From policy to practice: Discourses of mastery and "ability" in England

Recent policy discourse in England has adopted “mastery of mathematics” as a desired aim and approach to teaching, yet this is understood in a variety of ways. One key component of the official discourse is the claim that mastery will enable ALL pupils to achieve and move through the curriculum together. This paper explores the ways in which this claim is recontextualised in the discourses of agencies involved in teacher professional development

To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In this article we address the issue of how students over this period have been expected to engage with the specialised discourse of school mathematics. We explain our analytic methods and present some outcomes of the analysis. We identify changes in engagement with algebraic manipulation, proving, relating mathematics to non-mathematical contexts and making connections between specialised mathematical objects. These changes are discussed in the light of public and policy domain debates about “standards” of examinations

Using simulation studies to evaluate statistical methods

Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analysed and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting and presentation. In particular, this tutorial provides: a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods and performance measures ('ADEMP'); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine that included at least one simulation study and identify areas for improvement.Comment: 31 pages, 9 figures (2 in appendix), 8 tables (1 in appendix

Studying the role of human agency in school mathematics

Mathematical discourse is often described as abstract and devoid of human presence, yet many school curricula espouse an aim to develop active, creative mathematical problem posers and solvers. The project The Evolution of the Discourse of School Mathematics developed an analytic scheme to investigate the nature of school mathematics discourse through the lens of high-stakes examinations in England. Following an overview of the scheme, this article “zooms in” on the development of the sub-component addressing the question of how the origin of mathematical knowledge is construed, allowing investigation of the potential for students to see a role for themselves as active, creative agents in mathematical practices. Analytical tools operationalising this component are presented and their application illustrated. Results of analysis of examinations over a period of three decades suggest some increase in human agency, though some other aspects characteristic of higher-level mathematics may have reduced

Investigating changes in high-stakes examinations: A discursive approach

This article focuses on the theoretical-methodological question of how to identify reform-induced changes in school mathematics. The issue arose in our project The Evolution of the Discourse of School Mathematics, in which we studied transformations in high-stakes examinations taken by students in England at the end of compulsory schooling. We have adopted a conceptualisation that draws on social semiotics and on a communicational approach, according to which school mathematics can be thought of as a discourse. Methods of comparing examinations of different years developed on the basis of this definition enable identification of subtle disparities that are nevertheless significant enough to make an important difference in students’ vision of mathematics, in their performance and, eventually, in their ability to cope with problems that can benefit from the use of mathematics. In this article, we present these methods and argue that they have wider application for comparative studies of school mathematic

Semantic fluency in deaf children who use spoken and signed language in comparison with hearing peers

BACKGROUND: Deafness has an adverse impact on children's ability to acquire spoken languages. Signed languages offer a more accessible input for deaf children, but because the vast majority are born to hearing parents who do not sign, their early exposure to sign language is limited. Deaf children as a whole are therefore at high risk of language delays. AIMS: We compared deaf and hearing children's performance on a semantic fluency task. Optimal performance on this task requires a systematic search of the mental lexicon, the retrieval of words within a subcategory and, when that subcategory is exhausted, switching to a new subcategory. We compared retrieval patterns between groups, and also compared the responses of deaf children who used British Sign Language (BSL) with those who used spoken English. We investigated how semantic fluency performance related to children's expressive vocabulary and executive function skills, and also retested semantic fluency in the majority of the children nearly 2 years later, in order to investigate how much progress they had made in that time. METHODS & PROCEDURES: Participants were deaf children aged 6-11 years (N = 106, comprising 69 users of spoken English, 29 users of BSL and eight users of Sign Supported English-SSE) compared with hearing children (N = 120) of the same age who used spoken English. Semantic fluency was tested for the category 'animals'. We coded for errors, clusters (e.g., 'pets', 'farm animals') and switches. Participants also completed the Expressive One-Word Picture Vocabulary Test and a battery of six non-verbal executive function tasks. In addition, we collected follow-up semantic fluency data for 70 deaf and 74 hearing children, nearly 2 years after they were first tested. OUTCOMES & RESULTS: Deaf children, whether using spoken or signed language, produced fewer items in the semantic fluency task than hearing children, but they showed similar patterns of responses for items most commonly produced, clustering of items into subcategories and switching between subcategories. Both vocabulary and executive function scores predicted the number of correct items produced. Follow-up data from deaf participants showed continuing delays relative to hearing children 2 years later. CONCLUSIONS & IMPLICATIONS: We conclude that semantic fluency can be used experimentally to investigate lexical organization in deaf children, and that it potentially has clinical utility across the heterogeneous deaf population. We present normative data to aid clinicians who wish to use this task with deaf children

Narrative skills in deaf children who use spoken English: Dissociations between macro and microstructural devices

Previous research has highlighted that deaf children acquiring spoken English have difficulties in narrative development relative to their hearing peers both in terms of macro-structure and with micro-structural devices. The majority of previous research focused on narrative tasks designed for hearing children that depend on good receptive language skills. The current study compared narratives of 6 to 11-year-old deaf children who use spoken English (N=59) with matched for age and non-verbal intelligence hearing peers. To examine the role of general language abilities, single word vocabulary was also assessed. Narratives were elicited by the retelling of a story presented non-verbally in video format. Results showed that deaf and hearing children had equivalent macro-structure skills, but the deaf group showed poorer performance on micro-structural components. Furthermore, the deaf group gave less detailed responses to inferencing probe questions indicating poorer understanding of the story's underlying message. For deaf children, micro-level devices most strongly correlated with the vocabulary measure. These findings suggest that deaf children, despite spoken language delays, are able to convey the main elements of content and structure in narrative but have greater difficulty in using grammatical devices more dependent on finer linguistic and pragmatic skills