Automatic system for the detection and analysis of errors to support the personalized feedback

The study of errors in learning and the search for patterns to explain their causes have always been of great interest to researchers and educators alike. Mistakes are a constant in students’ solutions to mathematical problems and are inseparable from the learning process. It is essential, then, to diagnose and address the mistakes made by students so as to allow them to reflect on their errors and adjust their knowledge. To this end, we have created a system that tracks all the actions carried out by a student when solving a mathematical algorithm, not just the final results, and which is capable of diagnosing the faults and possible causes. It can also recommend the actions to be taken based on the individual difficulties encountered. In short, we have created a personalized teaching system whose features could be particularly useful for special-needs students, such as those with Down syndrome. This paper explains the error detection modules in the addition, subtraction and error-adapted assistance algorithms. This work is part of a multidisciplinary research effort financed by R&D project called ‘‘Divermates”, of the Ministry of Labor and Social Affairs, and involving personnel from the Computer Engineering and Mathematics and Fine Arts Education Departments of the University of La Laguna, as well as professionals from the Tenerife Trisomic 21 Association (ATT21). 2009 Elsevier Ltd. All rights reserved. 1. Problem description While arithmetic operations are present in a wide variety of everyday situations, most students, regardless of their personal characteristics, have problems properly understanding and applying them. Specifically, students with Down syndrome experience special difficulties when confronting abstract concepts. The comprehension and handling of algorithms requires a series of factors (intellectual level, graphomotor skills, attention, memory, and so on) in which a knowledge of the number concept and of the decimal numbering system plays a key role. In a 1987 study by Buckley and Sacks (1987) on an adolescent population of 90 subjects with Down syndrome, it was noted that only 18% were able to recite over 20 numbers and 50% were able to perform a simple addition. Only a few, however, were able to multiply or divide. Our research focuses on the simplest arithmetic operations: addition and subtraction. Taking these two elements as our main focus, and using previous research on students without disabilities and errors as source of learning in Mathematics (Baroody, 1988; Bruno et al., 2003; Dikson, Brown, & Gibson, 1991; Fernández, ll rights reserved. +34 922 318288. Llopis, & Pablo, 1991; Horacek & Wolska, 2006; Jiménez & Girando, 1993; Luseño, 1993; Mathan & Koedinger, 2003; Maza, 1989; Melis, 2004; Melis & Siekmann, 2004; Renkl, 2002; Zinn, 2006) as starting point of our proposal. Taking into account these previous works, we propose the following initial classification of possible mistakes students can make as shown in Table 1. Starting with this initial classification, we have designed an automatic system for detecting the mistakes made when working with the algorithms in question. Our stated goal is to identify the potential causes which result in the mistakes detected, as well as to supply assistance depending on the specific needs. To achieve this aim, we have designed a system that is capable of detecting arithmetic mistakes in addition and subtraction algorithms, of classifying them, of inferring the possible causes and of offering hints or helping depending on the mistake. The system is described in the sections that follow. 2. Error detection: analysis, treatment and presentation of results Once a detailed list of all the possible mistakes that can be made, and which the system must therefore be able to detect, is compiled, the next step is the development of an application that is capable of analyzing the information gathered as a result of