The model allows comparison of two views; a function view at the top, and a derivative view at the bottom. Using a set of seven graphical icons, learners can build their own function. As they build and manipulate the function, they view how the derivative changes. This model can be used for student-initiated problems or as part of the activities in the Visual Math curriculum.
The Rationale Behind the Feature (Specific Design Principle):
To enable students develop a qualitative understanding of the relationship between a function and its derivative, even before they are taught the formality of mathematics, Shternberg and Yerushalmy (2002) have developed the function and derivative model as part of the Visual Math project.
Shternberg, B. and Yerushalmy, M. (2003). Models of functions and models of situations: On design of a modeling based learning environment In H. M. Doerr & R. Lesh (eds.) Beyond constructivism: A model and modeling perspective on teaching, learning, and problem solving in mathematics education. pp. 479-500. Mahwah, NJ: Lawrence Erlbaum.