2017, Girnat, Boris, Kaur, Berinderjeet, Ho, Weng Kin, Toh, Tin Lam, Choy, Ban Heng

Cognitive diagnosis models (CDMs) are a relatively new technique to analyse pupils’ competencies. Two CDMs are presented to describe pupils’ algebraic skills: a stage model to locate a pupil’s skill profile on the steps from proto-algebraic thinking to formal algebra and a model to distinguish the use of different aspects of variables. The results are from a representative study with 636 participants in grade 8 and 9, indicating that both CDMs are empirically applicable and leading to some substantial results: Practically no gender differences are detectible; only 63.7% of the pupils reach the formal level of algebra; the learning effects are mainly located in syntactical skills; learning effects related to other aspects of variables (like inserting values or references to objects and real-world situations) remain in the background.