Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.

[1]  Charalambos Y. Charalambous,et al.  Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study , 2008 .

[2]  Pam Grossman,et al.  Learning from curriculum materials: Scaffolds for new teachers? ☆ , 2008 .

[3]  Daniel F. McCaffrey,et al.  Studying Large-Scale Reforms of Instructional Practice: An Example from Mathematics and Science , 2003 .

[4]  Miriam Gamoran Sherin,et al.  Curriculum strategy framework: investigating patterns in teachers’ use of a reform‐based elementary mathematics curriculum , 2009 .

[5]  Laurie Sleep,et al.  MKT and curriculum materials are only part of the story: Insights from a lesson on fractions , 2012 .

[6]  Edward A. Silver,et al.  Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom , 2005 .

[7]  D. Cohen.  A Revolution in One Classroom: The Case of Mrs. Oublier , 1990 .

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

[9]  J. Bruner.  The Process of Education , 1960 .

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

[11]  R. Heaton.  Who Is Minding the Mathematics Content? A Case Study of a Fifth-Grade Teacher , 1992, The Elementary School Journal.

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

[13]  Charalambos Y. Charalambous,et al.  Teaching (un)Connected Mathematics: Two teachers' enactment of the Pizza problem , 2012 .

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

[15]  J. Krajcik,et al.  Designing Educative Curriculum Materials to Promote Teacher Learning , 2005 .

[16]  Morey Schwartz,et al.  For whom do we write the curriculum? , 2006 .

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

[18]  Jeffrey Choppin.  Curriculum-Context Knowledge: Teacher Learning From Successive Enactments of a Standards-Based Mathematics Curriculum , 2009 .

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

[20]  D. Ball,et al.  Reform by the Book: What Is—or Might Be—the Role of Curriculum Materials in Teacher Learning and Instructional Reform? , 1996 .

[21]  Rachel M. B. Collopy.  Curriculum Materials as a Professional Development Tool: How a Mathematics Textbook Affected Two Teachers' Learning , 2003, The Elementary School Journal.

[22]  Doug Clarke,et al.  A designer speaks , 2011 .

[23]  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.

[24]  S. Raudenbush,et al.  Resources, Instruction, and Research , 2003 .

[25]  Charalambos Y. Charalambous,et al.  Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality , 2012 .

[26]  Jo Boaler,et al.  Experiencing school mathematics : traditional and reform approaches to teaching and their impact on student learning , 2002 .

[27]  Stacy Ann Brown,et al.  Reconceiving Fidelity of Implementation: An Investigation of Elementary Whole-Number Lessons , 2009 .

[28]  Richard S. Prawat,et al.  Teaching Mathematics for Understanding: Discussing Case Studies of Four Fifth-Grade Teachers , 1992, The Elementary School Journal.

[29]  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 .

[30]  H. Hill.  Learning in the Teaching Workforce , 2007, The Future of children.

[31]  Jean Hartley,et al.  Case study research , 2004 .

[32]  J. Remillard.  Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula , 2005 .

[33]  Charalambos Y. Charalambous,et al.  Teacher knowledge, curriculum materials, and quality of instruction: Unpacking a complex relationship , 2012 .

[34]  J. Remillard.  Can Curriculum Materials Support Teachers' Learning? Two Fourth-Grade Teachers' Use of a New Mathematics Text , 2000, The Elementary School Journal.

[35]  M. Kim.  The Role of Mathematics Curriculum Materials in Large-Scale Urban Reform: An Analysis of Demands and Opportunities for Teacher Learning , 2011 .