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2004 NSF K-12 Math, Science, and Technology Curriculum Developers Conference

THE DEVELOPMENT OF A COGNITION-BASED ASSESSMENT SYSTEM FOR CORE MATHEMATICS CONCEPTS IN GRADES K-5

Michael T. Battista

In an attempt to significantly improve the quality of students' mathematics learning, the NCTM Standards-guided reform movement calls for fundamental changes in the methods and content of school mathematics instruction. The major goal of reform is to change instruction so that ALL students (rather than the elite few) acquire the powerful mathematical reasoning and problem solving skills needed to productively participate in an increasingly technological society. Necessarily, this change requires a decided shift in instructional emphasis from rote learning of procedures to learning mathematics with understanding and sense making.

Assessment plays a critical role in this reform in two fundamental ways. First, appropriate assessment of student learning is a critical component in implementing instruction and curricula consistent with modern research on students' learning. Second, to validly evaluate the effectiveness of various education reforms and mathematics programs, assessments that precisely describe the quality of students' mathematics learning are critical.

This project is applying the results, theories, and methods of modern research in mathematics education to create a Cognition Based Assessment System (CBAS) that can be used to assess in detail the cognitive underpinnings of the progress students make in constructing understanding and mastery of core mathematical ideas in grades K-5. The CBAS consists of three components: (a) identification of core mathematical ideas in grades K-5; (b) research-based descriptions of students' cognitive milestones , fluencies, and levels of sophistication for each core idea; and (c) assessment tasks that identify exactly where students are in the "constructive itineraries" they travel to competence with these ideas.

The CBAS is designed for use by teachers in formative and summative classroom assessment, and for use by school districts, program evaluators, and researchers in evaluating the quality of student learning in various curricular and instructional programs. The CBAS will (a) support teachers who are trying to implement the type of cognition-based reform instruction recommended by research on students' mathematics learning and professional organizations; (b) motivate teachers who retain traditional teaching techniques to change their instruction when the CBAS reveals that their students are not learning mathematics as well as they assume; (c) provide a teacher-education vehicle to conceptually deepen teachers' understanding of core ideas in K-5 mathematics and enlighten teachers about how students learn those ideas; and (d) provide educators and researchers interested in examining the effectiveness of various curricula and instructional methods with an assessment system that can be used to evaluate the genuine progress students are making in acquiring powerful and deep understanding of core mathematical ideas.

The initial period of funding and development of the CBAS is focusing on geometry (including geometric measurement) and whole-number arithmetic.

This project is supported by the National Science Foundation (Grant No. ESI-0352345). Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.