Dave Pratt

Normalising: Children's activity to construct meanings for trend

This paper looks back over a number of exploratory studies which have researched young childrens construction of meanings for graphs, produced from data entered in spreadsheets. In this paper we discuss childrens 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.

The Construction of Meanings for Trend in Active Graphing

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 have suggested that the use of spreadsheets might have the potential to change fundamentally how children learn graphing skills. We describe research using a pedagogic strategy developed during this exploratory work, which we call Active Graphing, in which access to spread sheets allows graphs to be used as analytic tools within practical experiments. Through a study of pairs of 8 and 9 year old pupils working on such tasks, we have been able to identify aspects of their interaction with the experiment itself, the data collected and the graphs, and so trace the emergence of meanings for trend.

THE CONSTRUCTION OF MEANINGS FOR GEOMETRIC CONSTRUCTION: TWO CONTRASTING CASES

Dynamic geometry software seems to offer new approaches to the teaching and learning of geometry. Interest has been particularly intense in Britain where geometry has almost disappeared from the curriculum. In this paper we draw on our experiences of using Logo with children and adult students as a way of thinking about the design of geometrical activities for young children who lack cultural support in this domain and who are at early stages of conceptual development. We explore how the nature of Cabri Geometry activities, in conjunction with previous connected experiences, may influence the construction of meaning for geometric construction.

Connecting the equals sign

Children tend to view the equals sign as an operator symbol bereft of the rich relational properties of equality statements. It has been argued by some that this restricted view of the equals sign is due to cultural or cognitive factors. We suggest a significant factor is that rich relational meanings lack relevance within the context of paper-based arithmetic. One possible way to allow learners access to relational meanings is through interaction with technologically supported utilities for the equals sign. We report upon a trial in which two students draw on existing and emerging notions of mathematical equivalence in order to connect an onscreen = object with other arithmetical objects.

Effective Strategies for Information Technology in Teacher Education: the use of an evolving permeation model

ABSTRACT This paper examines the debate in recent years about the most effective strategy for establishing the use of information technology in teacher training establishments in the United Kingdom. Evidence is presented to support the notion that efforts should continue to permeate the use of information technology throughout the courses of such establishments. However, the paper suggests that staff development and the degree of permeation of information technology within the culture develop alongside each other. As one of these variables change, it feeds the development of the other; neither is an independent variable though both are influenced by external factors. Recognising this as a relatively slow process, the paper proposes a model of evolutionary permeation.

Constructive and instructive representation

Abstract Beginning teachers of mathematics are likely to have noted the development of powerful multiple representation software which offers children access to the many modalities through which mathematics is expressed. We argue that embedded, even hidden, within such software are many mathematics conventions, which the naive learner has to unravel in order to construct meaning for those representations. We contrast such representations, which we label as instructive, with those children construct through the use of expressive software; this contrast is seen as analogous to aspects of literacy. We identify various characteristics of these two distinctive forms of representation.

Research on Uncertainty

We discuss research on the teaching and learning of uncertainty, with a particular emphasis on quantifiable aspects as might be represented by probability. We acknowledge earlier reviews of the field by integrating research, especially from the last 10 years, with previous studies. In particular, we focus on three issues, which have become increasingly significant: (1) the realignment of previous work on heuristics and biases, (2) conceptual and experiential engagement with uncertainty and (3) adopting a modelling perspective on probability. The role of the teacher in shaping the learning environment in various critical ways emerges as a key finding. In the concluding section, we indicate promising directions for research, including the need for more exploratory research in new areas such as the role of modelling and carefully designed experiments to test hypotheses that are apparent from more established studies.

Introducing a special issue on constructing meanings from data

1. PREAMBLE The organising theme running through this special issue is ‘constructing meanings from data’. In this introduction, we wish to elaborate this phrase, which intentionally blurs distinctions between the internal mental processes, epistemological considerations and pedagogical contexts. This intent arises from a standpoint in which these three components are seen as deeply connected, each providing structuring forces upon the others. To put it simply, a student’s learning in the classroom is self-evidently contingent upon what that student already knows, on the nature of the mathematical content being addressed and on external tools and social resources available within the learning context. What is less obvious is the relationship between these factors. The juxtaposition of these three factors in the focus of the work of PME (mapping mental processes onto Psychology, epistemological processes onto Mathematics and pedagogical contexts onto Education) reflects the need to articulate this relationship. John Truran has elaborated further on the emergence of the related areas of data handling, probability and statistics within the P, the M and the E of PME in reflections appended at the end of this introduction Data Handling was chosen as the theme for one of the Research Fora at PME22 (Summer 1998) in recognition of the growing interest in this area of mathematics internationally, both in terms of curriculum development, and in terms of research within PME. The term ‘data handling’ itself reflects recent changes in the way in which the topic is approached within the school curriculum, extending ‘graphical representation’ within the primary age range, and broadening the accessibility of ‘statistics’ in secondary school. This change has no doubt been influenced by a number of factors, including the availability of technology, which makes it possible to handle, and present large quantities of data with ease, the increased public use and awareness of statistics, and the introduction into school curricula of notions such as relevance and citizenship. The development

Supporting Teachers’ and Children's Mathematical Thinking: a strategy for the effective use of information technology

ABSTRACT In this paper we consider some of the obstacles which have so far prevented the potential of information technology to support young childrens mathematical thinking from being realised. As well as the obvious limitations of resources, we discuss technical issues to do with hardware and software and organisational issues within schools. Perhaps more significantly, we focus on the stresses and demands which are placed upon primary teachers, and examine how current types and levels of access militate against computers being used for mathematical applications. Based on our experiences in the Primary Laptop Project, which has the long‐term aim of studying the effect on childrens and teachers’ learning and attitudes when offered high levels of access to personal technology, with particular .emphasis upon mathematical understanding, we go on to suggest strategies for change. As well as considering the potential for supporting childrens mathematical thinking, we focus on the professional development n...

“Visual Math: The Function Web Book” by Yerushalmy, M., Katriel, H., and Shternberg, B. (2002). Published by CET, Ramat Aviv, Israel. www.cet.ac.il/math/function/english

This article is a review of the above web (or interaction) book. The review considers the contribution of this book with respect to the authors’ own stated aspirations to support the teaching and learning of functions. These somewhat theoretical conclusions are hopefully given enhanced meaning through discussion with a trainee teacher. I conclude that the design of the web book has much to offer anyone working in this field. Teachers as well will find it a wonderful resource though they may need to work quite hard at motivating children’s work and interpreting the many rich tasks to make them more accessible to “ordinary kids”.