Читать книгу Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong - Страница 22

FIGURE 1.2 ADDITION AND SUBTRACTION PROBLEM SITUATIONS

Situation charts are available for download at http://resources.corwin.com/problemsolving6-8

FIGURE 1.3 MULTIPLICATION AND DIVISION PROBLEM SITUATIONS

Note: These representations for the problem situations reflect our understanding based on a number of resources. These include the tables in the Common Core State Standards for mathematics (Common Core Standards Initiative, 2010); the problem situations as described in the Cognitively Guided Instruction research (Carpenter, Hiebert, & Moser, 1981), in Heller and Greeno (1979), and in Riley, Greeno, and Heller (1984); and other tools. See the Appendix and the companion website for a more detailed summary of the documents that informed our development of these tables.

These problem structures are seldom if ever identified in middle-grades standards. They are typically addressed in the early elementary grades as students master basic whole number operations, and taken as known from there. Many of the challenges middle-grades students have with word problems may be rooted in a lack of familiarity with the problem structures, so it is helpful for middle school math teachers to understand them and recognize them within a word problem. We open each chapter in this book with a look at the new problem situation structure with positive rational numbers (whole numbers, fractions, and decimals); the second part of each chapter examines the same structure when the full range of values (positive and negative) are included.

In the chapters—each of which corresponds to a particular problem situation and a row on one of the tables—we walk you through a problem-solving process that enhances your understanding of the operation and its relationship to the problem situation while modeling the kinds of questions and explorations that can be adapted to your instruction and used with your students. Our goal is not to have students memorize each of these problem types or learn specific procedures for each one. Rather, our goal is to help you enhance your understanding of the structures and make sure your students are exposed to and become familiar with them. This will support their efforts to solve word problems with understanding—through mathematizing.

In each chapter, you will have opportunities to stop and engage in your own problem solving in the workspace provided. We end each chapter with a summary of the key ideas for that problem situation and some additional practice that can also be translated to your instruction.