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CALUMATH Features

CALUMATH pages enable users to draw or drag graphs, play animations, manipulate sliders, enter answers in text boxes, create tables of function values, and provide Html tools, such as buttons and drop down menus, that allow students to meaningfully interact with the pages. Since CALUMATH contains a computer algebra system, symbolic computations can be performed and analyzed. CALUMATH contains the functionality to analyze student responses and provide useful feedback.

Below are some pages that highlight the capabilities of CALUMATH. We provide a few comments about each page.

  1. Graphs of Story Problems. This links to pages that are not designed to show off the capabilities of CALUMATH, but instead, illustrate the philosophical leaning of many problems that appear in CALUMATH pages. Specifically, this page examines one problem from many points of view.
  2. Translations of Graphs A continuation of the above problem that allows the student to drag graphs.
  3. Average Rate of Change. Students draw the graph of a function with a prescribed average rate of change and the page checks their answer.
  4. Dragging an Exponential Function. Students are only permitted to drag points in the vertical direction to obtain a prescribed exponential graph. No ticks or labels are displayed on the y axis.
  5. Graph Coordinates This page contains 24 problems dealing with coordinates and graphs of functions. Many students will find the first few problems quite easy, but will not be able to continue unless they know exactly what it means for a point to lie on, or not lie on, the graph of a function.
  6. Piecewise Functions And Domain And Range. Students drag a graph so it is the graph of a function with a prescribed domain and range. The page determines the domain and range of the student's graph.
  7. Exponential Functions I. Students use sliders to adjust the values of the parameters a and b in the exponential function f(x) = abx.
  8. Animations and Parametric Functions. Students drag their mouse across a set of axes; the motion is captured and an animation is constructed.
  9. Riemann Sums. An interactive page that allows the student to draw Riemann sums of various types.
  10. Linear Functions Animation I. A page that employs an animation concerning Linear Functions.
  11. Linear Functions Animation IV A contrasting Linear Functions Animation.
  12. Graphing Workspace. This page contains extensive functionality that allows users to view functions graphically, symbolically and in tabular format.