Analysis of the psicometric properties of a multiplication and division processes assessment scale

The domain of multiplication and division operations depends on both algorithm managementand the ability to identify the semantic structure of the problem and to translate it into mathematical language. Many students present difficulties in identifying the semantic structure of the problem but not applying the algorithm when the problem is presented numericaly. The aim of the study is to validate an assessment tool of the processes involved in multiplication and division problems solving in order to identify the causes of mistakes. The administration to 368 ten-to-twelve yearsold children highlighted a three-factor structure of the test: a factor composed of tasks that require just the domain of the algorithm, a second one that demand the identification of the operation, and a third one requiring both processes. The reliability of the instrument has been satisfactory and a qualitative analysis of the responses to the error detection and correction is proposed