Erroneous examples in the ActiveMath TEL system are solutions including one or more errors that the student is asked to detect and to correct. Our hypothesis is that erroneous examples will give students the opportunity to find and reflect upon errors in a way that will lead to deeper, more robust learning, while at the same time not causing students to feel ashamed or demotivated, as is more likely when their own errors are exposed.
Our goal in ALoE is to help students learn mathematics by presenting erroneous examples together with exercises in a way that is adapted to the student and his/her context. We strive to improve students' cognitive competencies in math learning, as well as their meta-cognitive competencies in error discovery and self-monitoring. If students require help in detecting and correcting errors, ActiveMath will provide it.
Through empirical studies ALoE will not only try to understand when and how learners benefit from the study of erroneous examples and test the benefits of erroneous examples. It will also use that knowledge to extend ActiveMath to present erroneous examples adapted to the learner's needs, i.e. it will also employ -- for the first time -- the potential of technology-enhanced learning to make the examples beneficial for more students through tailored problem selection, frequency, help, and interaction type.