1. Leadership Knowledge and Skills that Mathematics Coaches Utilize to Make Instructional Shifts
Mason Coaching Institute for Math and Literacy
April 1, 2017
Laura E. Bitto, Ph.D.
Adjunct Faculty
George Mason University

2. Agenda The leadership knowledge and skills of mathematics coaches
AMTE’s EMS Standards
Study results
Teacher Leader dispositions and skills
Mathematical Instructional Shifts
Scenario discussions applying these leadership knowledge and skills to math coaching
Utilizing leadership knowledge and skills to make instructional shifts

3. Getting to Know You What’s your current position?
Teacher
Specialist/coach
Administrator or Supervisor
Student
Turn to a neighbor and introduce yourself
Name
Connection to coaching

4. Standards for Elementary Mathematics Specialists (AMTE, 2013)
Content knowledge for teaching mathematics (CKTM):
Deep understanding of mathematics for grades K–8
Further specialized mathematics knowledge for teaching
Pedagogical knowledge for teaching mathematics (PKTM):
Learners and learning
Teaching
Curriculum and assessment
Leadership knowledge and skills (LKS)
In 2010, AMTE created standards to assist states as they created the certification programs. These were revised in 2013.
AMTE has named 3 major areas in which the coursework for the certification should include:
CKTM: 1) lists math content- Number and Operations; Algebra and functions; Geometry and measurement; Data Analysis and Probability
2) Specialized knowledge- mathematical processes: precision, model with mathematics, reason abstractly… Support and develop mathematical proficiencies such as procedural fluency, conceptual understanding, Diagnose student errors
EX: not only knowing how to divide fractions but understanding why the “invert and multiply” algorithm works and being able to articulate that conceptual understanding precisely.
EX: Examine a student-invented algorithm or non-standard solution to a problem and be able to understand what and why the student is performing and if it will work in every situation
PKTM: learning trajectories, using questions to probe for mathematical understandings, choosing manipulatives to model mathematics
EX: Using a manipulative to let students conceptualize what division of fractions means
LKS: Broad view of mathematics; being a life long learner; facilitate collaborative learning; plan, develop, implement, evaluate professional development programs, coach, mentor, communicate professionally about students, curriculum and work with adult learners
I asked – what do the roles and responsibilities look like from place to place? Are the people in these roles certified? If not, what are their experiences enabling them to do their jobs?

5. AMTE’s (2013) Leadership Knowledge and Skills
“EMS professionals need to be prepared to take on collegial, non-evaluative leadership roles within their schools and districts. They must have a broad view of the many aspects and resources needed to support and facilitate effective instruction and professional growth” (p. 8).
“Use mathematics-focused instructional leadership skills to improve mathematics programs at the school and district levels, e.g., serve as coach/mentor/content facilitator – providing feedback to colleagues to strengthen practice and improve student learning; develop appropriate classroom- or school-level learning environments; build relationships with teachers, administrators and the community; collaborate to create a shared vision and develop an action plan for school improvement; establish and maintain learning communities; partner with school-based professionals to improve each student’s achievement; mentor new and experienced teachers to better serve students” (p. 9).

6. Study Results: Bitto (2015)
The 10 specialist participants used their CKTM, PKTM, and LKS simultaneously while acting in their roles and fulfilling their responsibilities.
LKS are at the forefront of their actions, serving as important vehicles for supporting, developing, and using CKTM and PKTM.

7. LKS are at the forefront of Specialists’ Actions
EMS are teacher leaders. Their LKS drive their actions.

8. Implications Elementary mathematics specialists are teacher leaders
Teacher leadership comprises the work of a variety of educational positions, both formal and informal, with all sharing the hope of “continuous improvement of teaching and learning in our nation's schools, with the result being increased achievement for every student” (York-Barr & Duke, 2004, p. 255)
Teacher Leadership Skills Framework (Center for Strengthening the Teaching Profession, 2009)
Teacher Leadership Competencies (Center for Teaching Quality et al., 2014)
Teacher Leader Standards (Teacher Leadership Exploratory Consortium, 2011)
Being “in between” teachers and administrators now has a name – T-L: they are not an administrator, nor do they only teach
When I situated results from this study within teacher leadership literature I realized:
Teacher leadership is a broad definition
But recently teacher leadership skills framework (Center for Strengthening the Teaching Profession [CSTP], 2009), teacher leadership competencies (Center for Teaching Quality et al., 2014), and teacher leader standards (Teacher Leadership Exploratory Consortium, 2011) have been developed
dispositions, knowledge, and skills utilized by teacher leaders are more clearly defined
TL’s dispositions, knowledge and skills parallel to math specialists’
The roles and responsibilities of math specialists are teacher leader roles and responsibilities. Their LKS drive their actions.

9. Teacher Leader Dispositions Skills Lifelong learner
Ability to balance their work demands
See the broader view of the educational system within which they work, and believe that they can impact it positively
Ability to work with adult learners
Effective communication

10. Context is Unique Not usually a “one-size fits all” response/action
What works for reaching one teacher may or may not work for reaching another
Focus of coach’s actions should be based on student learning/instructional shifts

11. Instructional Shifts: McGatha and Bay-Williams (2013) p. 167

12. Instructional Shifts: McGatha and Bay-Williams (2013) p. 167

13. Scenario Discussions
What are possible options of action for the math coach?
Which option encourages instructional shifts towards best mathematical teaching practices?

14. Scenario 1: The Lesson
A mathematics coach is in a 3rd grade classroom while the teacher is delivering the mathematics lesson.
The teacher is using a direct instruction style of teaching to introduce comparing and contrasting solid geometric figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the number of vertices, and edges, and the number and shape of faces. (SOL 3.14)
The teacher holds up a model of the figure and then has the class discuss the solid’s characteristics and then tells information about the characteristics.
The teacher gives correct information about the cube, rectangular, prism, square pyramid, and sphere but as she holds up the cone she tells the students it has 0 vertices, 1 edge, and 2 faces. As she holds up the cylinder she tells the students it has 0 vertices, 2 edges, and 3 faces.
Next, the teacher plans to have the students get into small groups and give each group models of the solid for them to complete a chart of the characteristics in the small groups.

15. Scenario 1: Contextual Background
The teacher is in her 4th year of teaching but spent her first 3 years teaching 1st grade. This is her first year teaching 3rd grade.
The teacher has been comfortable with the coach observing her lessons but has not yet been open to planning with the coach or sharing the instruction (neither co-teaching nor demonstration teaching)

16. Scenario 1: What does the coach do?
What are possible options of action for the math coach?
Which option encourages instructional shifts towards best mathematical teaching practices?

17. Scenario 2
The coach has scheduled a pre-conference with a teacher to help her plan an upcoming lesson
The teacher cancels on the coach three times with a variety of excuses about pop-ups on her calendar
Contextual Background:
The coach is the one asking the teacher to participate in a coaching cycle (the teacher did not seek out the coach)
The teacher has 12 years of teaching experience
The teacher tends to teach most lessons with a direct instruction/correct answer approach but her State assessment scores are “strong”

18. Scenario 2: What does the coach do?
What are possible options of action for the math coach?
Which option encourages instructional shifts towards best mathematical teaching practices?

19. Scenario 3
A teacher set a goal that she would like to shift her instruction from math being made easy for the students towards engaging the students in productive struggle
The teacher has tried a few lessons that she and the coach developed together but is feeling very frustrated with the results of the lessons. She feels that the students are not trying to solve the math but just giving up and waiting for her to show them what to do.
Contextual background:
The teacher has 6 years of experience
The teacher and a coach have been working together for a few years
The coach has been a part of the lesson development and lesson debriefing but because of scheduling conflicts has not seen the lessons delivered

20. Scenario 3: What does the coach do?
What are possible options of action for the math coach?
Which option encourages instructional shifts towards best mathematical teaching practices?

21. References
Association of Mathematics Teacher Educators (2013). Standards for elementary mathematics specialists: A reference for teacher credentialing and degree programs. San Diego, CA: AMTE.
Bitto, L. E. (2015). Roles, responsibilities, and background experiences of elementary mathematics specialists (Doctoral dissertation).  Available from ProQuest Dissertations and Theses database.  (UMI No )
Center for Strengthening the Teaching Profession. (2009). Teacher leadership skills framework. Retrieved from Center for Strengthening the Teaching Profession website:
Center for Teaching Quality, National Board for Professional Teaching Standards, & National Education Association. (2014). The teacher leadership competencies. Retrieved from Center for Teaching Quality website:
McGatha, M. B., & Bay-Williams, J. M. (2013). Making shifts toward proficiency. Teaching Children Mathematics, 20(3), 162–170.
Teacher Leadership Exploratory Consortium. (2011). Teacher leader model standards. Washington, DC. Retrieved from
York-Barr, J., & Duke, K. (2004). What do we know about teacher leadership? Findings from two decades of scholarship. Review of Educational Research, 74(3), 255–316. doi: /

22. Thank you!
Laura E. Bitto, PhD