Students define a linear function by choosing abscissa steps, initial ordinates, value, and change factors. The defined function is represented as a table of values and as points on a coordinate system. Students can enter an algebraic expression of the linear function and to see its graph on the same system of coordinates. Students can connect the slope of the linear function to the rate of change of the function and observe that a linear function has a constant rate of change.

The Rationale Behind the Feature (Specific Design Principle):

To enable students to understand constant rate of change in science disciplines and in mathematics, Yerushalmy (2005) has studied a new representation. Because students who learn the term “slope” have difficulties in making connections between a slope of the linear function and constant rate of change, they used this feature to create the “stair” model tool.

Context of Use:

Using this tool student can investigate the connection between three representations of the function ( expression, graph and table value) and to learn in visual way how the main property of the linear function (constant rate of change) is expressed in each of them.

References:

Models of functions and Models of situations: On the Design of Modeling-Based Learning Environments .by M. Yerushalmy & B Shternberg