**ERIC Number:**EJ1044547

**Record Type:**Journal

**Publication Date:**2014-Apr

**Pages:**5

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Graphing Inequalities, Connecting Meaning

Switzer, J. Matt

Mathematics Teacher, v107 n8 p580-584 Apr 2014

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an inequality, students may lack a deep understanding of the relationship between the inequality and its graph. Hiebert and Carpenter (1992) stated that mathematics is understood "if its mental representation is part of a network of representations" and that the "degree of understanding is determined by the number and strength of the connections" (p. 67). Therefore, Switzer developed an activity that allows students to explore the graphs of inequalities not presented as lines in slope-intercept form, thereby making connections between pairs of expressions, ordered pairs, and the points on a graph representing equations and inequalities. The design of the activity also aligns with and supports the Common Core Standards for Mathematical Practice. These standards describe mathematically proficient students as being able to identify important quantities in a practical situation and map mathematical relationships using such tools as diagrams, two-way tables, graphs, flow charts, and formulas. In this article, Switzer describes the fragile understanding and lack of connections his students had when graphing functions and inequalities. He then provides an overview of how he drew on the trichotomy axiom and evaluation of given expressions to connect students' understanding of functions, inequalities, and their corresponding graphs. Next, he discusses how students incorporated mathematical practices to make sense of the graphing process and the relationships between models.

Descriptors: Mathematics Instruction, Graphs, Learning Activities, Concept Formation, Mathematical Concepts, Symbols (Mathematics), Equations (Mathematics), Teaching Methods

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A