Читать книгу Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong - Страница 14

What would such instruction—instruction aimed at developing operation sense and learning how to mathematize word problems—look like? It would have a number of features. First, it would require that we give students time to focus and explore by doing fewer problems, making the ones they do count. Next, it would facilitate students becoming familiar with various ways to represent actions and relationships presented in a problem context. We tend to think of solving word problems as beginning with words and moving toward the use of variables and equations in a neat linear progression. But as most of us know, this isn’t how problem solving works. It is an iterative and circular process, where students might try out different representations, including going back and rewording the problem, a process we call telling “the story” of the problem. The model that we offer in this book is based on this kind of active and expanded exploration using a full range of mathematical representations. Scholars who study mathematical modeling and problem solving identify five modes of representation: verbal, contextual, concrete, pictorial, and symbolic representations (Lesh, Post, & Behr, 1987).

Problem context: The specific setting for a word problem.

Mathematical representation: A depiction of a mathematical situation using one or more of these modes or tools: concrete objects, pictures, mathematical symbols, context, or language.