Publications & Resources

Portfolio-Driven Reform: Vermont Teachers’ Understanding of Mathematical Problem Solving and Related Changes in Classroom Practice

Apr 1995

Brian M. Stecher and Karen J. Mitchell

The Vermont portfolio assessment program, conclude the authors of the report, has had substantial positive effects on fourth-grade teachers’ perceptions and practices in mathematics. “Through the Vermont state training materials and network meetings,” say CRESST/RAND researchers Brian Stecher and Karen Mitchell, “teachers have incorporated problem solving into their curriculum and have gained a greater insight into teaching problem-solving skills.” However, the researchers add that teachers do not yet share a common understanding of mathematical problem solving and have not reached agreement on the most essential skills to be taught. The emphasis on the scoring rubrics, for example, has helped teachers focus on some of the important and observable aspects of students’ problem solving, but may have caused teachers to neglect other important problem-solving skills not addressed in the scoring rubrics. Additionally, significant variability exists in teaching methods–some teachers “preteach” portfolio tasks by assigning similar, simpler problems prior to student work on portfolio pieces so that assessment problems are not overly novel or difficult for students. Differential help may threaten the validity of portfolio scores for comparison of students, classrooms or schools. The Vermont Department of Education, conclude the authors, should orient existing professional teacher development programs towards increasing teachers’ basic understanding of mathematical problem solving and related instructional practices. Effects of Introducing Classroom Performance Assessments on Student Learning is one of the first empirical examinations of the link between student achievement and performance assessment. Achievement results were compared for both treatment and control schools, where the schools were matched on demographics and socioeconomic factors. Assessments from the Maryland State Department were selected as independent measures of student performance in both sets of classrooms because they are still relatively standardized test-like compared to many performance assessments, but markedly different from traditional standardized tests. “Our concluding advice,” write the researchers, “is that reformers take seriously the current rhetoric about ‘delivery standards’ and the need for sustained professional development to implement a thinking curriculum. The changes that did occur… confirm our beliefs that many more students can develop conceptual understandings presently exhibited by only the most able students–if only they are exposed to relevant problems and given the opportunity-to-learn.”

Stecher, B. M., & Mitchell, K. J. (1995). Portfolio-driven reform: Vermont teachers’ understanding of mathematical problem solving and related changes in classroom practice (CSE Report 400). Los Angeles: University of California, Los Angeles, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).