Assessing Authentic Mathematical Performance
Richard Lesh and Susan J. Lamon
This chapter addresses the following four quesions: What are authentic mathematical activities? What kind of instructional objectives are priorities to address? What kind of problems are particularly useful for examining these priorities? What are some rules of thumb for creating such problems? To explain our answers to these questions, it is necessary to focus on the concept of models--in mathematics, in cognitive psychology, and in everyday situations.
Authentic mathematical activities are actual work samples taken from a representative collection of activities that are meaningful and important in their own right. They are not just surrogates for mathematical activities that are important in "real-life" situations.
To verify the mathematical authenticity of a collection of activities (beyond simply evaluating the authenticity of isolated items), both positively and negatively oriented criteria are relevant. That is, the activities as a whole should require students to use a representative sample of the knowledge and abilities that reflect targeted levels of competence in the field, and at the same time, the activities should avoid narrow, biased, obsolete, or instructionally counter-productive conceptions about the nature of mathematics, the nature of realistic problem-solving situations in which mathematics is useful, and the varieties of mathematical capabilities that are