This casebook is intended to support professionals who are working in a variety of contexts to use classroom-based assessment more effectively to support teacher learning and teaching change, and to enhance the opportunities for all students to develop mathematical power. It grows out of a collaboration of mathematics teachers and teacher educators, and mathematicians, to better understand the role of assessment as an ongoing activity to help teachers reshape their own teaching practices. At the heart of each case is using assessment to make sense of what students understand and what they are confused about, deciding what counts as evidence of that understanding, and using the analysis to consider what the teacher's next instructional moves might be.
All of the cases in this volume are built around actual episodes from mathematics classrooms. Intended as decision-making exercises, they present the raw data of classroom events in a straightforward way and are designed to stimulate analysis and reflection; provoke various and sometimes conflicting interpretations of an event; bring to the fore deeply held beliefs of beginning and experienced teachers so they can be reconsidered; and engage professionals in pedagogical problem solving in the context of complex classroom settings.
This volume reflects the growing interest in cases as a pedagogical tool in teacher professional development. The cases are organized to take up key themes of the NCTM Professional Teaching Standards in ways that will assist and support teachers, teacher educators, and curriculum and staff development specialists in learning to assess and in linking assessment with curriculum, teaching, and learning. Although each case contains many ideas for linking assessment with curriculum and instruction, the most powerful use of these materials resides in their design intended to foster conversations among groups of professional colleagues. The editors' field-testing of the cases--in initial teacher certification courses and in in-service workshops--has shown that they prompt engaging and demanding analysis through a variety of analytic lenses.
A videotape containing vignettes for four of the cases in the Casebook is available with this book. Transcriptions of the video vignettes are printed in the case materials in the book. Course instructors and professional development facilitators will need both the Casebook and the videotape and should order the Casebook/Video set. The video can also be ordered separately.
Table of Contents
Contents: Preface. Introduction. Part I: Listening to Students. M. Vince in Collaboration With the Project Team, Case 1--"They Favor Each Other": Making Sense of Similarity. S. Bethell in Collaboration With D. Chazan, M. Dennis, B. Rosenthal, P. Lanier, and S. Wilcox, Case 2--Nurturing a Disposition for Inquiry. D. Cantlon in Collaboration With K. Suzuka, S. Wilcox, and P. Lanier, Case 3--Learning Children's Understandings of Algebra. Part II: Assessing the Potential of Tasks. M. Sahloff in Collaboration With the Project Team, Case 4--Students' Knowledge of Linear Relationships as Represented in Concept Maps. R. Zielinski in Collaboration With S. Wilcox and M. Dennis, Case 5--Geometric Constructions: The Contributions of Context. Part III: Capturing Students' Engagement With a Task. K. Rohrs in Collaboration With the Project Team, Case 6--Making Sense of Multiple Snapshots of Students' Work. P. Wagner in Collaboration With S. Wilcox, Case 7--"Dang! This Can't Be Right": Computation in Problem Situations.
"The amount, depth, and timeliness of the materials and their level of quality in respect to the mathematics and pedagogy involved are excellent. The written text is clear and relevant to current issues, theory, and practice from a constructivist perspective, emphasizing the importance of discourse in learning....These materials would be an excellent resource for a series of workshops on using assessment for improving the teaching and learning of mathematics."
—Horizon Research Inc.
"The book is well structured and would be easy to use. Each of the case narratives is well written and contains good questions that have the potential to promote rich discussion about teaching and learning mathematics....The set would be a good resource for those involved in teacher education and staff development."
—Mathematics Teaching in the Middle School
"The casebook grew out of a 4-year collaborative project that brought together a group of mathematics teachers, mathematics educators, and mathematicians to learn more about how assessment can be used by teachers to improve their teaching and their students' learning....A unique feature of each case is the summary of deliberations that took place within the project team meeting around the data teachers brought documenting events in their classrooms."
—Zentralblatt fur Didaktik der Mathematik
"Well organized for easy use by the instructor--the questions that accompany each case focus the discussion on the important issues....Perfect for any course or presentation about the [NCTM] standards in that it gives the rather abstract standards a context....The power of the book is that readers can see and hear students engaged with a task or with their teacher in discussion of mathematical ideas."
—Mary Lynn Raith
Pittsburgh Public Schools
"A readable, accessible book...for preservice teachers in mathematics methods courses and for practicing teachers in graduate courses or in-service workshops. The cases provide an ideal jumping off point for talking about why and how we assess students' mathematical understandings, and how the information we gain from assessments can help us be more effective teachers."
—Diana V. Lambdin
"The focus on assessment is a valuable contribution to the growing collection of cases for the teaching profession. The combination of transcripts, artifacts, deliberations, video, and background information offer an authentic view of the situations presented in each case and are well organized for ease of use....Other features, such as the focus questions and the references for resources and research, also contribute to the view of teachers as professionals....The materials are on the cutting edge in terms of their professional and developmental approach and their view of assessment. The organization of the cases...will be very helpful for those trying to use the Standards as a focus for professional development in workshops and seminars. The cases themselves are based on lessons and materials that are on the forefront of mathematics education. My compliments to Wilcox and Lanier for creating case materials that will undoubtedly stimulate rich and productive discussions."
Far West Laboratory for Educational Research and Development