Content and School Effectiveness: Role and Impact December 12, 2006 William H. Schmidt Michigan State University

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Instructional Content Constructs  Curricular Coherence Curricular Structure  Curricular Focus Exposure Time (OTL)  Curricular Rigor Level of Cognitive Complexity

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Coherence Defined We define content standards, in the aggregate, to be coherent if they are articulated over time as a sequence of topics and performances consistent with the logical and, if appropriate, hierarchical nature of the disciplinary content from which the subject- matter derives. This is not to suggest the existence of a single coherent sequence, only that such a sequence reflect the inherent structure of the discipline.

© 2006 Center for Research in Mathematics and Science Education, Michigan State University TIMSS Mathematics Framework – An Example

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Two Topic Trace Maps

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Top Achieving Countries’ Mathematics Curriculum

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Mathematics Topics Intended at Each Grade by 1989 NCTM Standards

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Mathematics Topics Intended at Each Grade by 2000 NCTM Standards

© 2006 Center for Research in Mathematics and Science Education, Michigan State University 21 U.S. States’ Mathematics Standards

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Table 1

© 2006 Center for Research in Mathematics and Science Education, Michigan State University RANOMIZED STUDY  Design 2X2X2X2X2X2 randomized block  Unit of analysis District(62)  Outcomes Student achievement and content coverage

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Examples of the IGP Index

International Grade Placement of Curriculum Content Across Districts Grade Placement of Curriculum Content Grade © 2006 Center for Research in Mathematics and Science Education, Michigan State University

Teachers Coverage of Mathematics Topics in Two Types of Schools High SES Schools Low SES Schools © 2006 Center for Research in Mathematics and Science Education, Michigan State University

Variation in the mathematics content index (IGP) in schools having multiple tracks and schools having single tracks Single-Track Schools Multiple-Track Schools © 2006 Center for Research in Mathematics and Science Education, Michigan State University

Relationship between Parents’ Education and Student Achievement

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Relationship between Parents’ Education and Algebra Instruction

© 2006 Center for Research in Mathematics and Science Education, Michigan State University Relationship between Algebra Instruction and Student Achievement

Results of Fitting the Hiarchical Linear Model: Levels 3 Fixed Effects © 2006 Center for Research in Mathematics and Science Education, Michigan State University

NON EXPERIMENTAL STUDIES Bias is almost always inherent in school effectiveness studies when content is not adequately taken into account

Percent of U.S. Students Enrolled in Each Type of Math Course Using Each Type of Textbook © 2005 MSU PROM/SE Promoting Rigorous Outcomes in Mathematics and Science Education, Supported by NSF Cooperative Agreement EHR