BACK TO THE FUTURE Reclaiming Effective Mathematics Assessment Strategies

In this article, I describe some efforts initiated about 2 decades ago to reform mathematics assessment. Many, if not most, of those ideas have gradually eroded not only from school practice but also from the knowledge base of current day thinking and research in mathematics assessment. In addition to exploring and explaining the policy, political, and economic factors that led to the demise of these ideas, I want to recall and encourage current day mathematics educators to reconsider them and explore ways that they might be adapted and implemented once again. It is necessary first to provide a brief account of these developments and the forces that I believe led to the status of mathematics assessment today.More than 20 years ago, I edited a book titled Assessing Higher Order Thinking in Mathematics (Kulm, 1990) which was one of the first attempts by some leading mathematics educators and assessment experts to develop ideas for reforming the traditional paper-andpencil, multiple-choice approaches to assessing student achievement. In the book, I stated that "More comprehensive and thoughtful approaches should begin to replace the simplistic report cards, group comparisons, and minimal competency emphasis of earlier accountability and indicator efforts" (p. 77). The authors of chapters in the book addressed the issues of the day, including comprehensive assessment of higher order thinking (Baker), alignment of assessment and curriculum (Pandey), new assessment frameworks (Romberg, Zarinnia, & Collis), assessment of problem solving (Lester & Kroll), uses of technology in assessment (Lesh; Strong; Lipson, Faletti, & Martinez). Authors also reported research on assessing multiple dimensions of student learning (Nichols, Cobb, Yackel, Wood, & Wheatley), student knowledge schemas (Marshall), quantitative reasoning (McKnight), and structured problem solving items (Wilson).The book was inspired in part by a pilot study by the National Assessment of Educational Progress (NAEP), which explored and provided examples of innovative assessment items that emphasized student "hands-on" performance (NAEP, 1987). I was a member of the team of mathematics and science educators working with NAEP to develop about a dozen tasks, including group-administered openended problems, "station activities" that required students to use equipment, and "experiments" administered to individual students to investigate and discuss findings with the administrator. The tasks assessed skills and knowledge in classifying, observing and making inferences, formulating hypotheses, and interpreting data. NAEP field-tested the tasks with national sample of about 1,000 third, seventh, and eleventh grade students. The results indicated that conducting hands-on assessment is "feasible and extremely worthwhile" (p. 7). Participating teachers and administrators were enthusiastic about the promise of new information about student learning that might be obtainable through these new types of assessment tasks.As the momentum grew for these new assessment ideas, teachers, schools, and some states began to pilot test them. Various terms to describe the new assessments began to appear: authentic, performance, alternative. Grants from states and the federal government became available to develop new assessments (e. g. Kulm, 1994c), train teachers in their use (e. g. Kulm, Telese, & McMullen, 1993), and do research on their effectiveness (e.g., Kulm, 1994a, 1994b). At the same time, several states experimented with, and some implemented the new assessments as part of their state mathematics achievement and accountability measures. There was a national sense, in parallel with the reforms and mathematics standards movements (National Council of Teachers of Mathematics, 1989), that these new ment could reflect and reinforce the goals that students should leam not only the skills and procedures of mathematics, but also the concepts, processes, and problem solving applications that are essential in the modem world (Mathematics and Science Education Board, 1993; Webb, 1993). …