The TIMSS assessment materials are organised on the basis of two domains: a content domain and a cognitive domain. The content domain describes the content that is intended to be assessed; while the cognitive domain describes the cognitive abilities students use to answer the items. The content domains are fairly consistently and readily found in the curricula of the participating countries, and are the subject of the major international and national reports for TIMSS. Developing reliable and valid achievement scales for the cognitive domains is not as straightforward, and differences among students across and within countries in their mathematical knowledge and problem solving skills make it difficult to know which cognitive abilities students are using to solve a particular mathematical or scientific problem. This report examines findings about the TIMSS cognitive domains from an Australian perspective.