Understanding Mathematics + Domains towards Corridors
It is for others to judge - whether it is helpful or distracting; but I find concepts defined by other disciplines, or professions illuminating and insightful. Especially so, when it comes to 'domain'. In Hodges' model - all four of them. Five! When (not if), we include the spiritual:
'Greeno (1991) argued that students develop understanding when"a domain is thought of as an environment, with resources at various places in the domain. In this metaphor, knowing is knowing your way around ir the environment and knowing how to use its resources. This includes knowing what resources are available in the environment as well as being able to find and use those resources for understanding and reasoning. Knowing includes interactions with the environment in its own terms - exploring the territory appreciating its scenery and understanding how its various components interact. Knowing the domain also includes knowing what resources are in the environment that can be used to support your individual and social activities and the ability to recognize, find, and use those resources productively. Learning the domain, in this view, is analogous learning to to live in an environment: learning your way around, learning what resources are available, and learning how to use those resources in conducting your activities productively and enjoyably. (p. 175)"In particular, in chapter 8, Nemirovsky et al. use the metaphor of becoming familiar with a new place (e.g., a town, a train station) and the process of learning a new mathematical concept.' p.7.
Understanding Mathematics and Science Matters. Edited by Thomas A. Romberg Thomas P. Carpenter Fae Dremock University of Wisconsin-Madison. EA LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS 2005 Mahwah, New Jersey London. (I hope there is a 2nd edition?)
(I will try to add the Nemirovsky et al. reference when I can.)
orcid.org/0000-0002-0192-8965
