Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

Abstract

Let me give you a math story This sentence often strikes fear in many middle grades students as well as some teachers. As international comparisons, national commissions, and state assessment results confirm, students have difficulty solving mathematical applications problems (Lester, 2007; U. S. Department of Education Institute of Educational Science, 2007; TIMMS, 2003; McREL, 2002; National Research Council, 2002; Illinois State Board of Education, 1997). Improving students'problem-solving abilities is a major, if not the major, goal of middle grades mathematics (National Council of Teachers of Mathematics, 2000; 1995; 1989). To address this goal, the author, who is a university mathematics educator, and nine inner-city middle school teachers developed a math/science action research project. This article describes our unique approach to mathematical problem solving derived from research on reading and writing pedagogy, specifically, research indicating that students who use graphic organizers to organize their ideas improve their comprehension and communication skills (Goeden, 2002 ; National Reading Panel, 2000). Many teachers and students use graphic organizers to enhance the writing process in all subject areas, including mathematics. Graphic organizers help students organize and then clarify their thoughts, infer solutions to problems, and communicate their thinking strategies. We designed a classroom action research project to study a problem-solving instructional approach in which students used graphic organizers. Our goal was to improve student achievement in three areas of our state's math assessment in open-response problems: mathematics knowledge, strategic knowledge, and mathematical explanation. In this article, we discuss graphic organizers and their potential benefits for both students and teachers, we describe the specific graphic organizer adaptations we created for mathematical problem solving, and we discuss some of our research results of using the four corners and a diamond graphic organizer. Benefits of using graphic organizers in mathematics learning A graphic organizer is an instructional tool students can use to organize and structure information and concepts and to promote thinking about relationships between concepts. Furthermore, the spatial arrangement of a graphic organizer allows the student, and the teacher, to identify missing information or absent connections in one's strategic thinking (Ellis, 2004). Middle grades teachers already use many different types of graphic organizers in the writing process. All share the common trait of depicting the process of thinking into a pictorial or graphic format. This helps students reduce and organize information, concepts, and relationships. When a student completes a graphic organizer, he or she does not have to process as much specific, semantic information to understand the information or problem (Ellis, 2004). Graphic organizers allow, and often require, the student to sort information and classify it as essential or non-essential; structure information and concepts; identify relationships between concepts; and organize communication about an issue or problem. Consider the following middle grades math problem from a recent state assessment. How many (corners) are there in 1, 2, 3, 4, 5, 6 ... n squares when they are arranged in the following way? What did you first think when reading the problem? Did you first think of the meaning of the term vertices or that this is a mathematical pattern problem? Did you first think of counting the corners or that this looks like an arrangement of tables? Did you first think to discuss in your solution why you are not just adding four with every square? Did you first try to think of the singular form of the word vertices? Initial thinking is not a linear activity, especially in mathematical problem solving. Yet, the result of problem solving-the written solution-often looks like a linear, step-by-step procedure. …