As part of an investigation into the relationship between classroom dialogue and student outcome, a test of reasoning has been developed that is suitable for preadolescents (i.e. c.10-13-year-olds). Building on previous work but expanding this considerably, the test focuses upon four areas of reasoning: differentiation of facts from opinions,…

Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children's perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a…

This study examines expressions of reasoning by some higher achieving 11 to 18 year-old English students responding to a survey consisting of function tasks developed in collaboration with their teachers. We report on 70 students, 10 from each of English years 7-13. Iterative and comparative analysis identified capabilities and difficulties of…

Research indicates that understanding levels of abstraction (LOA) and being able to move between the levels is essential to programming success. For K-5 contexts we rename the LOA levels: problem, design, code and running the code. In our qualitative exploratory study, we interviewed five K-5 teachers on their uses of LOA, particularly the design…

This article reports on a study conducted to investigate the development of abstract thinking in preschool children (ages from three years to four years old) in a nursery school in England. Adopting a social influence approach, the researcher engaged in "close listening" to document children's ideas expressed in various representations…

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This…

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…

Drawing on her research into students' evidential reasoning, Elisabeth Pickles explores the possibilities for how such reasoning might be assessed. Existing exam mark schemes focus too heavily on generic processes involved in the analysis of source material and insufficiently on the historical validity of reasoning and conclusions produced.…

James Moffett's "Teaching the Universe of Discourse" set out an agenda for the study of development in writing, which influenced James Britton's work in the UK. Subsequently, however, the work of both these thinkers was largely set aside in the approach to writing taken by national strategies in England. In this article, we trace the…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

Employing a sample of 51 12-year-old British secondary pupils, a study analyzed children's written and oral responses to a series of (contradictory) historical questions concerning the Boston Massacre of 1770. Many students were capable of abstract historical reasoning--critiquing sources, detecting bias and ambiguity, and determining flaws in…

The aims of this study were (1) to test the dyadic superiority hypothesis by comparing dyadic performance on a logical reasoning task with the performance of children working alone, and (2) to determine whether the incorrect child's compliance with the correct child was a major factor in the dyadic production of correct answers. (Author/DB)

It has been suggested that cognitive style interacts with performance on tasks measuring formal thought. It is hypothesized that cognitive style interacts with task context rather than with the underlying formal thought processes. Experiments are reported to clarify the type of task that elicits an interaction and to determine whether such…