Assessing Student Growth in
Mathematical Problem Solving
FRANK K. LESTER, JR., and DIANA LAMBDIN KROLL
Problem solving should be the central focus of the mathematics curriculum. (p. 23)
If problem solving is to be the focus of school mathematics, it must also be the focus of assessment... [and] assessments should determine students' ability to perform all aspects of problem solving (p. 209).
Assessment must be more than testing it must be a continuous, dynamic, and often informal process (p. 203). -- NCTM Curriculum and Evaluation Standards for School Mathematics, 1989
Although much had been written prior to the beginning of this decade about the importance of problem solving in mathematics, it seems safe to say that during the past 10 years or so problem solving has been the most written and talked about part of the mathematics curriculum. Indeed, many writers mark the beginning of the "problem-solving era" with the publication in 1980 of the Agenda for Action of the National Council of Teachers of Mathematics. In that document, a call was made to make problem solving "the focus of school mathematics" ( NCTM, 1980, p. 1).
Since that time, a great deal of research and curriculum development has taken place concerning the upgrading of students' mathematical problem-solving abilities. Today most teachers are aware of the importance of problem solving and of the need to improve their efforts to help students become better problem solvers. As a result, rather dramatic changes have begun to take place in the K-12 mathematics curriculum. New types of problem-solving experiences are appearing in textbooks, as are new instructional techniques.
However, as promising as many of these innovations may be, there has been far too little attention paid to the related task of identifying or developing appropriate assessment techniques and instruments. Despite the appearance of reforms reflecting an emphasis on problem solving and mathematical thinking in several statewide testing programs, the extent of the changes has been far short of what is required. Moreover, teachers have been provided with almost no guidance about how to change their classroom evaluation procedures to fit these new emphases.
This chapter has a two-fold purpose: first, to present a model for the assessment of mathematical problem solving, and second, to illustrate and discuss several problem-solving assessment techniques developed over the past few years for use in mathematics classrooms.