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  Feature Name: The model of constant rate of change in a linear functions
 
Author: polina& Sofia

Category: Visualization Tools (pre-designed): Models, Visualization Tools (pre-designed): Visual Explanations (2D+3D), Inquiry Tools: Guided inquiry, Support for Problem solving

Subject: Math & Geometry

Kind: Element/Applet

Audience:
 Elementary School
 Middle School
 High School
 Higher Education
 Teachers & Principals
 Other


Projects:

Software URL: Visual Math:functions

Created by:

Reference URL

This Feature is connected to (2) Principles
  • Provide knowledge representation and organization tools
  • Use multiple representations
     
    Feature in Visual Map
     
    Description:
    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

    Image:(Click to enlarge)

    “Stair” model for constant rate of change in Visual Math