MATHEMATICS LESSON INTERACTIONS AND CONTEXTS FOR AMERICAN INDIAN STUDENTS IN PLAINS REGION SCHOOLS: AN EXPLORATORY STUDY Regional Educational Laboratory Contract #ED-01-CO-0006 Deliverable #2005-05 Prepared by McREL Research Staff December 1, 2005 © 2005 McREL This document has been funded at least in part with federal funds from the U.S. Department of Education under contract number ED-01-CO-0006. The content of this publication does not necessarily reflect the views or policies of the Department of Education nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government. TABLE OF CONTENTS Acknowledgements...........................................................................................................................................iii Executive Summary ...........................................................................................................................................1 Introduction.......................................................................................................................................................4 Regional Context........................................................................................................................................... 4 Study Purpose ................................................................................................................................................ 6 Conceptual Framework.....................................................................................................................................6 NCTM (1991) Standards of Professional Practice ..................................................................................... 7 Worthwhile Tasks .................................................................................................................................. 7 Discourse................................................................................................................................................. 7 Learning Environment and Assessment.............................................................................................. 8 Cultural Responsiveness ............................................................................................................................... 8 High Expectations.................................................................................................................................. 9 Cognitive Challenge .............................................................................................................................. 9 Emphasis on Cooperativeness & Helpfulness.................................................................................. 10 Making Connections to Out-of-school Experiences......................................................................... 10 Observational Learning Opportunities..............................................................................................10 Study Design ....................................................................................................................................................11 Research Questions ..................................................................................................................................... 11 Method.............................................................................................................................................................12 Sample .......................................................................................................................................................... 12 School Context..................................................................................................................................... 13 Classroom Context.............................................................................................................................. 14 Data Collection Procedures........................................................................................................................ 14 Videotaping and Lesson Transcription..............................................................................................14 Teacher Survey and Interview............................................................................................................. 15 Student Assessments............................................................................................................................ 15 Data Analysis................................................................................................................................................ 17 NCTM (1991) Principles of Professional Practice ............................................................................ 17 Verbal Instructions and Interactions.................................................................................................. 17 Cultural Responsiveness...................................................................................................................... 18 Student Assessment ............................................................................................................................. 20 Triangulation and Cross-Case Analysis..............................................................................................20 Mathematics Lesson Interactions and Contexts for American Indian Students in Plains’ Region Schools: An Exploratory Study i Results...............................................................................................................................................................20 Instructional Approaches............................................................................................................................ 21 Lesson Contexts........................................................................................................................................... 23 Saxon Lessons....................................................................................................................................... 23 Cognitively Guided Instruction Lessons............................................................................................24 Success For All MathWings Lessons..................................................................................................25 Adherence to NCTM (1991) Standards of Professional Practice........................................................... 25 Verbal Instructions and Interactions......................................................................................................... 26 Cognitive Challenge of Teacher Questions.......................................................................................30 Cultural Responsiveness ............................................................................................................................. 28 Student Aptitude and achievement........................................................................................................... 31 Patterns and Relationships ......................................................................................................................... 34 Discussion ........................................................................................................................................................35 References ........................................................................................................................................................39 Appendix A: Lists of Research Partnership and Advisory Panel Members................................................44 Appendix B: Examples of Statements and Questions in Saxon Lesson Teacher’s Talk....................... ....45 Appendix C: Student Performance...............................................................................................................47 Appendix D: Approach Descriptions........................................................................................................ ...49 Mathematics Lesson Interactions and Contexts for American Indian Students in Plains’ Region Schools: An Exploratory Study ii ACKNOWLEDGEMENTS This study was conducted as a collaborative effort between teacher educators and Mid- continent Research for Education and Learning (McREL) researchers. With different perspectives, areas of knowledge, and resources, the researchers and teacher educators developed methodology and carefully examined the implementation and potential impact of various approaches to mathematics in classrooms for Native American students. We gratefully acknowledge the contributions of Dr. Judith Hankes, McREL Visiting Scholar, and Associate Professor of Mathematics Education, University of Wisconsin Oshkosh, and Mr. RunningHorse Livingston, McREL Intern, and Curriculum Coordinator, Lake Superior Band of Bad River Chippewa. Dr. Hankes contributed tools for comparing pedagogy across lessons and a vision for mathematics that helped broaden the team’s approach to the study. Dr. Hankes’ deep knowledge and understanding of the intersections between cultural differences and mathematics learning and teaching added value to this research and report. Mr. RunningHorse Livingston contributed his professionalism and time to filming lessons, producing lesson tapes, and conducting site visits to participating schools. His field notes, record keeping, and insights provided the team rich sources of data and his astute interpretations of the experiences of teachers and