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Conceptualizing and Using Routines of Practice in Mathematics Teaching to Advance Professional Education

Authors:
E. Kazemi at University of Washington Seattle
E. Kazemi
Magdalene Lampert at New Visions for Public Schools
Magdalene Lampert
  • New Visions for Public Schools
Hala Ghousseini at University of Wisconsin–Madison
Hala Ghousseini
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Abstract

In this report, we describe our work on teaching and professional education in a conference held at the University of Michigan. The vision of teaching we assume in this work is what we would call " ambitious teaching. " Ambitious teaching has an ambitious goal: to enable students across racial, ethnic, social class, national, language and gender groups to succeed, not only on school-based assessments but performing competently and judiciously on tasks that involve complex problem solving of a sort that is often called " authentic. " Our purpose is to learn how to make this kind of teaching doable by novices, whether they are beginners or experienced teachers seeking to become more ambitious. The conference brought together members of six different research and development projects to examine our efforts to experiment with approaches to teacher education that focused on doing ambitious teaching. We intended to examine how each of the projects decomposed this kind of mathematical teaching practice in order to make the work of mathematics teaching an object of reflection, inquiry, and learning. Here we report on the activities of the meeting, the major outcomes, and our plans for further collaboration. Purpose of Work: All the participants at the conference had made choices about how to characterize the work of ambitious mathematics teaching, and in particular how to decompose that work in order to make it learnable and explicit to novice teachers. We all assume that ambitious teaching is a complex performance requiring not only skills, knowledge, and dispositions, but also the capacity to judge when, where, and how to use skills and knowledge in direct interaction with learners to further their learning. Large parts of ambitious teaching practice are contingent – that is, dependent on teacher/student interactions. Ambitious teaching requires that teachers teach in response to what diverse students are able to do as they engage in problem solving performances, all while holding students accountable to ambitious learning goals. This kind of work is both essential and challenging if all kinds of students are going to succeed in doing rigorous academic work, and we believe that the new approaches we generate for teacher education can make it more common.
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Conceptualizing and Using Routines of Practice in Mathematics Teaching to Advance
Professional Education
Conference Supported by the Spencer Foundation
Elham Kazemi
University of Washington
Magdalene Lampert, & Hala Ghousseini,
University of Michigan
Conference Co-Organizers
Ann Arbor, Michigan, May 22-23rd, 2007
In this report, we describe our work on teaching and professional education in a conference held
at the University of Michigan. The vision of teaching we assume in this work is what we would
call “ambitious teaching.” Ambitious teaching has an ambitious goal: to enable students across
racial, ethnic, social class, national, language and gender groups to succeed, not only on school-
based assessments but performing competently and judiciously on tasks that involve complex
problem solving of a sort that is often called “authentic.” Our purpose is to learn how to make
this kind of teaching doable by novices, whether they are beginners or experienced teachers
seeking to become more ambitious.
The conference brought together members of six different research and development projects to
examine our efforts to experiment with approaches to teacher education that focused on doing
ambitious teaching. We intended to examine how each of the projects decomposed this kind of
mathematical teaching practice in order to make the work of mathematics teaching an object of
reflection, inquiry, and learning. Here we report on the activities of the meeting, the major
outcomes, and our plans for further collaboration.
Purpose of Work:
All the participants at the conference had made choices about how to characterize the work
of ambitious mathematics teaching, and in particular how to decompose that work in order
to make it learnable and explicit to novice teachers. We all assume that ambitious teaching
is a complex performance requiring not only skills, knowledge, and dispositions, but also
the capacity to judge when, where, and how to use skills and knowledge in direct
interaction with learners to further their learning. Large parts of ambitious teaching
practice are contingent – that is, dependent on teacher/student interactions. Ambitious
teaching requires that teachers teach in response to what diverse students are able to do as
they engage in problem solving performances, all while holding students accountable to
ambitious learning goals. This kind of work is both essential and challenging if all kinds of
students are going to succeed in doing rigorous academic work, and we believe that the
new approaches we generate for teacher education can make it more common.
2
Our conference was organized to enable participants to develop a better understanding of
the ways we have parsed ambitious elementary mathematics teaching for study by novices,
and to begin a conversation about what ways teacher educators should decompose practice
in order to more productively engage novice and experienced teachers in learning to teach.
Although the field of mathematics teacher education has produced a wealth of knowledge
about the use of real artifacts of practice to ground analysis of teaching, we still have much
work to do in developing novice teachers’ actual practice with students in the classroom.
We hoped to make progress on examining and comparing our choices and identifying
fruitful areas for coordination and collaboration in future research.
Major Activities of Conference and Questions Considered
We organized the conference to ground our discussions in common objects of inquiry so
that we could have a set of shared referents for our discussions of the meaning and use of
“routines” in teaching and teacher education. Our conversations were focused around the
following depictions of the work of professional educators:
1. The instructional activity of Conversation Rebuilding
Drawing on research on teacher education that he conducted in collaboration
with Lampert, Filippo Graziani demonstrated a core activity used at all levels
of instruction in the Italiaidea School for Language and Culture, where he
teaches, in order to “make the familiar strange.” The activity is called
Conversation Rebuilding. The activity has the ambitious goal of engaging
students across all levels of competence in studying the language they are
trying to learn in use. On the morning of the first day, we experienced
Graziani using this instructional activity first hand with conference
participants in the role of novice speakers of Italian. We also viewed
videotaped recordings of a professional educator coaching novices to use
Conversation Rebuilding during the Basic Course for Teachers of Italian at
Dilit International House in Rome. On the morning of the second day, we
returned to Conversation Rebuilding, this time watching Graziani teaching
more competent speakers of Italian (two of the conference participants,
Lampert and Forzani) in order to compare how the “routine” was consistent or
different across different conversation topics and levels of language fluency.
This second experience enabled us to further observe the key architecture of
the activity at the same time that we were able to discuss the professional
judgment at play when Graziani worked with novice versus more experienced
Italian speakers.
2. Descriptions from each project about the units of teaching practice that were the
focus of our teacher education courses.
Using artifacts from courses for novice and experienced educators,
participants presented the ways in which they “decompose” complex practice
to engage learners in the study of teaching in, from, and for practice.
3. Videotaped depictions of novice teachers enacting discourse routines taught in
secondary math methods course by Hala Ghousseini and Patricio Herbst.
After playing a video recording of a novice participant attempting to enact
discourse routines that she had been taught in her methods course during her
student teaching semester, Ghousseini guided us in noticing elements of the
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routines and discussing what was “missing” from the practice we observed so
that we could consider the enactment of a set of routines during a lesson in a
classroom setting.
These depictions challenged us to think about how we were using routines and what we
meant when we used the term. We were concerned with making definitional progress by
examining the varied uses of particular terms such as “routines” and “practices.” We
agreed that it would be difficult to reach consensus in such a short period of time, but we
noted that our ability to coordinate and collaborate across research teams would
necessitate developing a lexicon that would allow us to be more precise about what we
were discussing, or at least to recognize our differences in assumptions and approaches.
Terms such as “activity structure,” “strategy,” and “technique” all became objects of
discussion. We also noted that the use and meaning of routine differed based on whether
we were talking about routine as a noun, an adjective, or an adverb: routine as the activity
itself; routine activity as the quality of an activity; or an activity done routinely as an
indication of the regularity of the activity. We also recognized that some aspects of
teaching, such as leading a discussion, cut across particular activities or what might also
be called “tasks” while other aspects of teaching refer to particular moves that a teacher
uses for particular effects, such as revoicing during a discussion. For the purposes of this
report, we continue to use the term routine as a placeholder, at the same time that we
agree that we need to develop constructs that are precisely defined.
Across our projects, examples of the ways we have parsed up the work of teaching
include:
Franke & Chan: getting the problem out (problem posing); choral counting tasks
Kazemi, Hintz, Hubbard, Kelley-Petersen: tasks that involve carefully sequenced
problems designed to work on particular computational procedures
UM Math Methods Planning Group: domains of teaching such as teaching while
students are working, leading a discussion, assessing student knowledge
Engle, Stein, Smith: five practices for orchestrating productive mathematical
discussions in order to connect mathematical ideas (anticipating, monitoring,
selecting, sequencing, connecting)
Ghousseini: discourse routines used in leading mathematical discussions aimed at
developing skills in mathematical argumentation
All of these foci seem to differ from the particular way in which Leinhardt has described
routines in her work. She has treated them as “small, socially shared, scripted pieces of
behavior”1 that may serve multiple functions such as managing student behavior,
providing support for presenting and accomplishing lessons, or fostering exchange
between teachers and students. Examples include routines for lining up, passing out
materials, and organizing talk between teachers and students. It appeared that
conference participants were unpacking practice differently. Leinhardt has used the term
1 Leinhardt, G & Steele, M. (2005) Seeing the complexity of standing on the side: Instructional dialogues. Cognition
and Instruction, 23 (1), 87-163.
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routine to refer to teaching tasks that become automated so that the teacher does not have
to think about them. It appeared that we were using routines to refer to the kinds of
activity structures that teachers could think with. Noticing these differences may help us
develop terms and definitions that best convey the foci of our work.
We determined that we are interested in designating those aspects of the work of
mathematics teaching that might have some specified, predictable, or planned structure.
Teaching actions can be anticipated and repeated in logical and sensible way that teachers
can learn about, learn to do and design for themselves. Learning to do these activities by
deliberately practicing them (in the sense of repeating enactments of the activity with
coaching) was a key thread across our work. We agreed that we should continue to
specify those aspects of the work as well as what we envision is improvisational or
flexible when using instructional routines. We agreed that it was as important to learn
how to structure teacher education for the learning of good judgment when improvisation
is required as it is to focus on the repeated aspects of an instructional activity which could
be rehearsed in advance.
Major Outcomes and Next Steps
Our conference ended with a discussion about the possible ways that we might engage in
future work together as well as critical research questions that we believed could be
pursued. We agreed that the field is struggling with issues about how professional
education impacts practice and that our continued collaboration and coordination, if done
carefully, could position us well to make a significant contribution to the field.
Our ideas about continued work included:
1. Proposing a set of “routines” that could be worked on across settings and comparing
what teachers learn from them (while keeping in mind that “routines” might not be
the best term for what we are working on).
Such a proposal would need to explain why any specific set of routines should be
selected, including an articulation of both what kinds of mathematical competence
they aim to develop in K-12 students, and why we consider them to be
particularly fruitful as structures within which to conduct professional education.
In addition, since there would be no singular way to enact a routine and no
version of a routine that would be appropriate for every situation, a challenge of
proposing such a set of routines in teacher education would make it necessary to
also choose and explain a set of principles that could guide professional
implementation of the routines by novices in the complex and nuanced arenas of
practice. Research questions would include: What is a productive “grain size” for
a pedagogical routine? How do we choose routines that are “high leverage” for
teacher education student learning while also enabling novices to do work that
spans a range of K-12 content? How might novice teachers acquire the
professional judgment to decide when to use and how to adapt routines? How do
routines enable novice teachers to learn in, from, and through practice? How do
issues of identity or the kind of teacher that one is becoming factor into how
teachers take up routines in their own classrooms?
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2. Analyzing the role of the teacher educator.
Identifying routines or instructional activities as the focus of teacher education
would mean that the teacher educator could not continue to function in ways that
we associate with the university professor. He or she would be engaged in
modeling, preparing structured lesson plans, and coaching, as well as observing
and debriefing practice. How would teacher educators learn to do these kinds of
work? How does the teacher educator support teacher learning through his/her
role in rehearsal and feedback to the novice teacher? How would these new roles
incorporate and complement the kind of teaching that now occurs in foundations
and methods courses, or workshops for practicing teachers?
3. Understanding, and learning to act on, the tension between specificity and precision
in teaching on the one hand and flexibility and creativity on the other.
Participants remarked several times on the work that Pam Grossman and
colleagues2 have done comparing the professional education of clinical
psychologists, social workers, and the clergy with teacher education, and their
focus on the extent to which those professions specify dimensions of the work in
contrast to the way teacher educators handle teaching as a global entity. The
instructional activity that Graziani demonstrated was found to be useful as an
example of what tightly specified teaching practice could look like, and we saw
how this specificity enabled a different kind of teacher education. Leinhardt also
raised other highly specified examples such as Montessori and theatre training.
Considering the specificity we find in other professions, we asked what we might
experiment with in order to study the impact of different ways of organizing and
arranging teacher education on teachers’ practice.
4. Engaging ideas about trajectory of learning for novices and experienced teachers.
The video of novice enactment we watched spurred the group to talk more
carefully about what a routine might look like with a beginner compared to a
more skilled teacher. The difference may partly be in the smoothness or fluency
with which the parts of the routine are put together, but also in how the novice
handles moments when the routine does not make clear what action to take in
response to student input. How might we study and build a trajectory for the
kinds of judgments and practices that teachers make as they learn in, from, and
through practice using routines as a form of disciplined improvisation?
5. Comparing our work to research on learning complex perfomance in other
professional and non-professional domains.
Throughout the meeting, both as planned by the organizers and in comments by
the participants, analogies were made to the role of routines in other complex
activities as a basis for discussing how the teaching and learning of routines could
contribute to more competent practice. How might such comparisons allow us to
better ask ourselves what our rationale and goals are for decomposing
mathematical practice and what it takes for novice teachers to bring these
decompositions back together into ambitious practice?
6. Studying K-12 student learning.
2 Grossman, P., Compton, C., Igra, C., Ronfeldt, M., Shahan, E., & Williamson, P. (unpublished manuscript).
Teaching practice: A framework for the teaching of practice in professional education.
6
We recognized that it would be important to study the effect that routines have on
the experience of students in the classroom. A major focus of our intent to
propose a set of routine activities is to help teachers teach ambitiously, to be
responsible to help all students perform competently. We need to better formulate
the hypothesis that routines, as we have conceived them, can support ambitious
teaching, and in turn, be useful tools for accomplishing ambitious learning goals.
SIGNIFICANCE OF OUR WORK
Mathematics educators are among the leaders in teacher education in theorizing about practice-
based education.3 Yet, we are not satisfied that we are preparing teachers in ways that enable
them to grow as professionals who take students’ disciplinary knowledge and dispositions
seriously. We recognize the need to advance our work as teacher educators. Our research and
development agenda promises to push on our successes in developing teachers’ ability to analyze
depictions of practice towards improving their ability to use such knowledge judiciously in their
direct interaction with students. We hypothesize that developing our efforts to help teachers
develop the performative aspects of teaching through carefully selected and specified
instructional routines will create stronger, more skilled teachers. Our experimentation and study
of instructional designs in teacher education can move the field forward as we take up
Grossman’s challenge of better developing teachers’ clinical practice and their ability to teach
ambitiously.
3 Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of
professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession (pp. 3-31).
San Francisco: Jossey-Bass.
Lampert, M., & Ball, D. L. (1998). Teaching, multimedia, and mathematics: Investigations of real practice. New York:
Teachers College Press.
Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of
Teachers of Mathematics.
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  • Apr 2013
  • TEACH COLL REC
Background For decades, scholars have argued that teaching and learning depend fundamentally on the quality of relationships between teachers and students, yet there is little research about how teachers develop relationships with students or how teacher education prepares teachers to do this work. Arguably, articulating the relational practices of teaching is critical for those aiming to prepare teachers to reach across differences, educate from a social justice perspective, and teach an increasingly diverse population of students. Noting the emphasis on relationships in community-based organizations (CBOs), the authors investigated preservice field placements in CBOs as potentially strategic contexts for learning about relational aspects of teaching. Objective The authors engaged the questions: What do candidates learn in CBO field placements? What are sources of variation between candidates’ learning outcomes? What are individual and contextual factors that shaped candidates’ opportunities to learn in CBOs? Specifically, which factors influenced candidates’ inclination and capacity to enact relational teaching practices (e.g., the methods and skills associated with learning about and connecting with students, families, and communities)? Research Design This study was a 3-year longitudinal investigation. Authors followed two cohorts of candidates from their first quarter of preparation into their first year of teaching. Qualitative methods, such as interviews, observations, and document review were employed in this inquiry of 12 case study candidates. To examine questions of variation, authors also conducted an in-depth comparative case analysis of a subset of two candidates and their CBO placement contexts. Findings CBO placements facilitated opportunities for candidates to “see students”: candidates developed deeper understandings about children and more nuanced conceptions of diversity; experienced and examined school from an out-of-school perspective; and demonstrated greater attentiveness to the role of context in learning. The more detailed comparative analysis of two cases revealed variation in candidates’ experiences and their enactment of practices involved in building relationships with children and families. This analysis identified individual and situational factors (in coursework and CBOs) that facilitated and impeded candidate learning in CBOs. Conclusions Findings from this study highlight the types of learning outcomes that preser-vice community-based placements potentially afford, as well as factors that make some placements more educative than others. The authors offer a theoretical lens that attends to variation in learning, which could be leveraged in future empirical work. This research contributes to the field's developing efforts to identify key social justice teaching practices and to conceptualize pedagogies of enactment for such practices.
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Teaching to "The Good Ones"? Examining the Relationship Between Inequity and the Practice of and Preparation for Postsecondary Mathematics Instruction.
Thesis
  • Jan 2016
This dissertation focused on inequity in calculus instruction through a two-part study that built on the findings from an earlier exploratory study. The exploratory study, conducted in the same department, revealed connections between personal theories of mathematics intelligence that doctoral student instructors (DSIs) held for themselves and those that they held for their students. The first component of the dissertation project was a design intervention study that examined a practice-based approach to preparing DSIs to give students equitable feedback, a core instructional practice, in their postsecondary calculus instruction. The second component was a comparative investigation of teacher/student interactions across identity difference in postsecondary calculus instruction. Four of the instructors from the intervention study were observed and interviewed throughout their first semester of teaching to examine their interactions with their undergraduate students across identity difference. The three articles in this dissertation focus on the findings from this second study. The findings suggested that the DSIs, who were members of overrepresented groups (i.e., majoritized students identifying as men and Asian or White), held some common understandings about what in meant to do mathematics well, which they used as lenses for gauging their own and others’ potential to successfully navigate mathematics as a discipline. Moreover, evidence from this study indicated that when the DSIs viewed students through these lenses that they noticed different characteristics for minoritized and majoritized students, even when they exhibited similar behaviors. These impressions formed the DSIs’ opinions about the potential of their students, which systematically disadvantaged women, especially those identifying as Latina and Black. Finally, the findings suggested that the DSIs acted on their ideas about intelligence through their teaching practices, creating differentiated access to learning opportunities and marginalizing minoritized students. The resulting inequitable approaches to instructional practices may reduce domain identification and motivation, create lower expectations, and depress performance for minoritized students in mathematics classrooms as explored in the pre-calculus case presented in the third article. These findings support the need for the design of equitable approaches to mathematics instructional practices and the explicit preparation of postsecondary instructors to engage in them.
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Teaching, Multimedia, and Mathematics: Investigations of Real Practice. The Practitioner Inquiry Series
Article
  • Jan 1998
This book describes efforts to develop an approach to teaching and teacher education that is deeply rooted in the study of practice. Drawing on video, graphic, and textual records of a year's worth of mathematics lessons in two elementary classrooms, research was conducted on curriculum and instruction, children's learning, and the culture of the classroom across the school year. Research on the process of using multimedia records of practice to understand teaching is also presented. First, the work discussed in this volume is situated in the context of teacher education and its epidemic challenges. It proposes the idea of investigation as a medium of learning to teach and explores what it might mean to investigate the practice of teaching. Opportunities to investigate how teaching might be designed and used in teacher education, and how beginning teachers might do such investigations using multimedia and computing tools are explored. In chapters 1 and 2, the foundations of this project are examined. Chapter 3 situates the work within the enduring arguments about teacher education and learning to teach. Chapter 4 describes the collection of records of practice that have been assembled. Chapter 5 illustrates the multimedia environment in which these records can be accessed and used to investigate teaching and learning, and the pedagogy of teacher education designed around this environment. Chapter 6 begins with reports on what happens when prospective teachers begin to investigate teaching with an overview of the character of a large number of investigations and case studies of a few projects. Chapter 7 continues with an example of work by one preservice student. Chapter 8 concludes with questions and challenges raised by this work. Finally, an essay by David Cohen is included, in which he analyzes where this work fits in with the history and politics of efforts to bring experience with "real" teaching into teacher preparation, and speculates on where the work might lead. (Contains 129 references.) (ASK)
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