**ERIC Number:**EJ858574

**Record Type:**Journal

**Publication Date:**2009-Oct

**Pages:**6

**Abstractor:**ERIC

**Reference Count:**1

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

On Fences, Forms and Mathematical Modeling

Lege, Jerry

Mathematics Teacher, v103 n3 p184-189 Oct 2009

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000) includes the following goals: (1) recognize and apply mathematics in contexts (p. 64); and (2) use mathematical models to ... identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the situation (p. 296). For students to be able to demonstrate these skills, they must recognize the need to use mathematics in a particular, concrete context and then select the function that they believe best represents the situation mathematically. They need to have the requisite thinking processes modeled and be given opportunities to wrestle with the new mathematical demands. Ideally, the context should be real and familiar to students. It should not trivialize the use of mathematics, which students should see clearly has been, or must be, used to understand the situation. This article presents an example of such a lesson, using fences as the context. The presentation illustrates the habits of mind that need to be employed in mathematical modeling, and the lesson can serve as a template for a classroom conversation with the students. The resulting equations are also fair game for the students to reproduce (or refine). (Contains 2 tables and 7 figures.)

Descriptors: Mathematical Models, Cognitive Processes, Mathematics Instruction, Mathematics Education, Equations (Mathematics), Regression (Statistics), Mathematics, Algebra, Mathematical Formulas

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