A Study of Mathematics Coaching in (U. S.) Elementary Classrooms

Elizabeth A. BurroughsMontana State UniversityDepartment of Mathematical Sciences

RCT ConferenceUniversity of York, York, U.K.11 September 2014

Research contributors

Principal InvestigatorsBeth Burroughs, Montana State UniversityJohn Sutton, RMC Research Corp. David Yopp, University of Idaho

Contributing ResearchersMark Greenwood, Megan Higgs, and Jennifer

Luebeck (Montana State University); Brandie Good, Clare Heidema, Dan Jesse, and

Arlene Mitchell (RMC Research Corp.).

Funded under NSF Award No. 0918326. Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.

Context

I’m a U.S. mathematics education scholar, spending the autumn and spring terms at the University of York in the Department of Education as a Fulbright Scholar.

My home is in Bozeman, Montana, at Montana State University

Mathematics classroom coaching A recent development in mathematics

professional development for practicing teachers.

Built on a foundation of coaching in other professions, like business and medicine.

Used by school districts nationwide and encouraged by the U.S. National Mathematics Advisory Panel.

There are a variety of educational coaching models coaches might follow.

Organizing question

What are next steps in mathematics coaching research, professional development, or other collaborations between researchers and coaches?

Examining Mathematics Coaching

EMC is a 5-year research and development project examining the effects of a coach’s knowledge for coaching on a diverse population of grades K-8 teachers

*(K – 8 is students aged 5 – 13, in U.S. elementary and middle schools, or sometimes a K-8 school.)

Mathematics coach: EMC definition

A mathematics coach is an on-site professional developer who enhances teacher quality through collaboration, focusing on research-based, reform-based, and standards-based instructional strategies and mathematics content that include the why, what, and how of teaching mathematics.

Coaching cycle for EMC Project

There are three distinct parts to each coaching cycle designed to examine mathematics instruction. Pre-Lesson Conference (~15

minutes) Lesson Observation (entire class

period) Post-Lesson Conference (~30

minutes)

Coaches conduct 8 cycles per year, with 4 focused on number and operations.*

Limitations

* This is not a study of coaching as an intervention (although it does produce some results along those lines).

Though we gave guidelines, school and district priorities superseded our research wishes. What this leaves is a study of coaching as it is enacted. Certainly this introduces limitations to our findings, but increases our inferential abilities.

EMC research hypothesis

The effectiveness of a mathematics classroom coach is linked to several domains of knowledge. Coaching knowledge and mathematics content knowledge both contribute to a coach’s effectiveness as measured by positive impact on teacher practice, attitudes, and knowledge.

Knowledge domains

Coaching Knowledge

Knowledge of Student

Learning

Knowledge of Teacher Learning

Mathematics Content Knowledge

Impacts of EMC study

Understanding of knowledge needed for effective mathematics coaching.

Understanding of what practices contribute to effective mathematics coaching.

Instruments to evaluate and monitor mathematics coaching

Research design

An observational design will answer: To what extent does a coach’s depth of content knowledge in coaching knowledge and mathematics content knowledge correlate to coaching effectiveness?

An experimental design randomly assigns coaches to one of two groups to answer: To what extent does professional development targeting these two knowledge domains improve coaching effectiveness? and To what extent are the effects of the targeted professional development explained by increases in knowledge?

Crossover designGroup 1 Group 2

Year 12009-10

Provide orientation to EMC coaching model

Year 22010-11 Mathematics Content Knowledge

Year 32011-12 Coaching Knowledge

Year 42012-13 Coaching Knowledge

Year 52013-14 Mathematics Content Knowledge

EMC participants

ColoradoCoaches: 11Teachers: 31

IdahoCoaches: 15Teachers: 44

MontanaCoaches: 19Teachers: 54

N. DakotaCoaches: 3Teachers: 8

NebraskaCoaches: 2Teachers: 6

WashingtonCoaches: 2Teachers: 4

WisconsinCoaches: 4Teachers: 11

Project variables and measures

Coaching Effectiveness

Project variables and measures

Implementation of Coaching

Model

Coaching beliefs,

knowledge, skills, and practice

Coaching Effectiveness

Mathematics Content

Knowledge

Project variables and measures

Implementation of Coaching

Model

Coaching beliefs,

knowledge, skills, and practice

Coaching Effectiveness

Mathematics Content

Knowledge

Teacher Variables

Mathematics Content

Knowledge

Classroom practice

Teacher anxiety, efficacy, engagement,

and preparedness

Coaching emphasis

Coaching impact

Project variables and measures

Implementation of Coaching

Model

Coaching beliefs,

knowledge, skills, and practice

Coaching Effectiveness

Mathematics Content

Knowledge

Teacher Variables

Mathematics Content

Knowledge

Classroom practice

Teacher anxiety, efficacy, engagement,

and preparedness

Coaching emphasis

Coaching impact

Mathematical Knowledge for

Teaching

Coach Reflection and Impact

Coaching Knowledge Survey & Coaching

Skills Inventory

Measures

Teacher Reflection and Impact

Survey

Inside the Classroom

Observation Protocol

Teacher Survey

Teacher Needs

Inventory

Classroom practices: Observational study

Year 5: 2014(N = 135)

Year 4: 2013(N = 153)

Year 3: 2012(N = 169)

Year 2: 2011(N = 189)

Year 1: 2010(N = 196)

16%

12%

6%

5%

3%

25%

27%

26%

22%

14%

16%

15%

11%

15%

8%

16%

15%

17%

15%

15%

17%

18%

23%

20%

26%

10%

12%

18%

22%

29%

0%

1%

1%

2%

6%

Level 1Level 2Level 3: LowLevel 3: SolidLevel 3: HighLevel 4Level 5

Percentage of Teachers

Teac

her O

bser

vatio

n

Level 5: Students highly likely to under-stand maths as a result of instruction

Level 1: Students un-likely to understand maths as a result of in-struction

Research question 1

To what extent does a coach’s depth of knowledge in coaching knowledge and mathematics content knowledge influence coaching effectiveness?

Models examine how variation in these aspects of the coaches propagates into teachers’ measures.

Four years of data included in the analysis.

Summary of findings for RQ1Improvements in coaches’ coaching knowledge scores and self-efficacy measure of coaching skills scores are related to increases in teachers’ mathematics knowledge

As coaches learn more about coaching, as measured both by how much they align with what coaching authors recommend and by their self-reports of effectiveness,

coached teachers perform better on mathematics assessments

Summary of findings for RQ1Coaches with higher mathematics for teaching scores are associated with teachers with higher mathematics for teaching scores.

We suspect that this is a relic of how teachers were chosen.

Research question 2

To what extent does professional development targeting these two knowledge domains improve coaching effectiveness?

Control for coaching intensity and outside PD

Effects are examined on changes in teachers’ mathematics for teaching scores, teachers’ attitudes, and teachers’ practice

Hierarchical linear models Four years of data

Summary of findings for RQ2 No detected coach-level PD effects on

teacher content knowledge or teacher attitude

Some evidence of PD effects on teacher practice

MathCoaching

Coaching

Summary of findings for RQ2

For all models, there are changes over time(Observational results that “coaching works”)

Suggestive evidence that changes happened in the different groups at different times; follow-up analyses are being conducted

Research question 3

To what extent are the effects of targeted professional development on coaching effectiveness explained by increases in coaching knowledge and mathematics content knowledge?

Analysis uses 51coaches randomly assigned to PD groups; 5 years of data

Analysis uses linear modeling, and controls for outside mathematics or coaching training

Summary of findings for RQ3 No evidence for direct effects of professional

development on coaches’ mathematics for teaching scores either in terms of differences in groups or differences in changes over time.

There is evidence of a change over time in mathematics for teaching scores of the coaches in the study, with the highest average score in the last year of the study.

There is evidence of a time effect and a PD effect on the mean scores of coaching knowledge (that is, increases in coaching knowledge that have an effect at the teacher level can be inferred to result from the PD).

Some thoughts about experiments Here, we’re using the model of RCTS,

which measure interventions, to measure effects of knowledge

Hope that this is one study to contribute to overall understanding – too complicated to expect a single study to determine causality

Ongoing struggle: what gets funded (experiments), but an appropriate next step is qualitative descriptions about what coaching entails in vivo.

What we learn from participants Coaches want to learn how to have hard

conversations with teachers about mathematics content —

And about student learning. Coaches expend a lot of energy on

resistant teachers. Professional development in coaching

knowledge is needed, and our model shows promise.

Organizing question

What are next steps in mathematics coaching research, professional development, or other collaborations between researchers and coaches?

Thank you!Beth Burroughsburroughs@math.montana.edu

www.math.montana.edu/~emc