Assessing Instructional Quality in Mathematics

Assessments of instructional quality based on classroom observations and artifacts have the potential to measure and improve mathematics instruction and learning. This article describes the Instructional Quality Assessment (IQA) Mathematics Toolkit and examines its ability to identify the nature and quality of classroom instruction. The IQA assesses elements of ambitious instruction in mathematics; specifically, the level of instructional tasks and task implementation, opportunities for mathematical discourse, and teachers' expectations. Results are reported from a study of 13 middle school teachers in a mid-sized urban district, following a professional development initiative and the adoption of standards-based mathematics curricula. The IQA identified high-quality assignments and student work, and that teachers who utilized cognitively challenging tasks could maintain the cognitive demands in lesson observations. The IQA also identified that observed instruction lacked high-quality whole-group discussions. The article closes by discussing how IQA can provide feedback for instructional improvement at the district level.

[1]  P. Cobb,et al.  Reflective Discourse and Collective Reflection , 1997 .

[2]  Mary Kay Stein,et al.  Architectures for Learning: A Comparative Analysis of Two Urban School Districts , 2008, American Journal of Education.

[3]  Education Professional Standards Board Evaluating Value-Added models for Teacher Accountability , 2004 .

[4]  Lindsay Clare Matsumura,et al.  Measuring Instructional Quality in Accountability Systems: Classroom Assignments and Student Achievement , 2002 .

[5]  Edward A. Silver,et al.  The Quasar Project , 1996 .

[6]  Edward A. Silver,et al.  Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development , 2009 .

[7]  John W. Moore Teaching for Understanding , 2002 .

[8]  Brian W. Junker,et al.  Measuring Reading Comprehension and Mathematics Instruction in Urban Middle Schools: A Pilot Study of the Instructional Quality Assessment , 2006 .

[9]  Lauren B. Resnick,et al.  LEARNING ORGANIZATIONS FOR SUSTAINABLE EDUCATION REFORM , 1998 .

[10]  A. Schoenfeld Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity , 2002 .

[11]  M. Stein,et al.  Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning. , 1997 .

[12]  Walter Doyle,et al.  Work in Mathematics Classes: The Context of Students' Thinking During Instruction , 1988 .

[13]  Lindsay Clare Matsumura,et al.  Measuring instruction for teacher learning , 2008 .

[14]  Alan H. Schoenfeld,et al.  Toward a theory of teaching-in-context , 1998 .

[15]  Descriptors Change Strategies paper presented at the Annual Meeting of the American Association of Colleges for Teacher Education , 1977 .

[16]  M. Wolf,et al.  Assessing Academic Rigor in Mathematics Instruction: The Development of the Instructional Quality Assessment Toolkit. CSE Technical Report 672. , 2006 .

[17]  Babette M. Benken,et al.  Teaching Mathematics for Understanding: An Analysis of Lessons Submitted by Teachers Seeking NBPTS Certification , 2009 .

[18]  Margaret S. Smith,et al.  Transforming secondary mathematics teaching: increasing the cognitive demands of instructional tasks used in teachers' classrooms , 2009 .

[19]  Courtney B. Cazden,et al.  Classroom Discourse: The Language of Teaching and Learning. Second Edition. , 2001 .

[20]  J. Boaler,et al.  Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School , 2008, Teachers College Record: The Voice of Scholarship in Education.

[21]  Margaret S. Smith Practice-Based Professional Development for Teachers of Mathematics , 2001 .

[22]  Stuart W. Elliott,et al.  Incentives and Test-Based Accountability in Public Education. (Panel Report) , 2011 .

[23]  Lindsay Clare Matsumura,et al.  Teachers’ assignments and student work: Opening a window on classroom practice , 2003 .

[24]  Sarah Michaels,et al.  Discourse, learning, and schooling: Shifting participant frameworks: orchestrating thinking practices in group discussion , 1996 .

[25]  Karen B. Givvin,et al.  Teaching Mathematics in Seven Countries: Results From the TIMSS 1999 Video Study , 2003 .

[26]  Deborah Loewenberg Ball,et al.  Introduction: Measuring Instruction , 2004, The Elementary School Journal.

[27]  Robert E. Reys,et al.  The Impact of Middle-Grades Mathematics Curricula and the Classroom Learning Environment on Student Achievement. , 2008 .

[28]  Mary Kay Stein,et al.  Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms , 1996 .

[29]  Hilda Borko,et al.  Artifact Packages for Characterizing Classroom Practice: A Pilot Study , 2005 .

[30]  Pamela R. Aschbacher,et al.  Exploring the Technical Quality of Using Assignments and Student Work as Indicators of Classroom Practice , 2001 .

[31]  L. Darling-Hammond,et al.  Teaching as the Learning Profession : Handbook of Policy and Practice , 1999 .

[32]  J. Stigler,et al.  Improving Mathematics Teaching. , 2004 .

[33]  James J. Kaput,et al.  Mathematics Worth Teaching, Mathematics Worth Understanding , 1999 .

[34]  D. Ball,et al.  Developing Measures of Teachers’ Mathematics Knowledge for Teaching , 2004, The Elementary school journal.

[35]  J. Stigler,et al.  The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom , 1999 .

[36]  W. Doyle Academic Work , 1983 .

[37]  Lindsay Clare Matsumura,et al.  Using teachers’ assignments as an indicator of classroom practice (CSE Technical Report 532) , 2000 .

[38]  E. Fennema,et al.  Teaching and Learning Mathematics With Understanding , 1999 .

[39]  J. Remillard Curriculum Materials in Mathematics Education Reform: A Framework for Examining Teachers' Curriculum Development , 1999 .

[40]  D. Clarke The Changing Role of the Mathematics Teacher. , 1997 .

[41]  Theresa M. Akey,et al.  Instructional Leadership, Teaching Quality and Student Achievement Suggestive Evidence from Three Urban School Districts. , 2007 .

[42]  Lindsay Clare Matsumura,et al.  Toward Measuring Instructional Interactions “At-Scale” , 2008 .

[43]  Gwendolyn M. Lloyd,et al.  Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum. , 1998 .

[44]  Kay McClain,et al.  Teacher's and Students' Understanding: The Role of Tools and Inscriptions in Supporting Effective Communication. , 2002 .

[45]  Joan D. Pasley,et al.  What Is High-Quality Instruction?. , 2004 .

[46]  B. Hamre,et al.  Conceptualization, Measurement, and Improvement of Classroom Processes: Standardized Observation Can Leverage Capacity , 2009 .

[47]  Rachael Gabriel,et al.  A Practice-Based Theory of Professional Education , 2011 .

[48]  J. Remillard,et al.  Teachers' orientations toward mathematics curriculum materials: Implications for teacher learning , 2004 .

[49]  Magdalene Lampert,et al.  Teaching Problems and the Problems of Teaching , 2001 .

[50]  Gwendolyn M. Lloyd Two Teachers' Conceptions of a Reform-Oriented Curriculum: Implications for Mathematics Teacher Development , 1999 .

[51]  James P. Spillane,et al.  Reform and Teaching: Exploring Patterns of Practice in the Context of National and State Mathematics Reforms , 1999 .

[52]  M. Stein,et al.  Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project , 1996 .

[53]  Brian Rowan,et al.  What Large-Scale, Survey Research Tells Us About Teacher What Large-Scale, Survey Research Tells Us About Teacher Effects on Student Achievement: Insights From the Prospectus Effects on Student Achievement: Insights From the Prospectus Study of Elementary Schools Study of Elementary Schools , 2015 .

[54]  Liping Ma,et al.  Knowing and Teaching Elementary Mathematics Teachers' Understanding of Fundamental Mathematics in China and the United States , 2010 .

[55]  Alexandria Ross,et al.  Using Data to Inform Instruction , 2011 .