It is obvious that children from different backgrounds and cultures bring differing prior knowledge and resources to learning. Strong supports for learning exist in every culture, but some kinds of cultural resources may be better recognized or rewarded in the typical school setting. There are cultural variations in communication styles, for example, that may affect how a child interacts with adults in the typical U.S. school environment (Heath, 1981, 1983; Ochs and Schieffelin, 1984; Rogoff, 1990; Ward, 1971). Similarly, cultural attitudes about cooperation, as opposed to independent work, can affect the degree of support students provide for each other’s learning (Treisman, 1990). It is important for educators and others to take these kinds of differences into account in making judgments about student competence and in facilitating the acquisition of knowledge and skill.
The beliefs students hold about learning are another social dimension that can significantly affect learning and performance (e.g., Dweck and Legitt, 1988). For example, many students believe, on the basis of their typical classroom and homework assignments, that any mathematics problem can be solved in 5 minutes or less, and if they cannot find a solution in that time, they will give up. Many young people and adults also believe that talent in mathematics and science is innate, which gives them little incentive to persist if they do not understand something in these subjects immediately. Conversely, people who believe they are capable of making sense of unfamiliar things often succeed because they invest more sustained effort in doing so.
Box 3–5 lists several common beliefs about mathematics derived from classroom studies, international comparisons, and responses on National Assessment of Educational Progress (NAEP) questionnaires. Experiences at home and school shape students’ beliefs, including many of those shown in Box 3–5. For example, if mathematics is presented by the teacher as a set of rules to be applied, students may come to believe that “knowing” mathematics means remembering which rule to apply when a question is asked (usually the rule the teacher last demonstrated), and that comprehending the concepts that undergird the question is too difficult for ordinary students. In contrast, when teachers structure mathematics lessons so that important principles are apparent as students work through the procedures, students are more likely to develop deeper understanding and become independent and thoughtful problem solvers (Lampert, 1986).
Knowledge of children’s learning and the development of expertise clearly indicates that assessment practices should focus on making students’ thinking visible to themselves and others by drawing out their current under-