GEMS (Geography, Enterprise, Mathematics and Science

In this reflective paper, we explore students' local and global thinking about informal statistical inference through our observations of 10-to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes in the frequency or relative frequency as the sample size grew larger. They generally failed to recognise that larger samples provided stability in the aggregated proportions, not apparent when the data were viewed from a local perspective. We draw on Mason's theory of the Structure of Attention to illuminate our observations, and attempt to reconcile differing notions of local and global thinking.

DiSessa et al.(2004) conducted a comparative study of how research teams design, develop and evaluate TEL software, in the context of component-based educational programming. They identified the issue of the social configuration of the production team as ���a critical family of issues that are easily marginalized���(p. 117). These social configurations are loosely equivalent to what Activity Theorists refer to as the rules and division of labour (Engestr��m, 1987) in the activity system of TEL production. DiSessa et al.(2004) studied ...

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as designing for abstraction. In this paper, we draw on detailed design experiments from our research on children’s understanding about chance and distribution to re-present this work as a case study in designing for abstraction. Through the case study, we

Four different situations were designed to act as ‘windows’ (Noss and Hoyles, 1996) on students’ experiences of dimension within a broad phenomenographic study. This paper describes two of these situations in terms of: (i) the nature of their setting; (ii) the resources offered to students; (iii) the students’ articulations of experience within each situation. Building on the idea of ‘designing for abstraction’ and the ways that designing and modelling fosters the utility of mathematical concepts, the examination of the these two situations gives an insight into what makes a window expressive both for the student as a means of ‘seeing’ the phenomenon of dimension and for the researcher to ‘see’ how the student experiences that phenomenon.

Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers, researchers and mathematics educators, and many teachers and researchers have been involved in the thinking behind this book, funded by the Nuffield Foundation. An associated website, hosted by the Nuffield Foundation, summarises the key messages in the book and connects them to examples of classroom tasks that address important learning issues about...

Active Graphing has been proposed as a spreadsheet-based pedagogic approach to support young children's construction of meaning for graphs, particularly as a tool for interpreting experiments. This paper discusses aspects of a detailed study, illustrating how Active Graphing emerges as a facilitator of the children's passage from a vague realisation of relationships to the articulation of rules and finally the construction of formulae.

The development of increased and accessible computing power has been a major agent in the current emphasis placed upon the presentation of data in graphical form as a means of informing or persuading. However research in Science and Mathematics Education has shown that skills in the interpretation and production of graphs are relatively difficult for Secondary school pupils. Exploratory studies

This paper looks back over a number of exploratory studies which have researched young children's construction of meanings for graphs, produced from data entered in spreadsheets. In this paper we discuss children's use of normalising, an activity in which children 'correct' data towards some perceived norm. Through normalising, children construct meanings for trend in data and in graphs. We discuss how particular aspects of the pedagogical setting including task design encourage the use of normalising.

Active Graphing has been proposed as a spreadsheet-based pedagogic approach to support young children's construction of meaning for graphs, particularly as a tool for interpreting experiments. This paper discusses aspects of a detailed study, illustrating how Active Graphing emerges as a facilitator of the children's passage from a vague realisation of relationships to the articulation of rules and finally the construction of formulae.

We present initial data from a collaboration between researchers in the UK and in Israel. We aimed to explore how young students (11-14 years of age) expressed uncertainty in partiallydetermined situations, where a signal might account for some, or even a substantial amount of, variation but additionally there is a need to account for noise in the system. The two teams collaborated to develop a task that drew on previous experience with Active Graphing and EDA. As well as collecting data through an experiment, the young students used the modelling functionality in TinkerPlots2 to create models (or 'machines') that generated similar data to that in the experiment. In the presentation, we describe the various ways in which the young students accounted for and expressed uncertainty verbally and through actions in TinkerPlots2.

In this article, we explore the growth of mathematical knowledge and in particular, seek to clarify the relation between abstraction and context. Our method is to gain a deeper appreciation of the process by which mathematical abstraction is achieved and the nature of abstraction ...

Our primary goal is to design a microworld which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This ...

This paper focuses on 6-8 year-old children's thinking about randomness. It reports the findings of a study in which the children engaged with a game-like environment to construct for themselves spatial representations of sample space. The system was designed so that the rules ...

This paper reports early work from a project examining the affordances offered by Interactive Whiteboards (IWBs). Here the focus is on the teaching of the definition of quadrilaterals through the use of Cabri Geometre. We discuss the work of two 11-year-old children, who are ...

The paper builds on design-research studies in the domain of probability and statistics. The integration of computers into classroom practice has been established as a complex process involving instrumental genesis (Verillon and Rabardel, 1995), whereby students and teachers need to construct ...

We are investigating how secondary teachers make sense of the concept of risk, how it figures in their teaching, and what possibilities exist when a cross-curricular and technology-enhanced approach is taken. We have developed decision-making scenarios for socio-scientific ...

This paper considers task design related to the geometrical understanding of a class of nine-and ten-year old children. The research was interested in identifying the principles underpinning these tasks. A first iteration involved a nationally-recognised sorting task (National ...

We describe the work of two groups of six 8 year-old children as they plan Father Christmas's epic journey on December 24 th. We trace how the children draw upon formal and personal knowledge to make connections with a range of external representations. We conclude that the context, despite its distracting potential, is critical in supporting engagement, while the representations act in mutual support of the construction of a utility for directed number (Ainley & Pratt, 2002).