Course Guide - USAID Teacher Education Project

) Similarly, because algebraic graphing is often introduced in a unit on linearfunctions, youngsters may assume that algebraic graphing is just a matter of drawing astraight line between two points, and that all algebraic graphs are "line graphs."c) By using multiple forms of representation, youngsters who formerly had thisvision of algebraic graphs can begin to see important connections between diagrams,tables, graphs, equations, and written and oral narratives.Although all of these representations can model the mathematics in real worldsituations, the most important reason for using multiple representations is to illustratea mathematical connection. When students realize this, they begin to understand thepower of algebra more deeply.d) When entering data into a table of values (T-chart), youngsters often createcolumn headings that use the first initial of the variable. Thus, when exploring therelationship between the side length of a square and its area, they may label the firstcolumn "s" and the second column "A." At some point youngsters need to generalizethe idea of the variable and understand why those columns are conventionally labeled"x" and "y."This becomes especially important when students have access to graphing calculators(either hand-held or on the Internet at: http://tinyurl.com/Graph-Calc-Free)because calculators only accept x and y as variables (unless a hand-held one has beenprogrammed with a specific formula).3. What is essential to know or do in class?a) Introduce the idea that a graph can be interpreted to tell a story of change overtime.b) Have students use the real world context of increasing and decreasing ingredientsin a recipe to illustrate the difference between a discrete and continuous graph.c) Have students develop a symbolic expression that could show the relationshipbetween x and y.d) Have students discuss the connections among all the various representations usedin solving the problem.