Interactive Exercises in ActiveMath

Interactive exercising is one of the major ingredients of technology-enhanced learning. It reaches its full potential only, when appropriate feedback is given to the learner.

In ActiveMath a principled approach for representing and processing interactive exercises is developed. This approach relies on:

• a modular architecture of the exercise player
• a separation of different types of knowledge that have to be handled to generate feedback
• a generic representation of interactive exercises

ActiveMath offers a general system-independent semantic markup language for representing interactive exercises of dirent kinds. The exercise subsystem of ActiveMath is playing such exercises in a browser. The exercise subsystem can connect to CASs and to other external programs in order to diagnose the learner input and to generate feedback. There are no explicit calls to a particular external program in the exercise content.

An exercise can be manually authored, generated completely, or partially generated/authored. In order to generate feedback and next interactions, the diagnosis of the learner's input has to be made. For this, the connection to a reasoning component is established.

Example of parametrized exercise using CAS is shown in the figure. In this exercise, the coefficients of a polynomial to be differentiated are selected at random each time the exercise is strated. For evaluating the answer of the learner, CAS is used.