Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Investigating Texts

The first chapter called 'Investigating texts' asks students to investigate the concept of text and what it might mean to 'behave like a reader'. After reading and comparing two short stories, the question, 'what is a story?' is posed. Students are then asked to distinguish a fiction text from a number of non-fiction texts and to identify the sources of the latter. It is suggested that although it is quite easy to perform these tasks, it is not so easy to describe texts in terms only of their features or ingredients; that it is necessary to talk about how texts are read, and what is more, how they are read on particular occasions. 'Making texts', the second chapter, asks students via a series of activities to consider what they expect of texts, and to investigate the conventions of fiction and non-fiction. They are given the opportunity to manipulate the 'ingredients' of texts, to read in terms of commonalities and to speculate about the rules by which both the composition and consumption of texts are organised. The ways in which particular kinds of reading and writing activities assume the text as a certain kind of object - as a model, for example, or as an object of criticism or as an occasion for self-questioning - is made explicit, and students are encouraged to investigate a range of uses of texts and the implications of these for reading and writing. Chapter three, 'Changing texts' asks students to consider, through a number of fascinating examples, how both fiction and non-fiction texts have changed over time, and how the ways in which readers read texts can change too. The 'retelling' of texts in terms of changing norms is considered via an 'updated' version of 'Scheherazade'; a student's feminist adaptation of her own text (initially written using a romance as a model), and an encyclopedia entry. 'Reading practices', the fourth chapter, poses further questions about different ways of reading. Through reading a number of didactic texts alongside three stories from a genre that is not usually read for morally improving lessons, students are asked to consider how different their reading practices can be.

The trouble with English

So much has been made over the crisis in English literature as field, as corpus, and as canon in recent years, that some of it undoubtedly has spilled over into English education. This has been the case in predominantly English-speaking Anglo-American and Commonwealth nations, as well as in those postcolonial states where English remains the medium of instruction and lingua franca of economic and cultural elites. Yet to attribute the pressures for change in pedagogic practice to academic paradigm shift per se would prop up the shaky axiom that English education is forever caught in some kind of perverse evolutionary time-lag, parasitic of university literary studies. I, too, believe that English education has reached a crucial moment in its history, but that this moment is contingent upon the changing demographics, cultural knowledges, and practices of economic globalization.