Toward a new science of educational testing and assessment

Toward a New Science of Educational Testing and Assessment provides multiple perspectives on the need for new assessments to meet the challenge of changes in curricular agendas and political demands. The book is a collection of eight essays written by subsets of authors, loosely connected under the general theme of the inadequacy of the old assessment practices and the need to investigate new approaches. The chapter by Thomas A. Romberg, Assessing Mathematics Competence and Achievement, argues for a new understanding of mathematics to meet the needs of the information age. Calculators and computers make tasks such as computation, graphing, manipulation of models, and repetition of processes easy; thus, it is less important to be able to carry out a computational algorithm to reach a correct answer and more important to pursue more profound questions such as, Which of the many available procedures is best? Romberg asserts that such changes in the discipline of mathematics, as well as changes in the view of the learning process from passive to constructive, support the need for a new approach to the understanding of mathematics. He provides a quick summary of current assessment instruments by citing his view of the strengths and weakness of standardized tests, criterion-referenced tests, and profile achievement tests. Though some strengths are presented-such as, predictive validity, ease in scoring, usefulness for informing progress in instruction focused on the acquisition of a specific skill, and the ability to provide a profile for group performance-many weaknesses are cited. The major weakness in Romberg's view is that standardized tests present mathematics as a single domain rather than a collection of domains, with items reflecting independent concepts rather than a network of structured, interdependent constructs; thus, the tests are judged incapable of evaluating reasoning skills. Criterion-referenced tests are said to specify behavioral objectives in a way that fractionates mathematical knowledge and does not include higher level or complex objectives. Profile achievement tests are said to be hard to administer and score and difficult to interpret because of the profile of scores; Romberg avers that such tests are based on an outdated assumption of