UCL Institute of Education, London
In secondary school mathematics classrooms in the UK, students are typically taught mathematics through teacher-led pedagogies that focus on students passing Mathematics GCSE. The school where this study was conducted is transitioning to teach with a hybrid of project based learning (PBL) and teacher-led pedagogies, with the year nine mathematics students. There is limited research that looks at utilising a hybrid such as this or the challenges teachers face in this transition. The study adopted a qualitative approach and found that the biggest challenge to teachers was facilitating student-led learning. The study explores why teachers found this demanding, highlights the particular challenges they encountered and reports on the strategies they developed.
Despoina Boli1, Timothy Bartlett2
1UCL Institute of Education, 1,2Westminster Kingsway College
Students who come into English Further Education (FE) and haven’t previously achieved a grade 4+ in GCSE (General Certificate of Secondary Education) Mathematics are now required to continue studying mathematics. Many of those students come into FE with negative predispositions towards mathematics and frequently a cycle of examination failure follows them. The emphasis on improving learners’ problem-solving skills is very clear in the recent development of the mathematics curriculum in the UK and the Socratic Method was used to enhance those skills. The method involves the use of a series of questions that guide students to understand the mathematical problem. The main aim is to encourage learners to be less dependent on the teacher and develop problem solving and reasoning skills. To achieve the latter, we conducted lesson studies for two academic years. The findings suggest small improvements in the students’ ability to approach problems and some development of independence.
University College London Institute of Education
Problem-solving has a renewed, well-valued, focus in English mathematics curricula at all levels, yet teaching for it is complex and unfamiliar to many teachers. I report on longitudinal studies of age 5-18 classrooms, evidencing development of problem-solving over early curriculum enactment. In all phases, classroom enactment varied considerably, throughout the studies. Alignment of ‘educative’ curriculum materials and of assessments appeared necessary for widespread enactment consistent with intentions, but teacher capacity, including subject-specific knowledge and pedagogical knowledge, and affect, constrained development of such opportunities in all phases. I discuss implications.
In this paper, I draw on the findings of my doctoral study into all- mathematics teaching in English secondary schools in which I seek to answer the question: Who are the teachers who introduce all-attainment teaching in mathematics in English secondary schools and what sustains them? In it I discuss the teachers interviewed and their approach to the curriculum. Something which marks many of them out from many other mathematics teachers is their love of mathematics. All of them are actively engaged in developing their teaching resources both in terms of skills and materials. Interestingly almost all of the teachers are interested in either curriculum development or research in mathematics teaching or more usually in both.
Marie Joubert, Dominic Oakes, Sofya Lyakhova
In response to teachers’ complaints about an overcrowded curriculum, FMSP in Wales initiated a research project into the Flipped Classroom Approach in two phases. This presentation relates to Phase 1, which aimed to research the responses of teachers and students to the use of ‘flipped classrooms’ for mathematics. In a previous paper (Oakes, Davies, Joubert, & Lyakhova, 2018), we reported on mainly teachers’ views. This paper provides a more detailed look at the students’ views.
Emma M. Owens and Brien C. Nolan.
CASTeL, School of Mathematical Sciences, Dublin City University
We discuss the approach to mathematical problem-solving of nine pre-service post-primary mathematics teachers on a concurrent, initial teacher education programme in an Irish university. The context of the study is an ongoing research project on teaching the teaching of problem-solving in mathematics. The conceptual framework of the study draws on Chapman (2015), who identifies different characteristics that underpin the effective teaching of mathematical problem-solving. Included here is the capacity to solve problems effectively. The participants in the study had previously received instruction on problem-solving in a formal university module. Each participant undertook two mathematical problems in a ‘Think Aloud’ manner in recorded interviews. The interviews were then analysed using a general inductive approach. We identified seven key themes in the students’ responses, which we use to describe their overall approach to mathematical problem-solving. We report on this analysis and on how it will be embedded in the ongoing research project.
University of East Anglia, Norwich, UK
‘Knowledge at the mathematical horizon’ refers to a particular domain of teachers’ knowledge related to connections across mathematics. This construct has been used and elaborated in research. Nonetheless, ‘knowledge at the mathematical horizon’ is still considered a ‘grey area’ with different interpretations and meanings. In this paper, I report a preliminary commognitive analysis of a sample of papers about knowledge at the mathematical horizon attending to the use of the term in the related research. The aim of this paper is to investigate different narratives in relation to the construct and how these narratives might be linked to how knowledge at the mathematical horizon is conceptualised and operationalised into research. To conclude, I argue that a discursive approach might provide better insight about the nature and use of mathematical horizon in research and set the scene for further development of these ideas as part of mathematics teachers’ discourses.
Hilary Povey, Fufy Demissie and Gill Adams
Sheffield Hallam University
The increased emphasis on pupils’ reasoning capabilities in primary mathematics foregrounds conceptual understanding and associated skills and dispositions (such as critical thinking, conjecturing, evaluating and evidencing). In the absence of pedagogical approaches to support this curriculum change, P4C offers an approach that can enable teachers to support pupils’ reasoning and conceptual understanding. In this workshop, we reflected on the use of the P4C pedagogy in the Project for Citizenship and Mathematics (PiCaM), a European Erasmus project in global citizenship and mathematics education. In particular, we explored the affordances and limitations of the P4C pedagogy in addressing global learning and mathematics education that also reflects ongoing debates within the P4C community and raised questions about the extent to which it may support either a neo-liberal interpretation of citizenship and global competence and / or a critical citizenship linked to affirmative politics. We considered the implications of this approach for social justice.
Ben Redmond1, Jennie Golding2, Grace Grima1
1Pearson, 2 UCL Institute of Education
English 5-18 education until recently offered limited scope to develop increasingly important concepts related to authentic data set data handling, representation and interpretation skills. However, for examination from summer 2018, A-level Mathematics students are now required to engage with a ‘large data set’ using appropriate software. Their learning is then summatively assessed drawing on pre-release material. We report on a study which evaluates emerging opportunities to support and assess such learning within one such course. We focus on the challenges teachers and students faced, and their perceptions of the nature and extent of the support provided, during the first year of operation. We show that for both teachers and students there were tensions between education for appropriate use of software and an effective focus on the underpinning conceptual understanding. Teachers and students also experienced challenges in formative assessment of the related learning.
Ipek Saralar, Shaaron Ainsworth and Geoff Wake
University of Nottingham
It is argued that spatial thinking and geometry are related to each other. This relation can be described as two sets having an intersection which shows issues common to both. Our current work situated in this intersection focuses on improving children’s geometrical drawings. For this purpose, a set of lessons was designed by the researchers and tested with initial samples. The lessons are based on the RETA principles which support realistic, exploratory, technology-enhanced and active learning. This approach was found to be an effective and engaging way of teaching two-dimensional drawings. Consequently, we scaled this approach to include more teachers and students to be able to report how this approach works in mainstream contexts. This study with 205 students in middle schools was the final cycle of our design-based research. The findings confirmed the results of previous cycles and showed that RETA-designed lessons provided more effective instruction than traditional methods.
Ozdemir Tiflis, Gwen Ineson, Mike Watts
Brunel University London, UK
The purpose of this study was to identify the types of errors students make when attempting ratio and proportion problems. A total of 32 GCSE mathematics resit students selected from a public Further Education College in London with a mean age of 16, constituted the sample for the study. The types of errors are based on Newman’s Error Analysis model, which include errors in: reading, comprehension, transformation, processing skills, and encoding. Data was analysed by using percentage and frequency descriptive statistics. The study found that most students made transformation errors and processing skills errors in solving ratio and proportion problems. There were no common errors found in reading or encoding among students in the sample. The students’ errors in solving ratio and proportion problems seems to be due to difficulties in basic arithmetic. Therefore, it is suggested that the results of this study can be used in developing teaching approaches to eliminate the difficulties experienced by the students in learning about ratio and proportion.