BOX 3–5 Typical Student Beliefs About the Nature of Mathematics
SOURCE: Greeno, Pearson, and Schoenfeld. (1996b, p. 20).
standing so that instructional strategies can be selected to support an appropriate course for future learning. In particular, assessment practices should focus on identifying the preconceptions children bring to learning settings, as well as the specific strategies they are using for problem solving. Particular consideration needs to be given to where children’s knowledge and strategies fall on a developmental continuum of sophistication, appropriateness, and efficiency for a particular domain of knowledge and skill.
Practice and feedback are critical aspects of the development of skill and expertise. One of the most important roles for assessment is the provision of timely and informative feedback to students during instruction and learning so that their practice of a skill and its subsequent acquisition will be effective and efficient.
As a function of context, knowledge frequently develops in a highly contextualized and inflexible form, and often does not transfer very effectively. Transfer depends on the development of an explicit understanding of when to apply what has been learned. Assessments of academic achievement need to consider carefully the knowledge and skills required to understand and answer a question or solve a problem, including the context in