University of Leicester
Fractions are considered to be a complex concept as they are associated with part-whole, quotient, operator, ratio and magnitude interpretations, and have a range of representations. Evidence indicates that drawing attention to magnitude interpretations enriches learning opportunities, but the part-whole perspective dominates in England. One lesson on fractions from a larger video study in England is analysed here, where the teacher’s focus was the role of multiple representations. Whilst the students described fractions using language associated with a range of interpretations, the part-whole perspective remained central to the teacher’s management of classroom discourse; the implications for learning are considered.
University of Brighton, UK
This UK classroom based doctoral research employed a pedagogical focus on mathematical awareness. Three primary class teachers worked alongside the researcher to design lessons which aimed to provoke pupil awareness of the mathematical properties and structures embedded in their mathematical activities. Through this focus we sought to enable lower attaining primary school pupils to make meaningful mathematical contributions to the progress of tasks in the context of mixed attainment pair working. Video recording captured the activity and interaction of lower attaining pupils and their partners. Analysis focused on the nature of the mathematical awarenesses demonstrated by the lower attaining pupil and the impact of these on mathematical progress for the pupil pair. Each of the lower attaining pupils developed and demonstrated important mathematical awarenesses demonstrating the potential of lower attainers to make valid contributions to mixed pair working.
Catherine Gripton1, Andrew Clapham1 and Matt Woodford2
1Nottingham Trent University, 2University of Nottingham
Teaching for Mastery (TfM) is a high profile pedagogical and policy narrative in mathematics education in England. In schools developing a TfM approach with 5-11 year old children, the pedagogical position for teaching mathematics to children of 4-5 years of age can be ambiguous. This paper focuses upon a Reception class teacher, and her class, from a primary school in the East Midlands of England. Drawing on Panopticism (Foucault), and performativity (Lyotard), the paper examines the development of TfM for this teacher as she struggles with the demands of an increasingly neo-liberal, marketised, education system. Through thematic analysis, the paper demonstrates how ‘Horizon Content Knowledge’ (HCK) – allied to the prevalent performative zeitgeist – frames the intersection between TfM pedagogy and mathematics policy. The paper concludes by suggesting, that the class teacher illustrates the complexities of mathematics education located on the ‘other side’ of the TfM policy agenda.
İpek Saralar, Shaaron Ainsworth and Geoff Wake
University of Nottingham, UK
As a part of a design-based research study, the present study focused on seventh grade students’ understanding of problems based on two types of polycubical shapes. The first of these asks students to draw two-dimensional representations (i.e., the orthogonal views from the front, left, right and above) of the given three-dimensional representations. In the second type, students were asked to construct polycubical shapes and then represent them isometrically in a two-dimensional environment where orthogonal views corresponding to type 1 −from the front, left, right and above− were provided. The current study found various types of common errors specific for both types of problems. Examples of these errors and their correct answers are illustrated in this paper. The next iteration of this study will be focusing on designing lessons to overcome such errors.
University Claude Bernard Lyon 1 France
An integration of Sésamath association resources (http://www.sesamath.net/) took place in the mathematical workshop of an Algerian college by a trainer. We are approaching the teacher’s resource system based on concepts already present in the documentary approach. We consider static and dynamic aspects of this resource system. We propose a model of articulation between the system of resources and their schemes, specifically the rules of action and the operating invariants.
University of Nottingham
There is an increase in assessment questions that probe students’ reasoning in the latest design of the English mathematics curriculum. Analysis of this new genre of General Certificate of Secondary Education (GCSE) questions, that demand students engage in reasoning, provides evidence of the need for students to have knowledge of key ideas, fluency with basic procedures and contextual conceptual understanding. As part of an ongoing design research that seeks to support teaching and learning towards answering such questions this paper illustrates the issues at stake through one exam question. Focusing on the particular context of statistical measures and representations this paper explores what we mean by reasoning and how procedural understanding embodied in rhymes such as “hey diddle diddle, the median’s the middle” fails to provide students with the necessary grounding for success at GCSE – let alone statistical competence to make sense of the world in which we live.