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Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students' achievements of intended instructional outcomes. Formative assessment means assessment embedded in instruction. That definition was adopted in 2006 by the Council of Chief State School Officers' (CCSSO) Formative Assessment for Students and Teachers State Collaborative on Assessment and Student Standards. Tasks are both instructional and informational; children learn mathematics and teachers have data and a framework that helps them continually notice and gather knowledge about their students' thinking. Formative assessment blends seamlessly into instruction, guiding teaching without stealing instructional time. In this article, the authors focus on only one component of formative assessment--the instructional task--and how teachers can design and choose tasks.

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are written by Al Cuoco, E. Paul Goldenberg, June Mark, and Sarah Sword--a team of curriculum developers at the Educational Development Center who pioneered work using mathematical habits of mind central to the work of mathematicians for organizing school mathematics curricula. The TCM article considers the ideas, logic, techniques, and habits of mind that algebra entails, as well as when and to what extent they can be learned with intellectual integrity in the elementary school grades, before a formal course on algebra. (Contains 4 figures and 2 tables.)

The article offers suggestions for incorporation of a formative assessment process to improve a student's mathematical understanding though feedback mechanism. Topics discussed include according to the Council of Chief State School Officers (CCSSO), formative assessment is assessment through instructions; several aspects of assessment like understanding students knowledge, encouraging and minimizing lengthy instructions; establishment of critical-thinking environment; and relevant examples.