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James L Mcclelland - One of the best experts on this subject based on the ideXlab platform.

  • different presentations of a mathematical concept can support learning in complementary ways
    Journal of Educational Psychology, 2018
    Co-Authors: Andrew K Lampinen, James L Mcclelland
    Abstract:

    Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of that concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with deeply interconnected concepts and many distinct aspects of understanding of each concept, and we discuss difficulties with the idea that differences among presentations can be ordered on a concrete-abstract dimension. To move beyond this, we explore how different presentations of a concept can affect learning of subsequent concepts and assess several distinct aspects of understanding. Using the domain of elementary group theory, we teach adult participants a group operation using a visuospatial or an arithmetic presentation. We then teach them concepts that build upon this operation. We demonstrate that our presentations differentially support learning complementary aspects of the system presented. We argue that these differences arise from the fact that each presentation supports learning by connecting to different systems of reasoning learners are already familiar with, and that it is these connections to extant knowledge systems, rather than differences in concreteness versus abstractness, that determine whether a presentation will be helpful. Furthermore, we show that presenting both presentations and encouraging participants to recognize the relationship between them improves performance without requiring additional time, at least for some participants. (PsycINFO Database Record (c) 2018 APA, all rights reserved)

Daniel Gabay - One of the best experts on this subject based on the ideXlab platform.

  • a viability analysis for a bio economic model
    Ecological Economics, 2001
    Co-Authors: Christophe Ene, Luc Doye, Daniel Gabay
    Abstract:

    Abstract This paper presents a simple dynamic model dealing with the management of a marine renewable resource. But instead of studying the ecological and economic interactions in terms of equilibrium or optimal control, we pay much attention to the viability of the system or, in a symmetric way, to crisis situations. These viability/crisis situations are defined by a set of economic and biological state constraints. The analytical study focuses on the compatibility between the state constraints and the controlled dynamics. Using the mathematical concept of viability kernel, we reveal the situations and, if possible, management options to guarantee a perennial system. Going further, we define ‘overexploitation’ indicators by the time of crisis function. In particular, we point out irreversible overexploitation configurations related to the resource extinction.

Martin A Simon - One of the best experts on this subject based on the ideXlab platform.

  • Explicating mathematical concept and mathematicalconception as theoretical constructs for mathematics education research
    Educational Studies in Mathematics, 2017
    Co-Authors: Martin A Simon
    Abstract:

    mathematical understanding continues to be one of the major goals of mathematics education. However, what is meant by “mathematical understanding” is underspecified. How can we operationalize the idea of mathematical understanding in research? In this article, I propose particular specifications of the terms mathematical concept and mathematical conception so that they may serve as useful constructs for mathematics education research. I discuss the theoretical basis of the constructs, and I examine the usefulness of these constructs in research and instruction, challenges involved in their use, and ideas derived from our experience using them in research projects. Finally, I provide several examples of articulated mathematical concepts.

  • participatory and anticipatory stages of mathematical concept learning further empirical and theoretical development
    Journal for Research in Mathematics Education, 2016
    Co-Authors: Martin A Simon, Nicora Placa, Arnon Avitzur
    Abstract:

    Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. In this article, we discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment. We describe our modifications to and further explicate and exemplify the theoretical underpinnings of these stage constructs. We introduce a representation scheme and use it to trace the development of a concept from initial activity, through the participatory stage, and to the anticipatory stage.

Gregor Snelting - One of the best experts on this subject based on the ideXlab platform.

  • assessing modular structure of legacy code based on mathematical concept analysis
    International Conference on Software Engineering, 1997
    Co-Authors: Christian Lindig, Gregor Snelting
    Abstract:

    Christian Lindig, Gregor Snelting Technische Universitat Braunschweig Abteilung Softwaretechnologie Bultenweg 88 D-38104 Braunschweig, Germany +49 531 391 7577 lindig@ips.cs.tu-bs.de to appear in Proc. International Conference on Software Engineering, Boston 1997 ABSTRACT We apply mathematical concept analysis in order to modularize legacy code. By analysing the relation between procedures and global variables, a so-called concept lattice is constructed. The paper explains how module structures show up in the lattice, and how the lattice can be used to assess cohesion and coupling between module candidates. Certain algebraic decompositions of the lattice can lead to automatic generation of modularization proposals. The method is applied to several examples written in Modula-2, Fortran, and Cobol; among them a >100kloc aerodynamics program.

  • reengineering of configurations based on mathematical concept analysis
    ACM Transactions on Software Engineering and Methodology, 1996
    Co-Authors: Gregor Snelting
    Abstract:

    We apply mathematical concept analysis to the problem of reengineering configurations. concept analysis will reconstruct a taxonomy of concepts from a relation between objects and attributes. We use concept analysis to infer configuration structures from existing source code. Our tool NORA/RECS will accept source code, where configuration-specific code pieces are controlled by the preprocessor. The algorithm will compute a so-called concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tine-grained dependencies between configurations, but also visualizes the overall quality of configuration structures according to software engineering principles. In a second step, interferences between configurations can be analyzed in order to restructure or simplify configurations. Interferences showing up in the lattice indicate high coupling and low cohesion between configuration concepts. Source files can then be simplified according to the lattice structure. Finally, we show how governing expressions can be simplified by utilizing an isomorphism theorem of mathematical concept analysis.

Márcia Maria Fusaro Pinto - One of the best experts on this subject based on the ideXlab platform.

  • School Practices With The mathematical Notion Of Tangent Line
    New Directions for Situated Cognition in Mathematics Education, 2008
    Co-Authors: Márcia Maria Fusaro Pinto, Valeria Guimaraes Moreira
    Abstract:

    We seek to understand the process of learning mathematical notions as forms of practice in the classrooms of two different technical school courses. More specifically, we investigate students’ and teachers’ experiences and use of the mathematical concept of tangent line in these different contexts. We use empirical data collected through non-participant observation, analysis of students’ written responses to a questionnaire, and semi-structured interviews with groups of six students from each course observed. We take a situated perspective of learning which enables us to see these classroom activities as genuinely mathematical, though distinct. Through our analysis, we describe aspects of what we see as the common direction of learning mathematics in the two vocational course lessons; this is found to be closer to ‘being mathematical’ in work settings than in school mathematics classrooms.

  • Teaching School Students' conceptions of Tangent Lines.
    International Group for the Psychology of Mathematics Education, 2004
    Co-Authors: Valeria Guimaraes Moreira, Márcia Maria Fusaro Pinto
    Abstract:

    This paper reports ongoing research investigating how students experiences with the notion of tangent line in different lecture courses at a technical school are being integrated to the related mathematical concept. Focusing on a technical course case study, we examine how aspects of the notion of tangent line are related to features of the context in which they are being produced. In addition, we discuss whether it is appropriate, from the perspective of situated learning, to account for practices of school mathematics in the various lecture courses in the curricula as distinct school mathematics practices, or, distinct communities of practices of (school) mathematics.