caa a22 4500 46320591X CHVBK 20180405153126.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s11191-006-9041-y doi (NATIONALLICENCE)springer-10.1007/s11191-006-9041-y Teaching the Conceptual Revolutions in Geometry [Elektronische Daten] [Robert Carson, Stuart Rowlands] Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact symbols to enable efficient calculation and to begin raising a consciousness of this activity we call mathematics. And it takes the sustained development and discussion of mathematical conventions and practices to create entire domains of mathematical thought, such as we find in geometry. The major innovations and conceptual reformulations are few in number, but these represent perhaps the greatest challenges to learners. Historically significant transformative events have their counterpart in the cognitive growth of the individual. This article examines the interplay between these big ideas in cultural history and the deliberate processes of cognitive change that are their counterpart in the educational process. Springer Science+Business Media, Inc., 2006 Abstraction nationallicence cultural-historical nationallicence Greek geometry nationallicence Platonic forms nationallicence Thales nationallicence transformative events nationallicence Carson Robert College of Education, Montana State University, Department of Education, 59717, Bozeman, MT, USA aut Rowlands Stuart Centre For Teaching Mathematics, University of Plymouth, Plymouth, PL4 8AA, UK aut Science & Education Springer Netherlands 16/9-10(2007-10-01), 921-954 0926-7220 16:9-10<921 2007 16 11191 https://doi.org/10.1007/s11191-006-9041-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11191-006-9041-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carson Robert College of Education, Montana State University, Department of Education, 59717, Bozeman, MT, USA aut NATIONALLICENCE 700 1- Rowlands Stuart Centre For Teaching Mathematics, University of Plymouth, Plymouth, PL4 8AA, UK aut NATIONALLICENCE 773 0- Science & Education Springer Netherlands 16/9-10(2007-10-01), 921-954 0926-7220 16:9-10<921 2007 16 11191 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer