ABSTRACT
The probability of making informed educational decisions increases with improved understanding of student cognitive processing within a domain. Regardless of the domain, decision making benefits when problem demands and individual characteristics are well specified. Contrast the educational implications drawn from the statement “John did poorly on the difficult problems” with the more informative “John did poorly on all the problems that required him to make inferences from a piece of text.” The second interpretation is more useful because an intermediate analysis of the contribution to difficulty has been done. In this chapter, we present intermediate analyses of mathematical problems as a forum for developing alternative techniques of test analysis. The purpose of the present work is to examine how advances in the understanding of mathematical problem-solving processes, together with new measurement models, can improve the quality of information that can be derived from standardized test items. Despite the many constraints imposed by using existing test items, there is a great deal of information surrounding these items that can be brought to bear on any interpretation of problem-solving performance.
