Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

Research recurrently indicates that children who have difficulty with arithmetic often use systematic routines that yield wrong answers. Recent research has focused less on identifying the most common errors among groups of children and more on analyzing individual children's errors. This paper considers the source of systematic errors in…

Diagnosing cognitive errors possessed by examinees can be considered as a pattern classification problem that is designed to classify a sequential input of stimuli into one of several predetermined groups. The sequential inputs in this paper's context are item responses, and the predetermined groups are various states of knowledge resulting from…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

Much valuable information can be gained by analyzing the students' wrong responses. When a student answers a free response item she/he gives the response which she/he considers to be the correct one. Therefore, diagnosing the algorithm that led the student to his/her answer provides an important source of information for assessing his/her…