Multi-Level Assessment for Enhancing Mathematical Discourse, Curriculum, and Achievement in Diverse Elementary School Classrooms

Principal Investigator: 
Co-Investigator: 
Project Overview
Background & Purpose: 

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 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.

Setting: 

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.

Research Design: 

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.

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.

Findings: 

Findings will be posted as they become available.

Publications & Presentations: 

Kilic, H., Cross, D. I., Mewborn, D. S., Ersoz, F. A., Kim, J. (2010). "Teacher facilitation techniques for small group discourse," Teaching Children Mathematics, v.16, p. 350.

Hickey, D. T., & Anderson, K. (2007). "Situative approaches to assessment for resolving problems in educational testing." P. Moss (Ed), Evidence and decision making. The 103rd NSSE Yearbook. National Society for the Study of Education. University of Chicago Press.

Lewison, M., Graves, I., Sanchez, L. (2006). "Enhancing mathematical discourse in elementary classrooms." In S. Barab, K. Hay, & D. Hickey, Proceedings of the 7th International Conference on the Learning Sciences, pp. 954-955. Hilldale, NJ: Erlbaum.

Mewborn, D. S., Ersoz, F. A., Cross, D. I., Kilic, H. May, D. K., & Kim, J. (2007). "Open-ended assessment, formative feedback routines, and classroom discourse: Influences on student learning." In T. Lamberg, Proceedings of the twenty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 235-237. Reno, NV: University of Nevada--Reno.

Mewborn, D. S., Kilic, H., Ersoz, F. A., Cross, D. I., May, D. K., & Kim, J. (2008). "Elementary school students' discourse practices." Paper presented at the Research Presession of the National Council of Teachers of Mathematics, Salt Lake City.

Mewborn, D. S., Ersoz, F. A., Cross, D. I., Kilic, H. May, D. K., & Kim, J. (2008). "Student discourse as motivated by rich mathematical tasks." Paper presented at the annual meeting of the American Educational Research Association, New York City.

Anderson, K. T. (2007). "Re-positioning "ability": Participation frameworks and the discursive mediation of learning." Paper presented at the annual meeting of the American Anthropological Association, Washington, D.C.

Anderson, K. T. (2007). "Discursive meta-tools for the development of practice and identity in an elementary math classroom." Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

Cross, D. I., & Hickey, D. T. (2005). "Enhancing the potential of learning environments. Bridging cognitive and sociocultural principles." Paper presented at the annual meeting of the American Educational Research Association, San Francisco.

Gresalfi, M. & Lewison, M. (2009). "Deconstructing professional development: Understanding teachers and researchers competing cultural models and practices." Paper presented at the Annual Meeting of the American Educational Research Association, San Diego CA.

Gresalfi, M.S., Williams, C. (2009). "Constructing opportunities to learn: An analysis of teacher moves that position students to engage procedurally and conceptually with content." Paper presented at PME-NA, Atlanta, GA.

Hickey, D. T., & Anderson, K. N. (2007). "Situative Approaches to Mathematics Discourse and Formative Assessment: Enhancing Learning and Achievement in Mathematics Instruction." Paper presented at the 2007 annual meeting of the American Educational Research Association, Chicago, IL.

Hickey, D. T., & Cross, D. I. (2005). "Technology-supported, multi-level assessment for enhancing discourse, learning, curriculum, and achievement in elementary mathematics." Paper presented at the annual meeting of the American Educational Research Association. Montreal.

Hickey, D. T., & Cross, D. I. (2006). "Design-based multi-level assessment for enhancing discourse, learning, curriculum, and achievement in elementary mathematics." Paper presented at the annual meeting of the American Educational Research Association. San Francisco.