Approaches to Studying the Enacted Mathematics Curriculum
reviewed by Angelo Collins - January 11, 2013
Title: Approaches to Studying the Enacted Mathematics Curriculum
Author(s): Daniel J. Heck, Kathryn B. Chval, Iris R. Weiss (eds.)
Publisher: Information Age Publishing, Charlotte
ISBN: 1617358770, Pages: 218, Year: 2012
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Having been on a team that edited a book, I am in awe at the skill of the editors in persuading seven sets of researchers to prepare chapters that include the same information in a relatively similar order. Each chapter, prepared by a different research team from a different institution about a different project, begins with an introduction that includes a description of the project, the reason that the instruments were designed, the definitional or theoretical grounding of the study and the intended users for the instruments. Next each set of authors describes what mathematics curricula were examined and for what grade levels, how the tools were developed and tested, including rater training and inter-rater reliability. Samples of the tools and modes of data displayed are presented. Each chapter ends with the authors ideas for what needs to be done next, whether within their project or across the field of mathematics curriculum development and evaluation. Some authors include critiques of their own work or lessons learned during the project. Of course, not every author followed this outline, but each chapter includes each of these elements in some form. An opening chapter by the editors explains why they believe understanding the enactment of curriculum is important, a brief history of the study of curriculum enactment, three conceptualizations of enacted curriculum and a paragraph introducing each chapter. A closing chapter, also by the editors, intended to highlight the differences in the chapters, addresses differences in purpose and intended use, difference in assumptions, conceptualizations of definitions, and differences in the scope of the work. This final chapter also addresses practical issues, the adaptation of existing tools and the development of new tools. Here the editors pose a series of questions for anyone considering developing a set of tools to study curriculum enactment in mathematics, and, I would argue, in any discipline, should consider. The introduction to this last chapter states A table in the appendix summarizes key features of the various sets of tools described in this book, providing a quick reference guide to these existing measures. (p. 196). Unfortunately, the paperback copy of the book I have does not contain this appendix.
Chapter Two, by Denisse R. Thompson and Sharon Senk is about the evaluation of the University of Chicago School Mathematics Project. In this chapter, looking specifically at high school geometry, eight instruments, primarily relying on self-report, are organized to document the constructs of chapter evaluation, instructional practice by teachers, students and observers. The last instrument evaluates the intersection between the taught and assessed curriculum, which provides information on the opportunity to learn. Data are illustrated in box-and-whisker diagrams and shaded tables. The authors discuss the possibility of hierarchical modeling of the data as a next step and propose that these instruments could be adapted to other curriculum materials.
Chapter Three, by Mary Ann Huntley is about using Innovation Configuration Maps to study middle school curriculum implementation. Derived from the concerns-based adoption model (CBAM), Innovative Configuration Maps display the various ways curriculum materials can be implemented. Components of Connected Mathematics and Math Thematics, such as teacher activity and group work respectively, as well as the role of the textbook and standards-based practice are presented to illustrate how Innovative Configuration Maps are constructed and used. The results of how different teachers use these materials are displayed in charts. The author discusses the potential for developing Configuration Maps for other curricula.
Chapter Four, by Daniel J. Heck, Kathryn B. Chval, Iris R. Weiss, and Steven W. Ziebarth, the editors of the book, is about the work of the Center for the Study of Mathematics Curriculum Tools Group. The tools are intended to measure the extent to which the curriculum is implemented as the designers intend, as this intention is described in the published materials. Organized and scored by three constructs: Extent of use, Mathematics Storyline and Pedagogical Storyline, scores are produced for Adherence and Focus. Adherence compares the enactment of elements of the curriculum materials with elements in the design of the curriculum materials while Focus compares the enactment of the elements in the curriculum materials with the enactment of materials outside the curriculum materials. Numerical scores between 1 and 0 are recorded. Scoring guides aligned with the elements of the curriculum assist observers. Scoring guides can be developed for various levels of specificity from a single lesson to an entire curriculum package. Tools have been developed for three curriculum packages at elementary, middle and high school grade levels. Although validation studies continue, these tools can be found on the centers website.
Chapter Five, by James E. Tarr, Melissa D. McNaught and Douglas A. Grouws is about the Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) Project. The instruments in the project were specifically designed to compare Core-Plus, an integrated approach to high school mathematics, and textbooks that are organized by traditional mathematics topics such as Algebra and Geometry. Instruments were designed to measure content fidelity defined as what content is taught and presentation fidelity from the perspective of a researcher and the perspective of the teacher. Data can be presented in shaded representations and numerically. The authors expect to explore the interactions among implementation fidelity as measured by the instruments, teacher characteristics and student achievement.
Chapter Six by Jeanne Century, Cassie Freeman and Mollie Rudnick is about the Center for Elementary Mathematics and Science Education at the University of Chicago. A suite of eight tools were designed to measure the degree of fidelity of implementation of six science programs and one elementary mathematics program, Everyday Mathematics. The conceptual framework, organized by critical components, includes two major categories Structural Critical Components and Procedural Critical Components. Each of these has two subcategories; Structural Critical Components includes Procedural and Educative while the Procedural Components includes Pedagogical and Student Engagement. While the authors state that they are exploring different ways to present the scores, the example illustrated in the book, using space in the four quadrants created by the two major categories as axes and the two sub categories as the endpoints of these axes, was easy to interpret and quickly showed areas of high and low enactment. The authors indicate that next steps include continued testing of the instruments in districts with different student compositions, the creation of an instrument that includes gathering information from students and an attempt to bring coherence to the field studying fidelity of implementation through an open access website.
Chapter Seven by Linda Wilson and Jo Ellen Roseman is about Project 2061. The underpinning assumption of this work is that the enacted curriculum must be aligned with specific learning goals. From a set of 24 research-based criteria for the analysis of middle grades textbooks, five were chosen as the most likely to have the greatest impact on student learning. The evaluation system uses videos of instruction and is web-based. One criterion Asking Guiding Questions produced significant gains in student learning. The authors acknowledge that the system is labor intensive but may point to relationships between curriculum materials and student learning that may not be detected in other systems.
Chapter Eight by Jennifer McMaken and Andrew Porter is about the Surveys of Enacted Curriculum (SEC). Teachers are provided with a list of mathematics concepts derived from textbooks, tests and national and state standards and asked to report the time on the topic and the relative emphasis of five levels of cognitive demand. The analysis is presented as a topographic grid, with the topics and cognitive demand as axes and shading indicating relative emphasis. Similar grids are constructed for the curriculum materials and comparisons can be made. The authors are transparent that this instrument only measures the extent to which content is taught and that other instruments are needed to measure other factors such as pedagogical approach.
The authors of each of the chapters indicate who the intended users of the instruments they developed were. Almost every segment of the education enterprise is included: curriculum developers, curriculum evaluators, those who select curriculum, assessment developers, those who provide professional development, teachers, principals, superintendents, assessment developers and education researchers. I would concur. Everyone who uses curriculum materials to enable teaching and learning in mathematics, and other disciplines, and those who develop, evaluate and do research on these materials would benefit from this book.
As the authors of these chapters highlight, teaching is a complex activity and doing research on any aspect of teaching is very complex. Although starting with the evaluation of curriculum materials, each team of researchers was required to also look at other aspects of teachers and teaching, students and learning. All of the projects included teams of individuals and were multi-year endeavors, yet each team indicates that more work is needed. Some teams use the same term for a different concept and some use different teams for the same concept. Each chose a theoretical stance and a level of detail to study. Each team had to make decisions about areas of study to include and exclude. All authors report adjustments made subsequent to beginning the project. Some adjustments were the result of field tests, but others were made to accommodate limits of time or other resources. The variety of data displays is another indicator of the complexity of the work reported in this book. With this extensive diversity of decisions, taken together the chapters in the book present a broad view of a varied complex field.
Still, as I read I was left with three questions: where do these studies reside on the permeable boundary between curriculum and instruction, or is that distinction no longer relevant; is there a grain size that is too small or too large that face validity is lost; and, what are the assumptions about learning that underpin each of the curricula and these studies?