Automatic Generation of Analogous Problems for Written Subtraction

Learning in domains such as mathematics or programming, involves the acquisition of procedural knowledge (Young & O’Shea, 1981). For example, when learning written subtraction, students need to understand and apply an algorithm for calculation of differences column by column. Erroneous solutions most often are the result of procedural bugs (Brown & Burton, 1978) such as missing or faulty rules or the application of a rule in the wrong context. If such a procedural bug is diagnosed, a strategy is needed to support the student resolving this bug. Such strategies can be: written explanations, presenting additional problems, or giving bug-related feedback such as an explanation together with a worked-out example (Narciss & Huth, 2006). A worked-out example can be considered as an analogy to the given problem which a student could not solve correctly (Gick & Holyoak, 1983). That is, for the current (target) problem a structurally isomorphic base problem is provided where the correct solution can be demonstrated step by step. While Narciss and Huth (2006) make use of this feedback approach, they rely on predefined analogies stored together with an—also predefined—set of student problems. However, the automatic generation of such analogous problems for written subtraction can improve and facilitate feedback generation.