1,721,011 research outputs found
Intuitive and formal models of whole number multiplication: relations and emerging structures
No full textMultiplication can be presented to students through different models, each one with its pros and cons. In this contribution we focus on the repeated sum and the array model to investigate the relations between the two models and those between them and multiplication properties. Formal counterparts are presented. Taking both a mathematical and cognitive perspective, we highlight that even at a mathematical structure level the models are different. Relating to literature, we connect differences in the mathematical structure with possible educational difficulties. We conclude that experiencing relations between models is a source of learning about the operation and its structure
Etude didactique et cognitive des rapports de l'argumentation et de la démonstration dans l'apprentissage des Mathématiques
No full textFrom action to symbols: giving meaning to the symbolic representation of the distributive law in primary school
Full text linkThe use of artifacts to introduce the distributive law of multiplication over addition in primary school is a diffused approach: it is possible to find pre-constructed learning trajectories in instructional materials. However, it is still unclear how the teacher might support his/her students in transitioning from concrete to symbolic representations of the distributive law. In the theoretical frame of the Theory of Semiotic Mediation, we report on a study where Laisant’s table, an artifact embodying the rectangular model of multiplication, is used to introduce distributive law in second grade. Taking a microanalytical approach, we show how a group of students connects the representation provided by the artifact with the symbolic representation of the arithmetic property (as equivalence of numerical sentences). Two different semiotic chains are identified and presented, showing the continuity between the activity with the artifact and the mathematical signs emerging in following activities and promoted by tasks specifically designed. The role of the teacher in triggering and scaffolding this process is highlighted
Designing Non-constructability Tasks in a Dynamic Geometry Environment
No full textThis chapter highlights specific design features of tasks proposed in a Dynamic Geometry Environment (DGE) that can foster the production of indirect argumentations and proof by contradiction. We introduce the notion of open construction problem and describe the design of two types of problems, analysing their potential a priori, with the goal of elaborating on the potentials of designing problems in a DGE with respect to fostering processes of indirect argumentation. Specifically, we aim at showing how particular open construction problems, that we refer to as non-constructability problems, are expected to make indirect argumentations emerge
NARRATIVE CONTEXT AND PARADIGMATIC TOOLS: A TALE FOR COUNTING
No full textWe present a design study about the use of narration to frame a work on counting in a first grade class. We propose to use the ideas of ???narrative??? and ???paradigmatic??? ways of thinking (Bruner, 1986) in order to design, manage and analyse the development of children???s experience. In this specific experience the role of logical tools is played by the criteria used to carry on the count process, conceived as coordination of two different semiotic activities
Taking a look at Chinese pedagogy in 数学 [shuxue: Mathemathics]: a dialogue between cultures to approach arithmetic at first and second Italian Primary classes
No full textABSTRACT Aim of this paper is to exploit intercultural dialogue to analyze two cases of task design about straws and word problems in different cultural traditions (the Eastern and Western one). By means of two paradigmatic examples developed in Italy, we aim at showing, on the one hand, the effects and advantages of intercultural dialogue and, on the other hand, the need to take into account and to respect culturally rooted pedagogies, avoiding uncritical transfer from one culture to another
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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