CDT Research Papers & Books
Here is a list of publications that have been written by CDT staff members. Click on the link to download the linked PDF's where applicable. Due to copyright laws, published papers must be acquired by contacting the publisher.
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Nelson, Barbara S., Stimson, Virginia C, & Jordan, Will J. (2007).
Leadership Content Knowledge for Mathematics of Staff Engaged in Key School Leadership Functions. (click the link to download PDF)
Paper presented at the annual meeting of the University Council of Education Administration, Washington, DC.
Jordan, Will J. & Miller, Stephanie R. (2007)
Inter-Rater Agreement in Analysis of Open-Ended Responses:
Lessons from a Mixed Methods Study of Principals. (click the link to download PDF)
Paper presented at the Annual Meeting of the American Educational Research Association.
Nelson, Barbara S. & Sassi, Annette (2006) What to Look for in Your Math Classrooms. Principal Magazine, November/December 2006. 46-49.(click the link to download PDF)
Reed, Kristen E., Goldsmith, Lynn T., & Nelson, Barbara S. (2006)
Elementary and Middle School Teachers’ Perceptions of their Principals’ Instructional Leadership in Mathematics: Preliminary Results. (click the link to download PDF)
Paper presented at the Research Pre-Session of the Annual Meeting of the National Council of Teachers of Mathematics.
Schifter, Deborah
(2006). Proof in the Elementary Grades (click the link to download PDF)
This paper investigates the possibility and actuality of proof in the elementary
grades. How do young children consider mathematical claims that apply to
a general class? Which criteria for proof are appropriate to elementary
students, yet would support distinctions essential in the later grades?
And how does such work on proof support the work that is already at the
heart of the elementary mathematics program?
Schifter, D., Bastable,
V., Russell, S.J., Seyferth, L., & Riddle, M. (2006) Algebra in the
K-5 Classroom: Learning Opportunities for Students and Teachers
(click the link to download PDF)
For most Americans, the identifying feature of algebra is the formal equation
consisting of variables and signs for the operations and equality. However,
beneath the high abstraction of equations like a(b+c)=ab+ac lie ways of
reasoning about how quantities can be decomposed and recombined under different
operations—ways of reasoning, unlike the conventions of the notation
itself, fully accessible to elementary-aged students.
Nelson, B.S. & Sassi, A (2005). The effective
principal: Instructional readership for high quality learning. New York,
Teachers College Press.
This recent book reports on research about how principals' instructional leadership is affected by their own knowledge and beliefs about learning, teaching, and mathematics. Click here for more information and how to order.
Nelson, B.S., Benson, S. &
Reed, K.M. (2004) Leadership content knowledge: A construct for illuminating
new forms of instructional leadership. Paper presented at the annual meetings
of the National Council of Supervisors of Mathematics. Philadelphia, PA.
(click the link to download PDF)
Schifter, Deborah
& Bodner Lester, Jill (2003). Active Facilitation: What Do Mathematics
Specialists Need to Know and How Might They Learn It?. Research paper written
for Center for Development of Teaching. (click the link to download
PDF)
Nelson, B. S. & Stein, M. K. (2003). Leadership content knowledge. Educational
Evaluation and Policy Analysis. Winter 2003 25(4), 423-448.
Abstract: The construct of leadership content knowledge opens entirely new realms of thought about leadership -- connecting it directly to the core function of schooling, learning and teaching -- and raising the question whether generic studies of leadership can really get at the heart of what it means to lead schools and school districts. Without knowledge that connects subject matter, learning, and teaching to acts of leadership, leadership floats disconnected from the very processes it is designed to govern. Just as the construct of pedagogical content knowledge has marked out new and very generative research questions and sites for research, so the construct of leadership content knowledge may open up new questions about what it means to provide instructional leadership in schools.
Sassi, Annette (2002).Cultivating
Perception: Helping Teachers To Attend to the Salient Features of their
Mathematics Classrooms. 20 pp. (click the link to download PDF)
Abstract: Efforts to align mathematics instruction with NCTM’s (2000) Principles and Standards for School Mathematics have stressed the importance of teacher learning both as a goal of professional development and as an integral aspect of teacher practice itself. This paper explores the idea of teacher learning embodied in standards-based pedagogies and argues that at its core is the belief that teachers need to be intellectually curious and need to cultivate a particular type of attention toward and appreciation of their teaching situations. Using the theoretical framework of Aristotelian practical judgment as articulated by philosopher Martha Nussbaum and specified for educational contexts by education philosopher Shirley Pendlebury, the paper considers how a critical component of mathematics teaching is “perception” — the discernment of and responsiveness to the salient features of mathematics teaching and learning. It reframes Deborah Ball’s account of her teaching as an example of Aristotelian practical judgment, judgment that rests with perception rather than with general rules or formal procedures. It then uses a discussion from a teacher study group to illustrate how learning to deliberate about the actions one should take are inseparable from cultivating perception of the salient features of one’s situation. In this case, the salient features are the mathematical ideas behind the curriculum and to the ways children come to understand them. Using a teacher’s vignette written for the study group, it looks at how the writing and discussing of classroom stories with a focus on the mathematical ideas and the students’ thinking can help teachers cultivate and refine their attention to the salient features of their classrooms.
Lester, J. B. & Grant, C. M.
(2001). Mathematics supervision through a new lens. Educational Leadership,
February 2001 (click the link to visit the ASCD archive to purchase
a copy of this article)
Abstract: This article describes Lenses on Learning: A New Focus on Mathematics and School Leadership, a course designed to help administrators become more effective mathematics supervisors. The article chronicles the experiences of an elementary school principal who entered the program feeling poorly-equipped to evaluate or support mathematics teaching. In describing the Lenses on Learning program, the article illustrates how administrators learn to support mathematics instruction based on the NCTM Standards by engaging in mathematics activities and exploring students+ thinking and teachers' roles in Standards-based classrooms.
Schifter, Deborah & Hammer,
David (2001) Practices of Inquiry in Teaching and Research 29pp. (click
the link to download PDF)
Abstract:There are three central purposes in this paper. The first is to gain insight into the inquiry of teaching, that is, the ongoing, everyday inquiry teachers conduct into their students' understanding and learning. The second is to explore the similarities and differences between practices of inquiry in teaching and research. The third is to consider what these practices of inquiry may offer each other. We pursue these objectives by examining (1) a conversation among a group of physics teachers about a discussion that took place in one of their classes, and (2) essays by two elementary school teachers about their first and second grade students' early reasoning about triangles.
Nelson. B.
S. & Sassi,. A. (2000). Shifting approaches to supervision: The case
of mathematics supervision. Education Administration Quarterly, 36(4). 553-583.
(click the link for purchasing information from Education Administration
Quarterly)
Abstract: Standards-based instructional reform has been occurring in all major school subjects. However, administrators' supervisory practices have generally not taken account of subject-matter content but have focused primarily on pedagogical process. This article addresses how administrators can better support standards-based instruction by shifting their approaches to supervision to attend to the intersection of process and content. The article reports on a study that looked at what administrators thought significant when viewing the same videotape of a fifth-grade mathematics lesson at the beginning and end of a professional development seminar on supervision. It describes the different interpretations of the same events at these two times to illustrate the emergence of new principles to guide the exercise of administrators' professional judgment in classroom observation and supervision. The article concludes that there is a need to bring adequate subject-matter knowledge to the process of supervision and suggests several possible directions to achieve this shift.
Abstract: Administrators’ capacity to support standards-based mathematics education is affected by their understanding of its basic principles — i.e. the ideas they have about the nature of mathematics itself, the nature of learning, and the nature of teaching. This paper proposes a theoretical framework that specifies the relationship between administrators’ ideas about mathematics, learning, and teaching (standing commitments), the way they interpret the professional situations they are in (situational appreciation), what they think they should do in those situations (practical judgment), and what they actually do. Two cases of administrators’ efforts to enact new ideas in practice are examined.
Nelson, B. S. & Sassi,
A. (2000). Building new knowledge by thinking: How administrators can learn
what they need to know about mathematics education reform. Newton, MA: Center
for the Development of Teaching, Education Development Center, Inc.
(click the link to download PDF)
Abstract: The mathematics education reform movement is built on very different ideas about the nature of learning, teaching, and, indeed, mathematics itself, than the views that have prevailed in American schooling for many years. This has implications for administrative practice, since an enterprise that exists to support rigorous thinking on the part of students requires different administrative supports than one that exists to transmit accepted knowledge from teacher or textbook to student. Understanding new ideas about mathematics, learning, and teaching, and exploring the implications of these ideas for administrative practice, requires conceptual change on the part of many administrators. This paper describes the pedagogical principles that underlie a program designed to provide opportunities for such conceptual change for administrators.
Nelson,
B. S. (1998). Lenses on learning: Administrators’ views on reform
and the professional development of teachers. Journal of Mathematics Teacher
Education, 1, 191-215. (click the link to obtain for purchasing information
from the Journal of Mathematics Teacher Education)
Abstract: If the intellectual norms and values embedded in the mathematics education reform movement are to move beyond individual classrooms and significantly influence entire schools and districts, school and district administrators will need to become centrally, rather than peripherally, involved. This paper discusses the ways administrators’ ideas about the nature of mathematics, learning, teaching, and school culture affect their interpretations of the nature and intent of the elementary mathematics reform movement and their thoughts about how they might support it.
Nelson, B. S. (Ed) (1995) Inquiry and the Development
of Teaching: Issues in the Transformation of Mathematics Teaching. 65pp.
(click the link to download PDF)
Schifter, D. (1994) Voicing
the New Pedagogy: Teachers Write about Learning and Teaching Mathematics.
24pp (click the link to download PDF)
Abstract: Detailed descriptions of classroom process are needed in order to ground discussion of the principles animating the mathematics education reform movement. In response to this need, teachers who were already engaged in transforming their mathematics instruction were invited to write reflective narratives about their evolving instructional practice. This paper describes the structure of that project and presents excerpts from some representative narratives. It also considers how writing these narratives contributed to the continuing development of their authors and discusses how reading them affected students in teacher education courses. Finally, it urges that such narratives be seen as a medium through which teachers can become centrally involved in the national conversation about mathematics education reform.
Goldsmith, L. T. & Schifter, D. (1994) Characteristics
of a Model for the Development of Mathematics Teaching. 15pp. (click
the link to download PDF)
Abstract: The current mathematics reform movement has recognized that new forms of mathematics teaching will be needed to support the proposed curricular changes. These new forms extend beyond the acquisition of new teaching techniques and strategies to the reconstitution of fundamental notions of teaching, learning, and the nature of mathematics as a discipline, and also to the creation of different classroom opportunities for learning. The means by which teachers effect this kind of transformation are, as yet, little understood. This paper describes a set of components of developmental models that can be used to guide efforts to build models of the process of teachers' development in mathematics practice. Drawing from theories of cognitive development, the paper focuses on three components of the change process: (1) qualitative reorganizations of understanding; (2) orderly progression of changes; and (3) the contexts and mechanisms by which transitions are effected; and suggests a fourth component-individual motivational and dispositional factors.