School text books matter. They shape curriculum and pedagogy. In nations such as Finland, Hong Kong, China and Singapore, basing teaching around a textbook scheme is associated with high performance in international tests. Across European nations, there has been considerable focus on researching the role of textbooks in shaping pedagogy and classroom culture (Pepin & Haggarty, 2001). In many developing world nations, there is heavy dependence by teachers on textbooks and hence considerable potential for influencing pedagogy through the design of textbook schemes. Mathematics may be conceived as a set of eternal, immutable truths, which might lead to a pedagogy for school maths dominated by teacher demonstration, individual practice, high stakes testing, strict rules, and right or wrong answers (Lakatos, 1976; Hudson, Henderson & Hudson, 2015). On the other hand, mathematics may be seen as a human activity and may be transformed into a school maths that is conceived as ‘fallible, refutable, and uncertain and which promotes critical thinking, creative reasoning, the generation of multiple solutions and of learning from errors and mistakes’ (Hudson, Henderson, & Hudson, 2015, p. 377).

In England, however, there has been considerable resistance to adoption of textbook schemes. For example, an estimate in mathematics of the percentage of teachers using textbooks as a basis for instruction is: England 10% Singapore 70% Finland 95% (Mullis et al., 2012). The same study found that teachers using textbooks ‘as a supplement’ was in reverse order: England 64% Singapore 23% Finland 3%. This resistance is in part due to concerns about direct control of curriculum and pedagogy by government ministers (Oates, 2012) and these concerns were reinforced by the ill-informed and erratic interventions of the minister for education during the 2010-2014 government. The influential paper on textbooks by Oates (2012) deserves careful evaluation, not least because it considers the curriculum to be the official specified national curriculum rather than that mediated by teachers in their classrooms (Alexander, 2012).

Textbooks form a significant element within the power knowledge interplay that transforms a subject discipline such as mathematics into the curriculum and pedagogy of ‘school maths’. This process has been theorised as three areas of rules governing transformation: ‘distributive’ rules (around knowledge production in the universities) through ‘recontextualisating’ rules (relating to official policy and the local pedagogical influence of teachers), and evaluative rules (related to reproduction of knowledge by pupils in classrooms, tests and examinations) (Bernstein, 2000; Puttick, 2015). Government departments and ministers may become involved in recontextualisation work involving textbooks by ‘approving’ a particular textbook or textbook scheme.

There is a body of mathematics textbooks research, including textbook analysis and the use of textbooks in teaching and learning (Fan, Zhu & Miao, 2013). This study focuses on teachers in England who are involved in a curriculum development project implementing a mastery approach to maths textbook scheme based on textbooks originally developed in Singapore. The commercial textbook scheme is entitled Maths – No Problem!^TM and it has been officially ‘approved’ by government agency as being suitable for delivery of the National Curriculum in England. Within this scheme, each lesson begins with whole class exploration of an ‘anchor problem’, a contextualised problem. This exploration considers possible solutions and methods of solving the problem rather than simply finding an answer. After perhaps 25 minutes, including some whole class consideration of strategies and solutions, the pupils record their solutions in a journal and check the solutions ‘found by the children’ in the textbook. The textbook then provides a guided practice task. The study asks: What is the role of the textbook scheme in mediating the beliefs and classroom strategies of the teachers?

This study is collaborative practitioner research consisting of a university-based researcher, seven teacher researchers based in seven Primary schools, and the director of the schools alliance as a co-researcher. The teachers joined the research project in response to an open invitation and had all been involved in implementing the Singapore Maths curriculum development project for between one and two years. The potential ethical risk created by the project to the professional reputation of the teachers was, in addition to informed consent and right to withdraw data, partly mitigated by their shared ownership of the project. These Primary teachers teach a broad curriculum to their assigned class of around 30 children, including mathematics. The aim of the collaborative approach, with teachers positioned as researchers and involved in design, data collection and most importantly analysis, was to co-create ‘strongly contextualised’ and ‘socially robust’ knowledge (Nowotny, Scott & Gibbons, 2001). Within an interpretivist methodology, the study consists of a multiple case study (Yin, 2014). Classroom video was for each teacher was captured and then used within a stimulated recall interview were used in which the teacher watched the video and commented on what they felt were distinctive elements within the lesson (Lyle, 2003; Lewis, 2014). The video and interview data was complemented by two teacher focus groups that particularly focused on the influence of the text books. In one focus group each teacher brought and discussed an annotated two page spread from the textbook for a lesson they had taught recently. In the second focus group the teachers contributed to some initial textbook analysis by focusing on how the text book scheme introduces and develops engagement with the specific topic of ‘fractions’. This paper focuses particularly on the textbooks as mediating artefacts. First, a textbook analysis is used to consider how the textbook scheme handles an exemplar topic of ‘fractions’ (Hook, Bishop & Hook, 2007; Wijaya, van den Huivel-Panhuizen & Doorman, 2015). The interview and focus group data is subjected to qualitative thematic analysis of the transcription of the teacher focus group on text books and of the seven teacher researcher interviews (Braun and Clarke, 2006; Nowell, Norris, White & Moules, 2017). The approach to analysis includes collaborative analysis workshops involving teacher researchers in coding raw data and then in shaping the emerging analysis.

The wider findings of this study, including some findings related to the textbooks, have been published in two open access journal papers (Boyd & Ash, 2018a; Boyd & Ash 2018b). Further analysis focusing in more depth on the influence of the textbooks as mediating artefacts will form the findings reported in this conference paper. The study has implications for international reform of teaching in mathematics, for the use of textbook schemes and for intercultural development of classroom teaching. Initial findings show that teachers were initially sceptical of the textbook scheme in terms of curriculum coverage and in providing sufficiently frequent return to practice previously learned skills. The scheme shares the idea of a mastery approach to maths by focusing on larger blocks of time studying a topic in depth, rather than moving on frequently to new topics (NCETM, 2014). However, they gained in confidence as they came to understand the textbook scheme, although they also continued to supplement it by including practice of maths skills across the curriculum and separately from the actual maths lessons. This is one advantage of the ‘class teacher’ approach in Primary schools in England, they have responsibility and an overview of the whole curriculum. The analysis also showed that lesson planning for the teachers focused more on developing maths knowledge and less on planning learning activities and practical preparation of worksheets. The teachers found they had to consider the different mathematical directions in which children might take the anchor problem during the exploring phase of the lesson. The teachers reported that they were gaining confidence and mathematical knowledge through their engagement with the textbook scheme, which includes pupil workbooks and teacher guidance. An in-depth analysis of the mediating effect of the textbooks will be developed and presented in the conference paper.

Alexander, R. (2012) Moral Panic, Miracle Cures and Educational Policy: what can we really learn from international comparison?, Scottish Educational Review 44 (1), 4-21. Available at: http://www.scotedreview.org.uk/media/scottish-educational-review/articles/335.pdf Bernstein (2000). Pedagogy, symbolic control and identity: Theory, research, critique. (Revised ed.) Oxford: Rowman & Littlefield. Boyd, P. & Ash, A. (in submission) Mastery Mathematics: Changing teacher beliefs around in-class grouping and mindset. Teaching and Teacher Education. Boyd, P. & Ash, A. (2018) Teachers framing exploratory learning within a text-book based Singapore Maths mastery approach. Teacher Educator Advancement Network Journal 10(1): 62-73. Available at: https://ojs.cumbria.ac.uk/index.php/TEAN/article/view/442 Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in Psychology, 3, 77-101. Fan, L., Zhu, Y. & Miao, Z. (2013) Textbook research in mathematics education: development status and directions. Zentralblatt fuer Didaktik der Mathematik, ZDM 45 (5): 633-645. Hook, W., Bishop, W. & Hook, J. (2007) A Quality Math Curriculum in Support of Effective Teaching for Elementary schools. Educational Studies in Mathematics 65: 125-148. Hudson, B., Henderson, S., & Hudson, A. (2015). Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics. Journal of Curriculum Studies, 47(3), 374-398. Lakatos, I. (1976). Proofs and refutations. Cambridge: Cambridge University Press Mullis I, Martin M, Foy P & Arora A TIMSS 2011 International results in mathematics Boston College National Center on accessible instructional materials 2014 http://aim.cast.org/learn/policy/state/massachusetts Nowell, L.S., Norris, J.M., White, D.E. & Moules, N.J. (2017) Thematic Analysis: Striving to Meet the Trustworthiness Criteria. International Journal of Qualitative Methods, 16: 1-13. Nowotny, H., Scott, P., & Gibbons, M. (2001). Rethinking Science: knowledge and the public in an age of uncertainty. Polity Press: Cambridge. Pepin, B. & Haggarty, L. (2001) Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning cultures. Zentralblatt fuer Didaktik der Mathematik, ZDM 33 (5), 158-175. Puttick, S. (2015). Chief examiners as prophet and priest: Relations between examination boards and school subjects, and possible implications for knowledge. The Curriculum Journal, 26(3), 468-487. Wijaya, A., van den Huivel-Panhuizen, M. & Doorman, M. (2015) Opportunity-to-learn context-based tasks provided by mathematics text books. Educational Studies in Mathematics 89: 41-65.