Space victualling

Victualling in space differs fundamentally from victualling on land or at sea because there is little chance of foraging or of finding local sources of oxygen and water, and all metabolic products have to be carefully collected even if they will ultimately be jettisoned. The need for a deliberate policy for coping with carbon dioxide, faeces, and urine leads naturally, to schemes for recycling. Entropy is increased when food is metabolised: energy will have to be expended for even partial restoration of the status quo.     

Problems, perseverance, and mathematical residue

This paper reports on a qualitative study in which three third grade students were presented with a mathematical challenge related to the volume of a cuboid. The task required the construction of containers and the enumeration of the multi-link cubes¹ held by each of the containers. The study videotaped and investigated the students working as a group through potentially seven different problem solving categories, and how they dealt with the student-generated mathematical dilemmas that surfaced during their exploration of the original problem. The tapes were examined for the problem solving actions that the students demonstrated, and an analysis of the students' counting strategies and solutions explored the connection between the children's spatial structuring and their use of numerical operations in enumerating 3-D rectangular arrays of cubes. The notions of perseverance and control are considered as they emerge during autonomous problem solving and the mathematical residue that results from the developing understanding of volume is discussed.This revised version was published online in October 2005 with corrections to the Cover Date.     

Within-Document Retrieval: A User-Centred Evaluation of Relevance Profiling

We present a user-centred, task-oriented, comparative evaluation of two within-document retrieval tools. ProfileSkim computes a relevance profile for a document with respect to a query, and presents the profile as an interactive bar graph. FindSkim provides similar functionality to the web browser “Find” command. A novel simulated work task was devised, where participants are asked to identify (index) relevant pages of an electronic book, given topics from the existing book index. The original book index provides the ground truth, against which the indexing results of the participants can be compared. We confirmed a major hypothesis, namely ProfileSkim proved significantly more efficient than Find-Skim, as measured by time for task. The study indicates that ProfileSkim was as least as effective as FindSkim in identifying relevant pages, as measured by traditional information retrieval measures, and there is some evidence that ProfileSkim is a precision-enhancing tool. Based on qualitative data from questionnaires, we also provide strong evidence to support our conjecture that the participants would be more satisfied when using ProfileSkim than FindSkim. The experimental study confirmed the potential of relevance profiling for improving within-document retrieval. Relevance profiling should prove highly beneficial for users trying to identify relevant information within long documents.     

The Equation, the Whole Equation and Nothing But the Equation! One Approach to the Teaching of Linear Equations

There exists an extensive range of research looking at the teaching and learning of linear equations, resulting in many papers highlighting a range of teaching approaches and illustrating a variety of significant cognitive problems and stumbling blocks to the learning of linear equations with understanding. Building on this literature, this paper presents some of the results of a case study which looked at the mathematics classroom of one particular teacher, Alwyn, trying to teach mathematics with meaning to less able pupils at secondary school level. Our interest here is those lessons which dealt specifically with the learning of linear equations, in which firstly a different approach was utilised and secondly many of the problems referred to in the literature were not present. We contrast this method with the teaching of linear equations to a variety of ability levels in several other classrooms that we have studied and we attempt through use of the Pirie-Kieren model, to analyse and account for the successful growth of understanding of the lower ability, year eight pupils in one particular classroom.     

Film and Society

Bill Nichols IDEOLOGY AND THE IMAGE: SOCIAL REPRESENTATION IN THE CINEMA AND OTHER MEDIA (Bloomington: Indiana University Press, 1981 —$29.95/$9.95)

David Pirie ANATOMY OF THE MOVIES (New York: Macmillan, 1981—$15.95)

Nancy Lynn Schwartz THE HOLLYWOOD WRITER'S WARS (New York: Alfred A. Knopf, 1982—$17.95)

Gilbert Ad air VIETNAM ON FILM: FROM THE GREEN BERETS TO APOCALYPSE NOW (New York: Proteus, 1981— $13.95). Adair begins with John Wayne's The Green Berets (1968)

Edward D. C. Campbell, Jr. THE CELLULOID SOUTH (Knoxville: The University of Tennessee Press, 1981—$17.50)

Elizabeth Weatherford NATIVE AMERICANS ON FILM AND VIDEO (Available from Museum of the American Indian, Broadway at 155th Street, New York, NY 10032— $4.95, paper)     

Growth in mathematical understanding: How can we characterise it and how can we represent it?

There has been a variety of approaches to the study of mathematical understanding, and some of these are reviewed before outlining the background to the model we are proposing for the growth of such understanding. The model is explained in detail and illustrated with reference to the concept of fractions. Key features of the model include don't need boundaries, folding back, and the complementarities of acting and expressing that occur at each level of understanding. The theory is illustrated by examples of pupils' work from a variety of topics and stages. Finally one of the practical applications of the theory, mapping, is explained in some detail.     

Mathematical discussion and mathematical understanding

A longitudinal study is being undertaken into the question of whether or not discussion in the mathematical classroom is an aid to understanding. Preliminary analysis shows that, while the hypothesis that discussion aids understanding is very attractive, evidence to support the hypothesis has been limited. Classroom observations during the first year of the study have led to a method of classification of mathematical talk in the classroom which we expect will prove useful in investigating links between mathematical discussion and mathematical understanding.The ability to say what you mean and mean what you say should be one of the outcomes of good mathematics teaching .... Pupils need the explicit help, which can only be given by extended discussion, to establish these relationships (between different mathematical topics); even pupils whose mathematics attainment is high do not easily do this themselves. (Cockcroft, 1982, England)In all other topics, we saw teachers there (Kitamaeno School in Tokyo) using peer group dialogues ... (they) justified their use of group dialogue because of their large classes (35–43) and the unusually independent spirit of many of the 600 pupils. Mathematics achievement was very high by American standards. (Easley, 1984, on a Japanese project)We need to recognise the importance of verbalisation. Putting thoughts into words requires students to organise their thinking and to confront their incomplete understanding. Listening to others affords them the opportunities to contemplate the thinking of others and to consider the implications for their own understanding. (California State Department of Education, 1987)This article is based on the first year of a longitudinal study intended to shed light on the question of whether or not discussion in the mathematics classroom is an aid to mathematical understanding. Before looking further at the research context in which this project is set, we wish to offer our definitions of the two notions in the title.