Interactions between defining,explaining and classifying: the case of increasing and decreasing sequences

This paper describes a study in which we investigated relationships between defining mathematical concepts — increasing and decreasing infinite sequences — explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and the effect of classifying on subsequent explaining and defining. We report that (1) student-generated definitions and explanations were highly variable in content and quality; (2) explicitly considering the meaning of the concept facilitated subsequent classification, and giving a personal definition or explanation had a greater effect than studying a given definition; (3) classifying before defining or explaining resulted in significantly poorer definitions and explanations. We discuss the implications of these results for the teaching of abstract pure mathematics, relating our discussion to existing work on the concept image/concept definition distinction and on working with examples.     

‘You feel ashamed that you are not in the higher group’—Children’s psychosocial response to ability grouping in primary school

The impact of performative focused agendas on how teachers ‘do’ teaching and how children ‘do’ learning cannot be understated. While research continues to highlight the negative impact of ability grouping on children’s academic and social learning experiences in the classroom, policy imperatives (both global and local) continue to promote ability grouping as an ‘effective’ pedagogic tool for meeting the diverse needs of children, especially in the areas of numeracy and literacy. We argue that this is a symbolically violent process that negatively impacts the psychosocial positioning of children as they negotiate their identities within the figured world of the primary school classroom. This in turn influences their learner identities, as well as their perceptions of their ability to learn. Drawing on data collected with 100 children in three case study schools, we show how ability grouping evoked strong emotional and psychosocial responses characterised by feelings of ‘shame’, ‘upset’ and ‘inferiority’ for those in the low-ability groups. In contrast, children placed in higher-ability groups felt a sense of ‘pride’, ‘happiness’ and ‘confidence’. Ability grouping maps a geography of affect within the classroom demarcating not only how children ‘do’ learning, but also how they embody learning through a particular feeling of ‘being’ a learner in the classroom.     

Assessing pupils’ intelligence through self,parental, and teacher estimates

This study examined the accuracy of self‐ and other‐estimated intelligence in relation to tested cognitive ability and gender. Three groups of raters were examined: 187 (102 male, 85 female; mean age 14.33 years, SD = .32) pupils of single‐sex comprehensive schools, 109 (55 mothers and 54 fathers) parents, and six teachers of the pupils. Pupils estimated their own overall IQ, while their parents and teachers estimated the pupils’ overall, mathematical, spatial, and verbal abilities. Self‐ and other‐estimates were compared to each other, and to the child’s psychometric test scores in verbal, quantitative, and figural/non‐verbal reasoning ability. Results suggested that participants were reasonably accurate at estimating pupils’ intelligence – teachers significantly more so than parents, and pupils significantly more so than fathers. Although both parents significantly overestimated their child’s IQ, this overestimation was more pronounced in fathers.     

Some Functions are More Equal than Others: The Development of a Macroappraisal Strategy for the National Archives of Australia

In 1999–2000 the National Archives of Australia (NAA) adopted a functions-based approach to appraisal. Since that time functional appraisal projects have for the most part been conducted in cooperation with individual agencies. What has been missing is a broad whole-of-government or macroappraisal framework which might assist with the strategic prioritisation of projects, the allocation of resources and the identification of high-value functions, activities and record classes. This article describes a project commenced by the NAA during 2003–2004 to research and develop a functions-based macroappraisal framework for current and prospective appraisal and for retrospective application to records of the past 30 years of the Australian Government. The article compares the Australian approach with macroappraisal strategies pursued in Canada, the Netherlands and South Africa.     

The World Bank's policy paper on vocational and technical education and training

In addition to numerous articles in professional journals, some of his major works include The Neglected Source of Human Wealth: A Study of Formal Education and Training during the Adult Years(1982) and The Lingering Crisis of Youth Unemployment (1978).