@inbook {MATHEDUC.06528307,
author = {Shimizu, Yoshinori},
title = {Defining, extending, and creating: key experiences in mathematics.},
year = {2014},
booktitle = {Learning experiences to promote mathematics learning. Yearbook 2014, Association of Mathematics Educators},
isbn = {978-981-4612-90-6},
pages = {115-130},
publisher = {Hackensack, NJ: World Scientific;},
doi = {10.1142/9789814612920_0006},
abstract = {Summary: Definitions play critical roles in understanding a concept, in reasoning, in problem solving, and in communicating with others in mathematics. Moreover, key experiences in learning mathematics include examining a given definition of a mathematical term at the phase of extending the meaning of a concept and creating a new definition for the concept in an expanded system or theory. However, students seem to have difficulties in using definitions in various contexts of learning mathematics, while they have few experience of extending the meaning of a mathematical concept on their own. In this chapter the author discusses the role and nature of definitions in teaching and learning mathematics and illustrates rich experiences provided in the process of defining, extending, and creating mathematics concepts. Data from a teaching experiment are presented to exemplify how pairs of tenth grade students could examine and create definitions of various mathematical objects, including unfamiliar quadrilaterals such as a kite and ``boomerang''.},
msc2010 = {E40xx (D30xx D70xx)},
identifier = {2016a.00433},
}