Instructional coaching in mathematics requires drawing upon knowledge and expertise from multiple domains of knowledge, such as mathematics content knowledge and knowledge of teacher practice, to name just two.  The theory of change envisioned by most proponents of mathematics coaching is that the coach helps the teacher increase both mathematics content knowledge and pedagogical content knowledge, which results in changes in teacher practice, which impacts student knowledge.

Relationships between subject area knowledge of teachers and teacher practice are of interest in understanding the preparation and professional development of teachers as well as in assessing teacher performance. Additionally, if teacher practice is changed, student understanding in mathematics should improve.  This session explores the relationship between Mathematics Knowledge for Teaching (MKT) and Inside the Classroom – Classroom Observation Protocol (ITC-COP) in a sample of 129 teachers from 25 school districts across seven states. Using linear and ordinal mixed models to account for a random district effect on ITC-COP measurements, modest relationships were identified between MKT and seven of eight different aspects of the ITC-COP.  

This session investigates claims that teachers’ mathematics knowledge for teaching explains facets of teacher practice. It uses a sample of 129 teachers from 25 school districts across seven states to explore relationships between data from a commonly used, valid and reliable multiple-choice measure of teacher mathematics knowledge for teaching (the Mathematics Knowledge for Teaching, MKT, Hill et al., 2004) and data from a commonly used, valid and reliable classroom observation protocol (the Inside the Classroom – Classroom Observation Protocol, ITC-COP, Horizon, Inc., 2000). The analysis explores the question whether data about teacher mathematics knowledge is useful in explaining elements of teacher practice and compares teaching practice ratings between low, medium, and high knowledge teachers.

This research situates well among recent studies (Hill et al., 2008; Hill et al., under review; and Stein and Kaufman, 2010) that have also investigated the relationship between teacher knowledge and practice. This research differs from these recent studies because it uses a larger sample of teachers, a more diverse setting (in terms of district type and curriculum used), and two instruments that are widely used but not necessarily designed to work in concert.

Additionally, impacts on student mathematics achievement, based on a sample of teachers being coached in one state and a comparison group, is examined using a traditional 2 (participating teachers vs. comparison teachers) by 2 (2009 ISAT mathematics vs. 2010 ISAT mathematics) repeated-measures ANOVA[1] and an alternative analysis approach based a value-added model which uses “binning” of student growth scores.  The primary question of interest was whether teacher participation in the coaching project had an impact upon the mathematics achievement of their students.

The results of the ANOVA showed that students of teachers in the project increased their mathematics achievement scores in 2010, while comparison students did not, although the effect size for this result is very small.  The results of this binning procedure for the students of participating teachers compared to other students in the same districts suggests that students of teachers working with coaches grew more on the state mathematics assessment from 2009 to 2010 than did other similar students during the same time period. This was particularly true for the students at the highest bin levels.

The session will be organized around the three central questions described below.

 

1. Can a paper and pencil assessment of a teacher’s mathematics knowledge for teaching significantly explain aspects of the teacher’s classroom practice, as measured by a classroom observation protocol?
2. If teachers are binned as displaying low, medium, or high levels of mathematics knowledge for teaching, are there significant differences in the practices of teacher in these bins?
3. In what ways are student achievement in mathematics impacted by teachers engaged in a mathematics coaching process?

The session will be organized according to the following timeline.

10 minutes: Project introduction and overview

15 minutes: Presentation of methodology and results for teacher content knowledge and practice relationships

10 minutes: Small group discussion of findings and ideas for changes in analysis

15 minutes: Presentation of methodology and results for student impact

10 minutes: Small group discussion of findings and ideas for changes in analysis methods

20 minutes: Large group discussion and share out

10 minutes: Summary and next steps

------------

90 minutes total

This session will address the priority area of professional learning by examining the research regarding relationships of mathematics content knowledge to practice to student impacts.