The concept of function is a central idea in mathematics. Functions have many facets, which often cause problems to students. On the one hand the nature of functional dependencies has various aspects: the mapping aspect, the aspect of change, and the object aspect. On the other hand there are various representations for functions. Each representation emphasizes different aspects of the functional dependency. To establish subconcepts like injectivity within the function concept some representations are more suitable than others. One needs to integrate these subconcepts in the concept of function by transferring them to other representations.
We present an interactive learning environment for the conceptualization of the notions of “function”, “injectivity”, “surjectivity”, and “bijection”, using a three-stage approach basing on different representations and linking them dynamically.
The learning environment “Squiggle-M” allows the integration of the mentioned subconcepts in the concept of function. “Squiggle-M” is a mathematical exploration tool offering a bundle of experimentation laboratories. Different representation forms of functions are implemented using an interactive geometry software. The environment also presents a collection of open study questions that can be answered within the laboratories by making use of different representation forms. The individual learning process of the student is reflected by the software’s feedback module based on an intelligent (semi-)automated assessment system.