Adaptive Learning with Erroneous Examples

• Applicant: Professor Dr. Jörg H. Siekmann, since 10/2011
• Subject Area: Theoretical Computer Science
• Term: from 2008 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 81713970

Correct worked examples have traditionally been used to help students learn mathematics and science problem solving and have proven to be quite beneficial, as demonstrated in many learning science studies. However, erroneous examples have rarely been investigated or used as a learning intervention, either within a technology-enhanced learning (TEL) system or within the classroom. Here, erroneous examples 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 project ALoE is to help students learn mathematics by presenting erroneous examples together with correct examples and exercises in adaptive fashion within the TEL system ACTIVEMATH, a web-based learning environment for mathematics that has proven to be highly successful. We hope 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. ALoE will not only test the benefits of erroneous examples but 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, help, and interaction. We will try to understand better when and how learners benefit from the study of erroneous examples through empirical studies and will use that knowledge to extend ACTIVEMATH to present erroneous examples adapted to the learner s needs. In other words, ACTIVEMATH will adapt the frequency and sequence of its presentation of erroneous examples to learners, the amount and kind of help it provides, and the type of the interactions students will be asked to perform. The domain we will focus on is fractions, a subarea of basic mathematics with a long and well-documented history of difficulty for students. ALoE will make a contribution to cognitive and learning science by further examining the value of and specific use of erroneous examples for learning. Work in this nascent area of cognitive research has not shown conclusively, first, that erroneous examples can be used to support human learning and, second, how and when such examples should be presented to students to enhance learning. Moreover, ALoE will make a contribution to artificial intelligence and educational technology by developing novel and dynamic adaptation within ACTIVEMATH, by extending its student modeling to capture meta-cognitive aspects, and by inventing a semantic knowledge representation that contains enough information for the updating of the student model and that enables different ways of presenting the erroneous examples. The project will extend ACTIVEMATH with a student model that includes the variables related to the effect of erroneous examples, with specific help for the detection of errors, with adaptive interaction choice, and with mechanisms for learner-dependent selection of appropriate erroneous examples in concert with examples and exercises.

• DFG Programme: Research Grants
• Ehemalige Antragstellerin: Privatdozentin Dr. Erica Melis, until 10/2011 (†)