The Experts below are selected from a list of 48618 Experts worldwide ranked by ideXlab platform
Fumiaki Ozaki - One of the best experts on this subject based on the ideXlab platform.
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Seki Takakazu’s Method of Calculating the Volume of Solids of Revolution and His Mathematical Object
Springer Proceedings in Mathematics & Statistics, 2013Co-Authors: Fumiaki OzakiAbstract:It is usually said that Seki Takakazu (ca. 1642 – 1708) calculated the volume of a solid of revolution using the Pappus-Guldinus theorem. However, it is difficult to say that Seki was influenced by Mechanics. In fact, Seki calculated the volumes of all parts which constitute a figure and added them. We may claim that Seki found the Pappus-Guldinus theorem from these calculations and will explain Seki’s method of construction for Mathematical Objects.
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seki takakazu s method of calculating the volume of solids of revolution and his Mathematical Object
2013Co-Authors: Fumiaki OzakiAbstract:It is usually said that Seki Takakazu (ca. 1642 – 1708) calculated the volume of a solid of revolution using the Pappus-Guldinus theorem. However, it is difficult to say that Seki was influenced by Mechanics. In fact, Seki calculated the volumes of all parts which constitute a figure and added them. We may claim that Seki found the Pappus-Guldinus theorem from these calculations and will explain Seki’s method of construction for Mathematical Objects.
John Mason - One of the best experts on this subject based on the ideXlab platform.
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seeing an exercise as a single Mathematical Object using variation to structure sense making
Mathematical Thinking and Learning, 2006Co-Authors: Anne Watson, John MasonAbstract:In this theoretical article, we take an exercise to be a collection of procedural questions or tasks. It can be useful to treat such an exercise as a single Object, with individual questions seen as elements in a Mathematically and pedagogically structured set. We use the notions of dimensions of possible variation and range of permissible change, derived from Ference Marton, to discuss affordances and constraints of some sample exercises. This gives insight into the potential pedagogical role of exercises, and shows how exercise analysis and design might contribute to hypotheses about learning trajectories. We argue that learners' response to an exercise has something in common with modeling that we might call micromodeling, but we resort to a more inclusive description of Mathematical thinking to describe learners' possible responses to a well-planned exercise. Finally we indicate how dimensions of possible variation inform the design and use of an exercise.
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THE EXERCISE AS Mathematical Object: DIMENSIONS OF POSSIBLE VARIATION IN PRACTICE
2004Co-Authors: Anne Watson, John MasonAbstract:By treating collections of questions as Mathematical Objects, that is ordered sets containing individual questions as elements, we gain insight into the potential role of exercises in learning mathematics. We use the notion of ‘dimensions of possible variation’, derived from Ference Marton, to discuss some exercises. There are implications for the design of question sets, for pedagogical decisions in the use of question sets, and for reflective questioning by learners.
Vicenç Font Moll - One of the best experts on this subject based on the ideXlab platform.
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Pre-service Teachers’ Common Content Knowledge Regarding the Arithmetic Mean
Journal for Research in Mathematics Education, 2014Co-Authors: Juan Jesús Ortiz De Haro, Vicenç Font MollAbstract:The main goal of this study is to determine the common content knowledge of a group of pre-service primary teachers regarding the arithmetic mean. The cognitive configuration tool proposed by the Onto-semiotic Approach of Cognition and Mathematics Instruction shows that the arithmetic mean can have a variety of meanings, and the application of this tool here revealed significant difficulties related to the students’ understanding of this Mathematical Object and some of its properties. This article concludes with some educational implications for teacher training in the field of statistics.
Anne Watson - One of the best experts on this subject based on the ideXlab platform.
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seeing an exercise as a single Mathematical Object using variation to structure sense making
Mathematical Thinking and Learning, 2006Co-Authors: Anne Watson, John MasonAbstract:In this theoretical article, we take an exercise to be a collection of procedural questions or tasks. It can be useful to treat such an exercise as a single Object, with individual questions seen as elements in a Mathematically and pedagogically structured set. We use the notions of dimensions of possible variation and range of permissible change, derived from Ference Marton, to discuss affordances and constraints of some sample exercises. This gives insight into the potential pedagogical role of exercises, and shows how exercise analysis and design might contribute to hypotheses about learning trajectories. We argue that learners' response to an exercise has something in common with modeling that we might call micromodeling, but we resort to a more inclusive description of Mathematical thinking to describe learners' possible responses to a well-planned exercise. Finally we indicate how dimensions of possible variation inform the design and use of an exercise.
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THE EXERCISE AS Mathematical Object: DIMENSIONS OF POSSIBLE VARIATION IN PRACTICE
2004Co-Authors: Anne Watson, John MasonAbstract:By treating collections of questions as Mathematical Objects, that is ordered sets containing individual questions as elements, we gain insight into the potential role of exercises in learning mathematics. We use the notion of ‘dimensions of possible variation’, derived from Ference Marton, to discuss some exercises. There are implications for the design of question sets, for pedagogical decisions in the use of question sets, and for reflective questioning by learners.
Juan Jesús Ortiz De Haro - One of the best experts on this subject based on the ideXlab platform.
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Pre-service Teachers’ Common Content Knowledge Regarding the Arithmetic Mean
Journal for Research in Mathematics Education, 2014Co-Authors: Juan Jesús Ortiz De Haro, Vicenç Font MollAbstract:The main goal of this study is to determine the common content knowledge of a group of pre-service primary teachers regarding the arithmetic mean. The cognitive configuration tool proposed by the Onto-semiotic Approach of Cognition and Mathematics Instruction shows that the arithmetic mean can have a variety of meanings, and the application of this tool here revealed significant difficulties related to the students’ understanding of this Mathematical Object and some of its properties. This article concludes with some educational implications for teacher training in the field of statistics.
