Examining
Mathematics Coaching (EMC) Defining
Coaching Knowledge: The Results of a Modified
by John
T. Sutton, RMC Research Corporation Elizabeth
Burroughs, David
Yopp, The Examining Mathematics Coaching (EMC) project has identified two major
knowledge domains that are postulated as primary contributors to effectiveness
for classroom mathematics coaches: Mathematical Content Knowledge and Coaching
Knowledge. While the literature is quite rich in providing details and
definitions surrounding what constitutes Mathematical Content Knowledge, there
is very limited information related to what constitutes Coaching Knowledge. In
an effort to define Coaching Knowledge at the outset of the project to inform
and guide instrument development to measure Coaching Knowledge, the EMC project
decided to conduct a modified Delphi study to develop an operational definition
of Coaching Knowledge that capitalizes on the existing knowledge of experts in
the field of mathematics coaching. For the EMC efforts to define Coaching Knowledge, a three-phase
process engaged 12 national experts and practitioners in the area of
mathematics coaching (see Acknowledgments below) over an 18-day period (October
1–18, 2009) to: Additionally,
as part of the third phase, respondents had the opportunity to provide
additional comments intended to clarify, refine and enhance the definitions
based on their unique perspective and expertise. The schedule and timeframe for
the EMC modified Phase 3 provided respondents the opportunity to rate their
level of agreement regarding the definition for Coaching Knowledge, unique from
teaching knowledge, derived from responses in Phase 2, in each of seven areas:
Leadership, Relationships, Assessment, Teacher Learning, Teacher Development,
Teacher Practice and Student Learning. (The full survey can be downloaded as a PDF
file by clicking this link.) In addition to rating levels of agreement for the four
questions, respondents also were provided the opportunity for additional
comments as part of the Phase 3 validation process. Four open-ended questions addressed
words, phrases or key features that respondents may have considered missing,
unclear, worthy of removal, or necessary to enhance the overall definition. (The
actual questions can be viewed by accessing the file using this link.) Definitions provided for Phase 3 review will inform the
definitions that EMC staff will use to develop instruments to measure Coaching Knowledge
in each of the seven areas, along with Communication, an area sufficiently
identified as a knowledge area in Phase 1 that required no additional
elaboration or agreement. The following definitions are provided as part of
this summary. Additional comments provided by respondents will be considered in
future reviews and possible modifications to Coaching Knowledge definitions by
EMC researchers or others. Results of ratings for each question are conveyed as a table
before each of the agreed-upon definitions. As can be seen, for all questions,
across all seven Coaching Knowledge definition areas, the majority of responses
were in the “Agree” or “Strongly Agree” responses. Coaching Knowledge of Leadership Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 1 2 5 2 This definition captures my
thinking related to … 0 2 4 3 1 This definition enhances my
thinking related to … 1 1 5 1 2 This definition can help
inform my work. 0 1 3 3 3 Knowledge of
Leadership A coach knows leadership models and possesses the ability to
identify, define, and communicate specific goals and objectives that relate to
student success and align with the institution’s vision for mathematics. The
coach uses this vision and knowledge to inform work with other school leaders,
to highlight the gap between teachers’ espoused beliefs and actions, to develop
trust with teachers and administrators, and to develop a deep understanding of
the professional development process and impacts. A coach knows various ways to
address challenges and how to communicate in ways that advocate for, negotiate
with, and influence others. Coaching Knowledge of Relationships Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 0 3 7 0 This definition captures my
thinking related to … 0 0 3 7 0 This definition enhances my
thinking related to … 0 0 4 6 0 This definition can help
inform my work. 0 0 5 5 0 Knowledge of
Relationships A coach knows how to communicate professionally with a
variety of audiences, and knows how to establish and maintain rapport and
credibility with teachers based on trust, empathy, mutual understanding and
confidentiality. A coach knows about environments where positive relationships
take place, including challenging and safe learning environments for teachers
and students, collaborative working environments, and environments where people
share common beliefs and goals with honest reflection. The coach knows how
autonomy, issues of authority, and sociocultural aspects of class, race and
gender for students and teachers influence relationships. A coach knows a range
of concepts, theories and frameworks (e.g., adult development, educational
belief systems, cognitive styles, etc.) and how those relate to teachers,
teachers’ views of teaching and learning, and students. Coaching Knowledge of Assessment Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 0 5 4 1 This definition captures my
thinking related to … 0 0 5 4 1 This definition enhances my
thinking related to … 0 1 5 2 2 This definition can help
inform my work. 0 1 6 2 1 Knowledge of
Assessment A coach knows how to diagnose teachers’ needs – personal,
instructional, content and management – and how data and assessment of student
thinking inform instruction and work with teachers. The coach knows how to
assess and use teacher content knowledge and pedagogical content knowledge to
inform, grow and support teachers. A coach deeply understands formative and
summative classroom assessment and knows how to set goals for assessing
effectiveness of lessons. A coach also knows how to select, adapt and align
curricula with assessments; knows how to use common learning trajectories; and
knows when looking at student work is better than looking at numerical
assessment results. The coach knows how to help teachers use assessment data to
make informed decisions about instruction and student learning, and knows what
teachers know about assessment, including different types, their uses, and
limits. Coaching Knowledge of Teacher Learning Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 1 6 3 0 This definition captures my
thinking related to … 0 2 5 3 0 This definition enhances my
thinking related to … 0 2 5 3 0 This definition can help
inform my work. 0 1 6 3 0 Knowledge of Teacher
Learning A coach knows about teacher motivations; the myriad ways
that teachers know and understand mathematics content; and the teacher’s
pedagogical and pedagogical content needs, which may or may not be recognized
by the teacher. A coach knows developmental continuums, potential learning
trajectories, and teacher beliefs about learning. A coach knows how to develop
tasks that support teacher learning through reflective practice and
self-directed goal-setting, and knows when to consult and when to collaborate.
A coach knows there can be a gap between a teacher’s knowing a strategy and
effectively using a strategy. Coaching Knowledge of Teacher
Development Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for …* 0 1 5 3 0 This definition captures my
thinking related to …* 0 1 5 3 0 This definition enhances my
thinking related to …* 0 1 7 0 1 This definition can help
inform my work.* 0 1 6 2 0 *One participant did not
respond to this item. Knowledge of Teacher
Development A coach knows various models of teacher stages of
development, adult change, and the continuum of learning that teachers often experience
(e.g., from beginning to experienced to expert teacher). A coach knows how to
diagnose where a teacher is, recognize potential learning trajectories, and
differentiate strategies to support an individual teacher’s growth. A coach
knows the motivations for growth and barriers to growth and recognizes the role
of reflection and feedback. Coaching Knowledge of Teacher Practice Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 1 6 3 0 This definition captures my
thinking related to … 0 1 6 3 0 This definition enhances my
thinking related to … 0 1 5 2 2 This definition can help
inform my work. 0 2 6 1 1 Knowledge of Teacher
Practice A coach knows teacher beliefs about teaching practice along
with a depth and breadth of knowledge of all types of practice for effective
management and learning, (e.g., lesson planning, school support structures,
learning environments, models of instruction, mathematical tasks, assessment,
and strategies that support students based on factors such as age, gender,
culture and ELLs, etc.). A coach knows when to use these and how they translate
into teacher actions in classrooms for effective teaching and learning. Additionally,
a coach knows research on effective teaching and learning, instructional
strategies, and cognitive development on how children and adolescents learn. Coaching Knowledge of Student Learning Strongly Disagree Disagree Agree Strongly Agree Neither Agree nor Disagree This is an accurate
definition for … 0 0 6 4 0 This definition captures my
thinking related to …* 0 0 4 5 0 This definition enhances my
thinking related to …* 0 0 4 4 1 This definition can help
inform my work.* 0 0 4 4 1 *One participant did not
respond to this item. Knowledge of Student
Learning A coach knows how to create and manage mathematical learning
environments that mediate factors in the K-8 spectrum including students’ prior
learning, age, race, gender, economic status, special needs, sociocultural events
and school/district dynamics. A coach knows how to analyze student thinking and
conduct mathematical error analysis, and has facility with a variety of
instructional formats and strategies (mathematical discourse, mathematical
exploration, metacognition, etc.) that help students engage in challenging and
meaningful mathematics problems and tasks. A coach knows how to develop and how
to provide teachers with learning opportunities aimed at improving student
learning by analyzing student work.
File Download of "Coaching Knowledge" Definitions Acknowledgments The EMC research team would like to thank the following
participants in this Delphi study. (This is a partial list; some of our experts
participated anonymously.) Mark Driscoll Diana Erchick Terry Goodman Loretta Heuer Ted Hull Jim Knight Maggie McGatha Amy Morse Liz Sweeney