from hand to heart to head – and that of Bruner in which understanding develops from the enactive to the iconic and thence to the symbolic. It also recognised that learning is fundamentally socialand that worthwhile learning is democratic. The MiMa partners produced practical activities for 8 to 10 year olds. Participating teachers experienced the activities themselves before running ‘laboratories’ with their children. Throughout, the teachers and children knew that they were preparing their objects and activities for public exhibition. We describe the exhibition in Sheffield and draw on our own reflections and those of participating teachers to argue that MiMa gave the children an opportunity to exercise responsibility and autonomy with respect to their own mathematics and that this led to many, particularly those previously low attaining, becoming successful and more confident learners.
Rüya Say1 and Hatice Akkoç2
1 Middle East Technical University; 2 Marmara University
Effective use of technological tools leads us to the mediating role of technology. This role is not only concerned with how to use technology in the classroom but also with how technological tools make the interaction between teacher and students possible. This study examines how prospective mathematics teachers provide a mediating role for technology in the classroom and use technology with the purpose of achieving teacher-student interactions. For this aim, a case study was conducted. Data collection tools were semi-structured interviews, lesson observations and lesson plans each of which includes a teaching activity using dynamic software such as Geometer’s Sketchpad and Geogebra. The analysis of data indicated that prospective teachers used technological tools with the aim of visualisation of mathematical concepts and emphasising relationships. They had difficulties with negotiating the meaning of mathematical concepts and establishing mediation between students, themselves and technological tools.
18 Improving early secondary school students’ abilities to create mathematical proofs: an action research study
Centre for Mathematics Education, Open University, UK
This action research study focuses on improving students’ proving abilities, over a four-week period, in the setting of a British school in Madrid. Student participants were given twenty-two conjectures to prove over this time-frame, with varied teaching inputs. Students’ proof responses were collected and coded using a proof response framework, with categories including empirical evidence, logical argumentation and visual demonstrations. The coded results were tabulated to look for patterns and to identify any increases in individual proof types. Finally, the timeline of these changes was compared with the timeline of planned teaching inputs to look for key influencing factors. It was found that (1) investigative lessons seem to support students’ logical argumentation; (2) teaching on notation appears to support students’ algebraic proving skill and (3) when faced with unknown conjectures, students tend to resort to using empirical evidence.
19 Working group report: building and sustaining active research collaborations with teachers of mathematics
Alison Clark-Wilson and Geoff Wake
UCL Institute of Education and University of Nottingham
This BSRLM working group met for the first time to explore collaborations between teacher and researchers in the processes of doing, reflecting upon and engaging with the findings, of mathematics education research. This theme is considered within the current English educational context where Teaching Schools and DfE-funded Maths Hubs are being encouraged to participate in ‘research-informed’ practice. In addition, the International Commission on Mathematics Instruction (ICMI) has identified the theme, ‘mathematics teachers working and learning in collaboration’ as one of five international survey topics that will present findings during ICME13 in July 2016 (Robutti et al. for publication 2016). This suggests that there is wide interest in brokering collaborative ways of working involving researchers and teachers to improve learners’mathematical outcomes around the world.
Leo Rogers and Sue Pope
British Society for the History of Mathematics (BSHM); Manchester Metropolitan University
Despite the words: ‘Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems.’ in the Purpose of Study section, the new English mathematics curriculum alludes only to Roman Numerals in the primary programme of study, and there is no further mention of historical or cultural roots of mathematics in the aims, or in the programmes of study. In contrast, the increased expectations for lower and middle attainers in the new curriculum challenge teachers to make more mathematics accessible and memorable to more learners. The history of mathematics can provide an engaging way to do this. There are also many opportunities in post-16 mathematics. Further to our recent article on quadratic equations, we use trigonometry to illustrate some of the ways that history of mathematics can enrich teaching of this topic.
University of Reading
The abstract nature of algebra causes challenge to many students, and attempts to access the subject using concrete approaches are often doomed to ultimate failure by the limited nature of the representations used, for example cups and counters cannot be used to represent negative variables or constants, and algebra tiles confuse length and area. This paper describes a hands-on approach that mimics formal algebraic procedures and accommodates both negative constants and variables, using playing cards in the context of a game. The topics of collecting terms, substitution, expanding and factorising, solving (including variables on both sides), linear graphs and simultaneous equations can all utilise this strategy, and it can be moderated to allow access for less confident students, for example by not using directed number.