The proposed study uses contemporary insights about assessment, language, mathematics education, psychometric theory, and educational research to "bridge the gap" between worthwhile mathematics instruction and high-stakes testing. The effort builds on the research summarized in several NRC expert panels and the ideas which have been emerging in interdisciplinary efforts to develop a broader understanding the impact of educational testing on teaching and learning. The project will start with a multi-level model of formative assessment that emerged in two prior NSF funded studies. In an unprecedented collaboration, this approach will be refined and validated by a team of experts representing mathematics education, mathematical sciences, linguistics, educational testing, and educational assessment. The project advisory panel consists of international leaders in each area, including individuals who are also spearheading interdisciplinary advance across these areas.
Broader Impact Broad impact is expected because the approach meets the demand of the NCLB act for immediate and continual gains on criterion-referenced tests for all students, without undercutting other educational goals. In addition to directly advancing elementary mathematics instruction, the project offers a scalable, worthwhile alternative to the ubiquitous "test-prep" interventions that often do more harm than good. The project will broaden classroom assessment to directly advance students' discourse, fluency, and understanding, and guide teachers' remediation and curricular refinement. As such the project will forge new insights for using classroom discourse and formative feedback for accomplishing these broad goals which oftentimes are treated as if they are in conflict. The approach features two levels of classroom assessments (semi-formal and formal) and an innovative "conversational" approach to formative feedback. Existing (commercial and public domain) assessments will be used to create 26 open-ended quizzes and 2 multiple-choice exams. The quizzes are aligned to existing curriculum, completed after appropriate regular lessons, and are ungraded. The exams consist of items that are aligned with the subdomains of the pertinent criterion referenced test, are completed at the end of the semester, and are formally graded. .Learner oriented formative feedback rubrics will be developed for both. The rubrics offer detailed, technically accurate explanations of the problems, without directly stating the "correct" answer. Students use their completed assessments and the rubrics to discuss their collective understanding of the assessed topics. Simple video-based coaches guide them toward worthwhile feedback conversations; materials and guidelines will help teachers (1) align assessments to their existing curriculum, (2) use initial performance and mathematical discourse to improve that curriculum, and (3) provide informal and formal remediation. The study will focus on fifth-grade mathematics, and take place in two Georgia elementary schools that serve a high proportion of ethnic and linguistic minorities. Across three year-long implementations, success is ensured by using design-based and linguistic methods to directly enhance students' mathematical discourse and teachers use of formative feedback , while indirectly maximizing students' performance on four outcome measures (an innovative discourse-based assessment, CTB's open-ended Balanced Assessment in Mathematic, Georgia's Criterion-Referenced Content Test, and the Iowa Tests of Basic Skills). The schools will be randomly assigned to implementation or comparison conditions. The first year will consist of piloting and iterative refinements with just one implementation teacher. During the second year, the three or four fifth grade teachers participating at the implementation school will be assigned to different conditions to test the individual and collective impact of the quizzes and exams. Gains on the outcome measures will be compared to similar fifth-grade classrooms at the comparison school. These results will be used to define a final version that will be implemented by all fifth-grade teachers at the implementation school. Students' performance at the implementation school will be compared to the performance of all of the fifth-graders in the comparison school on all four outcome measures.
