ABSTRACT
Anyone who has reviewed the recent outpouring of national and international assessments of mathematics achievement (e.g., Dossey, Mullis, Lindquist, & Chambers, 1988; LaPointe, Mead, & Phillips, 1989; Robitaille & Garden, 1989; Stevenson & Stigler, 1992; Stigler, Lee, & Stevenson, 1990) is confronted with an inescapable fact concerning the mathematics achievement of students in the United States: Although many students eventually learn to perform well on tests of low-level skills such as arithmetic computation, they tend to perform poorly on tests of high-level skills such as mathematical problem solving. For example, the 1986 National Assessment of Educational Progress found that nearly all tested 17-year-olds could solve basic arithmetic problems such as the one shown in the top of Fig. 2.1, but nearly all failed to solve multistep word problems such as the one shown in the bottom of the figure (Dossey et al., 1988). On average, many students may know how to carry out basic mathematical procedures when problems are presented in symbolic form but may not be able to apply these procedures to solve problems presented in words. In short, these assessments suggest that the difficulty for students lies in understanding problems rather than executing procedures. Two types of mathematics problems. From Dossey et al. (1988). https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203053270/7dc7a3d2-5ed9-4ccd-9521-1c6d516f2a03/content/fig2_1_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> © 1988 by Educational Testing Service. Reprinted with permission.
