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2015e.00721 Nagle, Courtney R. Moore-Russo, Deborah Connecting slope, steepness, and angles. Math. Teach. (Reston) 107, No. 4, 272-279 (2013). 2013 National Council of Teachers of Mathematics (NCTM), Reston, VA EN I20 G60 mathematical concepts concept formation activities representations trigonometry geometric concepts linear functions slope steepness angles tangent function
• http://www.nctm.org/publications/article.aspx?id=39783
• Summary: 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 Representation Standard [{\it National Council of Teachers of Mathematics}, Principles and standards for school mathematics. Reston, VA: NCTM (2000)] 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. (ERIC)