Proceedings of the Day Conference held online on Saturday 5th March 2022.
Canterbury Christ Church University
Volumes and websites that promote teaching mathematics for social justice present teachers with a list of non-traditional pedagogical goals and a selection of alternative pre-planned, project-based lesson plans. It is precisely this clarity that misrepresents the uncertainty embraced in Critical Mathematics Education, the philosophical tradition that the movement draws on. Both teachers and academics need tools to further scrutinise the pedagogical goals and lesson plans produced by the movement. The notion of generative themes introduced by Paolo Freire and the capability approach developed by Amartya Sen can serve as such tools. This paper analyses the relevance of both to teaching mathematics for social justice and explains how these tools can support democratic spaces for critique. In particular, it describes a workshop delivered at the British Society for Research into Learning Mathematics Conference as an example. It also discusses avenues for future research that arose from the delivery of this workshop.
Anirudh Agarwal, Ruchi Kumar, Arushi Bansal
Tata Institute of Social Sciences, Mumbai
Research on middle school mathematics teachers’ pedagogical content knowledge (PCK) in the global south is limited despite the claims that it is essential for student learning. This exploratory study analyses responses of 12 teacher educators from low-resource countries to understand their beliefs about teaching, their knowledge of general pedagogy and their subject and topic specific PCK using surveys and a case study. It was observed that most teacher educators exhibited student-centred beliefs about teaching-learning and believed in developing higher order skills along with procedural fluency. However, their pedagogy was heavily procedural in nature and with a relatively weaker grasp of domain and topic specific PCK. There might be a gap between teacher educators’ beliefs and their knowledge, and if such a gap is present, it is pertinent to investigate how it may be bridged to positively affect student teachers’ readiness to use appropriate PCK in their classrooms.
Nancy Barclay, Alison Barnes and Rachel Marks
University of Brighton
In 2016 the Department for Education (DfE) launched a match-funding scheme to support primary schools (ages 5-11) in England to purchase approved mastery textbooks. This funding opportunity – and the potential changes to mathematics pedagogy within a school that textbook adoption brings – comes at a time when there is a dearth of understanding around curriculum resource (including textbook) use in primary mathematics, particularly in terms of large-scale investigations. Our ongoing Nuffield funded project engages with this gap, using a population wide survey to identify what is being used and to understand some of the decisions primary schools make around resource adoption and use. This interim paper presents tentative outcomes from early analysis of our survey, providing an initial picture of resource adoption, identifying some of the reasons behind these decisions, and noting the influence of Covid-19 on the adoption decisions schools have made.
Busra Caylan Ergene1 and Mine Isiksal Bostan2
1Sakarya University, 2Middle East Technical University
The purpose of the study was to explore students’ reasoning while solving tasks about surface area and volume measurement. For this purpose, one-to-one task-based interviews were conducted with three middle school students (11-14 years old). For the first task, the students were asked to build as many different prisms as they can with twelve unit cubes and to determine the volume and surface area of the prisms they built. For the second task, they were asked to build a large cube with twenty-seven unit cubes and to explain how the volume and surface area changed when the unit cubes from some parts of the large cube were removed. The findings indicated that the students’ reasoning involved some misconceptions: Surface area changes depending on how the prism is positioned, and prisms with the same volume have the same surface area. The possible reasons behind these misconceptions were discussed.
Little attention has been paid to how mathematics teachers from developing countries respond to students’ errors. This research applied video-based observation to investigate how a Chinese expert mathematics teacher, Mr. Yinglong Hua, responded to students’ errors by analysing four videos of his mathematics classes. There were several findings: Firstly, the framework of teachers’ responses to errors needs to be adjusted in different cultural backgrounds. Secondly, the characteristics of Mr. Hua’s responses were summarised as: a) Mr. Hua had more adaptive responses than maladaptive responses. b) The categories of his responses to errors were diverse. c) Almost all adaptive responses occurred except waiting. d) No maladaptive responses happened except correction by the teacher. Thirdly, the pattern of Mr. Hua’s responses might be affected by many factors. Hence, it is necessary to analyse teachers’ responses to errors in a realistic and specific situation.
Mustafa Güler1, Ioannis Papadopoulos2, Athina Thoma3
1Trabzon University, 2Aristotle University of Thessaloniki, 3University of Southampton
This study reports on first-year Science Education students’ mathematical writing when solving tasks involving functions, logarithms, derivatives, and integrals. The focus of this paper is on students’ use of mental brackets, a concept which up to now has been mainly studied in primary school students’ scripts. When using mental brackets, the students do not write the brackets however they evaluate and manipulate the expressions as if brackets are present. In this pilot study, forty first-year Science Education students were asked to complete tasks that required the use of brackets in the above-mentioned topics. Students’ scripts were analysed focusing on instances where the students performed operations as if brackets were written. These occasions of mental brackets in students’ writing were further categorised using thematic analysis. The findings show that mental brackets in students’ scripts were used in instances related mainly to successive signs and grouping terms.
Emine Serap Karacan
University of Reading, UK
This study, which is part of my doctoral research, presents British primary teachers’ perspectives regarding social and emotional learning (SEL) in mathematics classrooms. Focus group research was used to elicit primary school teachers’ understandings of social and emotional skills and their integration into mathematics lessons for students aged 9 to 11 (years 5 and 6) in the UK. Three primary teachers spoke about SEL at an online meeting via Skype. Their responses corresponded to the Collaborative for Academic, Social, and Emotional Learning’s (CASEL) definition, and the five SEL competencies. Despite the participants identifying some barriers to the integration of SEL in mathematics classrooms, they acknowledged its importance and the presence of a standardised reference framework for SEL.
Ems Lord, Charlie Gilderdale, Oscar Gillespie
University of Cambridge
Schools seeking to increase parental engagement with mathematics face challenges including low parental mathematical confidence levels, lack of subject knowledge and awareness about current teaching approaches, and limited parental time and resources. To help to address these concerns, NRICH investigated increasing parental engagement through collaborative online mathematics games and tasks. Six secondary schools across England set a collaborative online activity as a weekly homework task for their 11-12 year-old students. Parental support was provided through email reminders about the set tasks, video clips modelling effective use of the activities and accompanying parental guidance notes. To address concerns regarding parental confidence and awareness of current teaching methods, the activities were chosen for their potential to reinforce previous classroom learning rather than introducing new topics. Data collection methods included pre- and post-intervention student drawings, questionnaires, student focus groups and teacher interviews. The findings indicated that parental engagement significantly increased during the collaborative Solving Together intervention.
Underpinned by the scholarly work on contextually and culturally responsive standards for mathematics education, this paper presents the case study of a mathematics curricular transfer experience between the UK and Egypt, situated in the Higher Education sector. The data is based on a wider extended observation of the Egyptian classroom implementing the UK based mathematics curriculum, which incorporated multiple checkpoints including a focus group discussion with students. The data were analysed using a mapping approach against the spectrum of philosophies in mathematics education, which also acted as a theoretical framework for the study. Rooted in a local traditional philosophy of mathematics instruction, the findings of this study indicate traces of an initial shift, in instructor approach, towards a more fallibilist approach for relating to mathematics as a subject matter. The study suggests tools that enable behavioral change in mathematics instructor agency.
Lucy Rycroft-Smith, Tabitha Gould
University of Cambridge
The research around number sense and spatial abilities suggests a rich area of overlap not always reflected in curriculum design. Representations of a number line (placing, reading or visualising numbers on a line, length, track, scale, or string) may form part of children’s sense-making of this overlapping area, helping support ideas of numbers in space(s) and space(s) in number. Research suggests children’s development in these concepts happens before and alongside attending school, and is supported by informal and playful mathematics at home, including board games. However, representations of number lines in board games are an under-researched area which could support or impede such development (and this could extend to older children and adults). A selection of representations from some board games are reviewed, and their implications suggested.
İpek Saralar-Aras1 and Özdemir Tiflis2
1Ministry of National Education, 2Brunel University London
Recent research shows that culture affects how individuals think and act. This case study aimed at investigating mathematics teachers’ use of technology in their lessons, and to what extent this is related to their cultural experiences of learning. The data was generated from four Chinese and four English teachers through semi-structured interviews where detailed questions are formulated ahead of time. Content analysis of socio-cultural aspects in NVivo was used for the data analysis. The socio-cultural theory was particularly chosen as it helps us to examine how ideas and values are passed down to future generations. The results showed that although the previous teaching experience of Chinese and English mathematics teachers is similar in their group, a Chinese teacher’s learning experience is quite different from an English mathematics teacher. In conclusion, these mathematics teachers teach as they are taught. Hence, we suggest further research investigating why this might be the case.
Mariam Siddiqa Rashid
This paper investigates the impact of ability sets at secondary schools on post 16 resit Mathematics learners’ long-term attitudes and learning apprehensions at FE colleges. In particular, I wished to study resit Mathematics learners’ experience of ability sets. I also included interviews with Mathematics teachers from secondary schools and FE colleges to understand the situation better. I interviewed 16 resit Mathematics learners from different vocational areas using focus group interviews. To further assess and understand the problem, I arranged semi-structured interviews with Mathematics teachers from different secondary schools and the FE colleges. The results indicated that the way learners are treated in low ability sets creates apprehensions for them, including experiencing feelings of upset, shame, and inferiority. Adopting a growth mindset, I suggest that such learners might be termed slower developing. I recommend that learners in lower ability sets be treated fairly and provide an equal chance to progress.
Sze Man Yeung and Taro Fujita
University of Exeter
Productive practices are well-designed packages of arithmetic learning environments which attempt to promote higher-order thinking skills while practising essential arithmetic skills. These practices allow students to understand and explain phenomena in a mathematical way with greater motivation. Regarding the whole learning environment as a complex ecosystem with continuous development, design-based research (DBR) is going to be conducted and both quantitative and qualitative data will be collected. This study aims to investigate how the design of the productive practices and the interactions between the teacher and students during the implementation can generate the process of mathematical thinking, thereby supporting deep procedural learning. A pilot study with small numbers of students has been conducted with the use of Zoom and Geogebra Classroom. Some of the preliminary discoveries from observations will be discussed in this paper.