Educational design in general is a largely underestimated and unexplored area of design, and its relationship with educational research can be characterized as somewhat less than satisfying. The design of assessments is often seen as an afterthought. And it shows.

Of course, there is a wealth of publications on assessment, but quite often these focus on psychometric concerns or preparation for high-stakes tests (a very profitable industry). What is lacking is a tight linkage between research findings and the creation of mathematically rich and revealing tasks for productive classroom use. The report “Inside the black box” [Black and Wiliam 1998], which looks in depth at current research, shows clearly that we should not only invest more in classroom assessment in mathematics, but also that the rewards will be high if we do so.

Linking Items with Framework

To provoke some discussion, and to invite the reader to reflect on the items and make a judgment, I start the examples with an item from the Third International Mathematics and Science Study (TIMSS). According to the TIMSS web site http://www.timss.org, TIMSS was “the largest and most ambitious international study of student achievement ever conducted. In 1994–95, it was conducted at five grade levels in more than 40 countries (the third, fourth, seventh, and eighth grades, and the final year of secondary school).” Mathematics coverage on TIMSS was, in essence, international consensus coverage of the traditional curriculum.