Comparison of student errors made during linear equation solving on paper and in interactive learning environment

T-algebra is an interactive learning environment for step-by-step solving of algebra problems in four areas of mathematics, including linear equations. To make the diagnosis of mistakes more complete and the program more intelligent we designed our own rule dialogue. Each solution step in T-algebra consists of three stages: selection of the transformation rule, marking the parts of expression, entering the result of the operation. The three-stage dialogue of T-algebra gives several advantages for precise diagnosis of student mistakes. We can diagnose separately incorrect choice of operation, wrong selection of operands for the chosen operation and erroneous application of the selected operation. While designing the program, we have taken into account the results of a study on student mistakes made with pencil and paper. The study was carried out in the winter of 2005 in Tartu. We have attempted to leave an opportunity for the student to make the same mistakes in T-algebra, but also to provide the program with information about the intentions of the student for exact error diagnosis. This gives T-algebra the ability to collect data for adequate research on student mistakes in expression manipulation. In the spring of 2006, we conducted a study on errors made by the students who solved linear equations in the T-algebra environment. This article thoroughly describes the errors made in the solution of linear equations on paper and the corresponding errors made in the T-algebra environment. It compares them and presents interesting findings arising from this comparison.