**ERIC Number:**EJ1044172

**Record Type:**Journal

**Publication Date:**2013-Nov

**Pages:**8

**Abstractor:**ERIC

**Reference Count:**9

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Connecting Slope, Steepness, and Angles

Nagle, Courtney R.; Moore-Russo, Deborah

Mathematics Teacher, v107 n4 p272-279 Nov 2013

All teachers, especially high school teachers, face the challenge of ensuring that students have opportunities to relate and connect the various representations and notions of mathematics concepts developed over the course of the pre-K-12 mathematics curriculum. NCTM's (2000) Representation Standard emphasizes the importance of students being able to represent a concept in various forms--for example, verbally, numerically, graphically, and analytically--but students' recognition that each representation depicts the same underlying concept is of equal importance. When given one ordered pair and a constant rate of change between two variables, students should be able to graph a line, identify the parameters of a linear equation, and complete a table. However, being able to use each representation independently is not sufficient; students need to connect the representations and recognize how each indicates a specific relationship between two simultaneously varying quantities. Thus, when teaching slope, the emphasis should be not only on using multiple representations but also on connecting various representations to form a coherent and complete conception of this mathematical idea. A student activity sheet in the appendix provides a series of tasks that can be used to engage students in a sense-making process by using GeoGebra or other similar dynamic geometry software. These activities encourage students to apply their prior knowledge of slope and steepness as they reason about new problem situations. Such activities give students a chance to make connections between the two ideas and, ultimately, to come to a deeper understanding of slope (Pirie and Martin 2000).

Descriptors: Mathematics Instruction, Mathematical Concepts, Academic Standards, Teaching Methods, Concept Formation, Mathematics Curriculum, Learning Activities, Computer Software, Educational Technology, Computer Uses in Education, Algebra, Trigonometry, Geometric Concepts, Secondary School Mathematics

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; Tests/Questionnaires

**Education Level:**Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A