To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Error Diagnosis and Categorization in Problem Solving Environment Using Action-Object-Input Scheme

Dmitri Lepp
dmitri@ut.ee
Institute of Computer Science
University of Tartu
Estonia

Abstract

This paper describes the student error diagnosis component of the T-algebra problem solving environment. In T-algebra students solve different expression manipulation problems step-by-step using different transformation rules and following the three stage input dialogue. When designing the T-algebra we followed the principle that all the necessary decisions and calculations at each solution step should be made by the student. For making a single solution step the student has to choose a transformation rule from the list of available rules, select the operands (certain parts of expression) for this rule and input the result of application of the rule.

Introduced scheme gives the student possibility to make different kinds of errors. The errors can be made either when selecting the rule or unsuitable objects of the rule or while applying the rule íV inputting the resulting expression. The program diagnoses different errors and attempts to identify the misconception underlying the mistake. The program checks whether suitable rule is selected, whether the form and number of selected objects and also form of entered result is suitable for the selected rule. T-algebra also checks for the correctness of every single part of the result entered into separate boxes. In general the introduced solution step scheme gives the program more information on the studentíŽs intentions than simple entering of the transformed expression. The program can explicitly and without guessing evaluate the decisions about operation and operands. The program can compute the result corresponding to the intentions of the student, and compare it with actual input. This makes the diagnosis of student errors more precise and easier to implement.

The paper also presents the categorization of errors types that are diagnosed. As an example two transformation rules are discussed (combining like terms, multiplication of polynomials) and lists of all diagnosable error types and common student misconceptions are presented. This categorization is what distinguishes T-algebra from other problem solving environments. We have designed 20 different categories and put all diagnosed error types into them. Categories include for example selection of objects of wrong form, selection of objects that are not compatible, errors in form of entered subexpression, calculation errors, errors in calculating the sign of entered subexpression and other categories.

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