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Society for Research on Educational Effectiveness

The focus of this research is to develop an initial framework for assessing and interpreting students' level of understanding of mathematical equivalence. Although this topic has been studied for many years, there has been no systematic development or evaluation of a valid measure of equivalence knowledge. A powerful method for accomplishing this task has been developed by Wilson (2005). Building upon item response theory, Wilson and his colleagues utilize an assessment instrument called a construct map. A key feature of this tool is that it can assist educational researchers in making criterion-referenced interpretations of instructional materials and student performances. Thus, a construct map of mathematical equivalence can provide a coherent framework for interpreting findings from across elementary and middle school mathematics curricula. A written assessment was administered to ten second- through sixth grade classrooms (two per grade) in an urban, parochial school serving a working- to middle-class population. Participants were 181 second- through sixth grade students. This set was comprised of 39 second-grade students (17 girls and 21 boys), 43 third-grade students (26 girls and 17 boys), 39 fourth-grade students (16 girls and 22 boys), 34 fifth-grade students (17 girls and 17 boys), and 28 sixth-grade students (14 girls and 14 boys). The students were predominantly Caucasian. Utilizing the construct map and Wright map instruments developed by Wilson (2005), the authors developed a framework for understanding mathematical equivalence across elementary and middle school curricula. This framework can provide educational professionals with a tool for more accurately diagnosing students' current skill level and providing guidance for how to foster students' movement along the pathway toward greater mastery of this topic. Furthermore, the framework can provide educational professions with a means of identifying gaps or obstacles in curriculum design and suggest ways for remedying such problems. (Contains 2 tables and 2 figures.)

Descriptors: Curriculum Design, Parochial Schools, Instructional Materials, Elementary School Students, Student Evaluation, Urban Schools, Educational Research, Item Response Theory, Mathematical Concepts, Elementary School Mathematics, Maps, Middle School Students, Mathematics Curriculum, Algebra, Equations (Mathematics)

Society for Research on Educational Effectiveness. 2040 Sheridan Road, Evanston, IL 60208. Tel: 202-495-0920; Fax: 202-640-4401; e-mail: inquiries[at]; Web site:

Author: Taylor, Roger S.; Rittle-Johnson, Bethany; Matthews, Percival G.; McEldoon, Katherine L.



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