This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with integrated use of technology, the PISA 2003 results suggest that this has been successful in educational practice only to a limited extent. The main difficulties encountered include institutional factors such as national examinations and textbooks, and issues concerning design and training. One of the main challenges is the design of good problem solving tasks that are original, nonroutine and new to the students. It is recommended to pay attention to problem solving in primary education and in textbook series, to exploit the benefits of technology for problem solving activities and to use the schools' freedom to organize school-based examinations for types of assessment that are more appropriate for problem solving.

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A common challenge for middle-grades mathematics teachers is to find ways to promote student understanding of mathematics. When an algorithm for adding or subtracting fractions is explained as clearly as possible and students have opportunities to practice it, the reality is that many students will continue to confuse the procedures and forget how they work. The primary intervention used to address student confusion is to reteach common procedures and give additional practice in the hope that the students will understand over time.

The past few years have seen the emergence of five mathematics curricula developed with support by the National Science Foundation for the middle grades: Mathematics in Context (MIC) (National Center for Research in Mathematical Sciences Education and Freudenthal Institute 2001), Math Thematics (Billstein and Williamson 1999), Connected Mathematics (CMP) (Lappan et al. 1998), MathScape, a View of the World from a Mathematical Perspective (Education Development Center 1998), and Pathways to Algebra and Geometry (Institute for Research on Learning 1997). One striking similarity that characterizes these middle school curricula, as well as their reform counterparts at the elementary and secondary school levels, is the pervasive use of context. Using a definition suggested by Borasi (1986), context is “the situation in which [a] problem is embedded” (p. 129). Context is usually supplied by the text of the problem, but it can also be contained in pictures, diagrams, or tables. A quick review of any of the curricula mentioned above shows that context is plentiful and varied. This abundance of context is in marked contrast with traditional textbooks, in which context appears only in brief introductions or end-of-section story problems.

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