Jan Wyndhamn

Heavenly talk : Discourse, artifacts, and children's understanding of elementary astronomy

In the literature on children’s understanding of astronomical concepts, such as the shape of the earth and gravitation, the difficulties that children have in conceptualizing these phenomena have been documented in many studies. The purpose of this research is to critically scrutinize these findings by taking a situated and discursive perspective on reasoning (and cognitive development). Instead of viewing understanding as the overt expression of underlying mental models, children’s responses in interview studies should be regarded as situated and as dependent on the tools available as resources for reasoning. By modifying the interview situation through the introduction of a globe as a tool for thinking, the outcomes are radically different from those reported earlier. None of the problems that have been reported, where children, for instance, claim that people can fall off the earth, can be detected. Even among the youngest participants gravitation is often invoked as an explanatory concept. It is argued that the globe in this case serves as an efficient prosthetic device for thinking, and this illustrates the tool-dependent nature of human reasoning.

Word problems and mathematical reasoning—A study of children's mastery of reference and meaning in textual realities

Abstract The mastery of word problems is seen as an important test of mathematical ability. When solving such problems, students supposedly go beyond rote learning and mechanical exercises to apply their knowledge to realistic problem situations in which mathematical reasoning becomes an important instrument for making concrete judgements. Research shows that performance on word problems is often surprisingly poor. Non-realistic, and even logically inconsistent, answers to word problems are often accepted by students, and there are many signs that students seldom make so-called realistic considerations when applying their mathematical knowledge to real world events. The study reported is a follow-up of the work by Verschaffel, De Corte, and Lasure (1994) in which the difficulties students have in making realistic considerations were clearly illustrated. In the present study, students (10–12 years of age) worked in groups, and the tasks given (estimating distances) were introduced as part of a general discussion of how to calculate distances to school. Results show that the participants were clearly able to entertain different assumptions regarding how to measure distances, and they make distinctions between alternative options when discussing, for instance, the distance between two villages as indicated on a road sign on the one hand, and when talking about the shortest possible distance on the other. It is argued that the problem of what constitutes a realistic consideration when solving word problems is far from simple but has to be understood in context.

The Forrnal Setting as Contextfor Cognitive Activities: An Ernpirical Study of Arithmetic Operations under Conflicting Premisses for Comrnunication

The general concern of the present article is to contribute to an understanding of the contextual determination of cognitive activities. More specifically, the focus of the empirical research reported has been to study how pupils define and deal with cognitive tasks in situations that are recognised as pedagogical in character. Within the context of their everyday mathematics teaching, 206 twelve year old primary school pupils were given work sheets containing elementary arithmetic problems. The experimental treatment consisted of introducing (through headings and instructions) pedagogical definitions of problems that were in conflict with the nature of the problems themselves. The results indicate that the predefinitions of cognitive activities typical of educational contexts have a strong impact on the way problems are dealt with. Clear differences could be discerned between groups at different achievement levels in the extent to which the cues present in pedagogical contexts were used in defining the problem. A crucial aspect of what are conventionally conceived as differences in mathematical ability seems, judging from the present results, to have more to do with the capacity to decipher ambiguous communicative situations than with the mastery of a mathematical algorithm per se.RésuméD’un point de vue général, le but du présent article est de contribuer à la réflexion sur la manière dont les activités cognitives sont déterminées par le contexte même dans lequel elles ont lieu. Plus spécifiquement, notre recherche empirique porte sur le problème de savoir comment les élèves définissent et traitent des tâches cognitives qui leur sont présentées dans des situations à caractère pédagogique. Dans le cadre ordinaire de leurs cours de mathématiques, 206 élèves, âges de 12 ans, eurent à résoudre par écrit des problèmes d’arithmétique élémentaire. La démarche expérimentale consistait à introduire pour ces problèmes (par le biais de titres et d’instructions) des définitions pédagogiques qui étaient en contradiction avec la nature même des problèmes. Les résultats révèlent que ces directives préalables, caractéristiques du contexte scolaire, influencent considérablement la manière dont les élèves envisagent le problème. Il est apparu nettement que, pour la définition des problèmes, le degré d’utilisation des indications fournies par le contexte pédagogique varie en fonction du niveau de réussite scolaire des élèves. Ce qui est conventionellement conçu comme des divergences d’aptitude en mathématiques, serait donc, à en juger par les résultats présentés, plus en rapport avec la capacité de s’orienter dans une situation communicative ambiguë qu’avec la maîtrise d’un algorithme mathématique en soi.

Cognitive Operations and Educational Framing of Tasks : School as a Context for Arithmetic Thought

Cognitive Operations and Educational Framing of Tasks. School as a Context for Arithmetic Thought. Scandinavian Journal of Educational Research 32, 61‐71. The purpose of the present study is to contribute to the understanding of the contextual determination of cognitive activities. In a naturalistic experiment in a primary school setting it is shown how performance at group level on an elementary arithmetic task is influenced by the immediate context in which this problem is presented. Differences in performance between groups at various achievement levels in mathematics are amplified by corresponding differences in discovering and utilizing analogies between problems as heuristic aids. This latter kind of difference reflects – it is argued – variations in abilities in analysing and deciphering cognitive tasks at a linguistic and meta‐communicative level rather than in mastering the specific algorithmic tools. It is also argued that the functional meaning of the task as pedagogical praxis may differ between contexts.