Changes in Cooperation and Self-Other Differentiation during the Second Year

Cooperation in peer interaction emerges during the second half of the second year. A consideration of the skills and knowledge entailed in these early forms of cooperation suggests that young children's emerging ability to differentiate self from other as causal agents may relate to their ability to coordinate behavior with age mates toward a common goal. Children at 12, 18, 24, and 30 months were observed in same-age, same-sex dyads (8 dyads per age) while attempting to solve a simple cooperation problem. They were also individually administered an elicited imitation task used to index decentration, or self-other differentiation. No 12-month-old dyad could cooperate, 18-month-olds did so infrequently and apparently accidentally, whereas 24- and 30-month-olds were able to coordinate behavior with one another quickly and effectively. Children who were better able to accommodate their behavior to one another during cooperation also represented the agency of others at a more advanced, decentered level.     

The significance of constructivist classroom practice in national curricular design

Evidence of the value of constructivist theory in the classroom is especially important for educational practice in areas of poverty and social challenge. Research was undertaken in 2010 into the application of constructivist theory on instructional design. The findings of this research are particularly relevant to the current curricular crisis in South Africa which threatens to side-line constructivist priorities and return learners to rote learning from textbooks. The findings are situated here within the national debate over curricular design and instructional models. Placing instructional design within the larger context of national pedagogical contestation provides important evidence of the central role of Freirean imperatives for South Africa’s educational future. This article indicates that a constructivist framework, when pertinently arranged, provides holistic and sustainable procedures for knowledge creation. The findings from the research project showed that, in an environment conducive to learning, learners become self-motivated and better able to master the next phase of the curriculum. As a result of the constructivist framing, participants grew into strategic and effective learners who took responsibility for their own learning. These findings add weight to the call for reconsideration of constructivist foundations in national curriculum design.     

Conservation in Physics Teaching,History of Science and in Child Development

The current work is an exploratory study on the ideas thatstudents in their fourth semester of engineering have about ``conservation'. Wereview the Piagetian position on the importance of conservations in logical operational structures inchild development and we comment upon other current trends in cognitive psychology. We discussbriefly the development of conservations in science during the 17th, 18th and 19th centuries and we pointout the contrast between this and how most textbooks introduce this subject. We have also carried out afirst, tentative analysis of the answers given by a sample of these students to a brief questionnaire about``conservation' and ``non-conservation'.     

Situating graphs as workplace knowledge

We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of “transparency”, a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the notion of transparency to characterise instances of graph use by highly educated scientists in cases where the context was familiar: the scientists were able to read the situation “through” the graph. This paper explores the limits of the validity of the transparency metaphor. We present two vignettes of actual graph use by a factory worker, and contrast his actions and knowledge with that of a highly qualified process engineer working on the same production line. We note that in neither case the graphs were transparent. We argue that a fuller account that describes a spectrum of transparency is needed, and we seek to achieve this by adopting some elements of a semiotic approach that enhance a strictly activity-theoretical view.     

Students' understandings of logical implication

We report results from an analysis of responses to a written question in which high-attaining students in English schools, who formed part of a longitudinal nation-wide survey on proof conceptions, were asked to assess the equivalence of two statements about elementary number theory, one a logical implication and the other its converse, to evaluate the truth of the statements and to justify their conclusions. We present an overview of responses at the end of Year 8 (age 13 years) and an analysis of the approaches taken, and follow this with an analysis of the data collected from students who answered the question again in Year 9 (age 14 years) in order to distinguish learning trajectories. From these analyses, we distinguished three strategies, empirical, focussed-empirical and focussed-deductive, that represent shifts in attention from an inductive to a deductive approach. We noted some progress from Year 8 to Year 9 in the use of the focussed strategies but this was modest at best. The most marked progress was in recognition of the logical necessity of a conclusion of an implication when the antecedent was assumed to be true. Finally we present some theoretical categories to capture different types of meanings students assign to logical implication and the rationale underpinning these meanings. The categories distinguish responses where a statement of logical implication is (or is not)interpreted as equivalent to its converse, where the antecedent and consequent are (or are not) seen as interchangeable, and where conclusions are (or are not)influenced by specific data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Next steps in implementing Kaput’s research programme

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These ‘design principles’ focus on the evolution of digital representations since the early 1990s, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput’s notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is Kaput’s notion of communication and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression.     

The computer as a mediating influence in the development of pupils’ understanding of variable

European Journal of Psychology of Education - Within a Logo environment, pupils routinely use the notion of variable. However, the process by which they come to develop understandings is more...     

Some Implications of a Diversifying Workforce for Governance and Management

Tertiary Education and Management - This paper suggests that as university missions have adapted to accommodate major developments associated with, for instance, mass higher education and...     

The pupil's view of mathematics learning

This article reports an exploratory study which set out to examine how 14-year-old pupils perceive good and bad learning experiences in school. In particular, it describes the significant features in learning experiences which were associated with mathematics. Eighty-four pupils were asked, in semi-structured interviews, to tell stories about times when they had felt particularly good or particularly bad when learning. A story consisted of a critical event actually experienced by the pupil and what the pupil had felt at the time. The structure of the interview used and the means by which the qualitative data were analysed are discussed, as well as the main findings of the research.