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Amu guide A Guide for Assessing Mathematical Understanding C C Portland OR A Guide for Assessing Mathematical Understanding CEducation Northwest SW Main St Suite Portland OR educationnorthwest org ? Education Northwest All rights reserved ISBN - - - Cover

A Guide for Assessing Mathematical Understanding C C Portland OR A Guide for Assessing Mathematical Understanding CEducation Northwest SW Main St Suite Portland OR educationnorthwest org ? Education Northwest All rights reserved ISBN - - - Cover images by Lucas Grzybowski CContents Preface v Acknowledgments vii Introduction Background Concept Areas and Learning Goals Organizational Framework Directions for Using Grade-Level Assessments Directions for Using the Diagnostic Assessment References Appendix A Pilot and ?eld tests Appendix B Reproducible records iii C CPreface Purpose Early high-quality instruction in mathematics that focuses on conceptual understanding procedural uency and the ability to solve problems is of critical importance Identifying what young students know about key mathematical ideas is the ?rst step in planning high-quality lessons that meet the needs of all students Assessing Mathematical Understanding is a collection of assessment tools developed to give teachers a way to access student thinking This assessment can be used to track student progress identify particular di ?culties and generally inform instructional planning By using the assessment process described in this guide and understanding the learning framework on which it is based teachers can increase their knowledge of how students learn Using students ? responses to the assessment items as a guide teachers can di ?erentiate instruction and create learning environments that better support their students ? mathematical development Rationale According to the latest available mathematics achievement data U S Department of Education National Center for Education Statistics n d percent of Northwest grade public school students were not pro ?cient in math This rate is slightly better than the rate for the nation as a whole percent of students were not pro ?cient across the U S U S Department of Education National Center for Education Statistics n d Such statistics underscore the need for early identi ?cation of students ? mathematical misconceptions and holes in their conceptual knowledge Addressing these problems will allow the teacher to act quickly to shore up areas of di ?culty Instructional strategies can be implemented to assist these children before they lose con ?dence in their ability to succeed in mathematics thereby shrinking or preventing an achievement gap between these students and their mathematically pro ?cient peers Applications The assessments contained in Assessing Mathematical Understanding should be administered by an adult in a one-on-one interview format The two grade-level assessments Kindergarten Items for Assessing Mathematical Understanding and First-Grade Items for Assessing Mathematical Understanding may be administered by a v Cteacher or paraprofessional Each grade-level assessment is divided into three parts intended to be used three times in the year with each section addressing two or three concept areas The comprehensive diagnostic assessment Diagnostic Items for Assessing Mathematical Understanding can be used to acquire extensive information about a student ? s understanding of one particular mathematical concept area This assessment should be administered by a teacher who has an understanding of the mathematics concepts identi ?ed at these grade levels and beyond A wealth of important instructional information can be gleaned by observing