Axioms

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tandfonline.com – Point-free foundation of geometry looking at laboratory activities

Posted on by Troels Gannerup Christensen - Læst 17 gange

tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”: Abstract Formulae display:?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to zoom. Abstract Researches in “point-free geometry”, aiming to found geometry without using points as primitive entities, have always paid attention only to the logical aspects. In this paper, we propose a point-free axiomatization of geometry taking into account not only the logical value of this approach but also, for the first time, its educational potentialities. We introduce primitive entities and axioms, as a sort of theoretical guise that is grafted onto intuition, looking at the educational value of the deriving… Continue Reading →

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Eric.ed.gov – Axioms of Excellence: Kumon and the Russian School of Mathematics. White Paper No. 188

Posted on by Troels Gannerup Christensen - Læst 26 gange

eric.ed.gov har udgivet: This paper looks at the popularity of after-school mathematics by focusing on the Kumon and Russian School of Mathematics models. In 1954, Toru Kumon, a high school math teacher in Japan, designed a series of math worksheets to help improve the test scores of his son Takeshi, a second grader. Toru’s goal was to teach Takeshi how to learn independently through the worksheets and improve his calculation skills prior to reaching high school. By working every day on the problems, Takeshi was able to reach the level of differential and integral calculus when he was just a few months into the sixth grade. The Kumon model is based on four elements: (1) Individualized instruction; (2) Self-learning; (3) Small-step worksheets; and (4) Kumon instructors. Parents who want to… Continue Reading →