Accounting for Co-Teaching: A Guide for Policymakers and Developers of Value-Added Models

Abstract

We outline the options available to policymakers for addressing co-teaching in a value-added model. Building on earlier work, we propose an improvement to a method of accounting for co-teaching that treats co-teachers as teams, with each teacher receiving equal credit for co-taught students. Hock and Isenberg (2012) described a method known as the Full Roster Method (FRM) that is feasible and practical, but it effectively counts co-taught students more than once—these students receive a full weight with each of their teachers, so such students receive extra weight when calculating the relationship between student characteristics and achievement. The improvement, known as the Full Roster-Plus Method, allows co-taught students to receive full weight with their teachers, but all students contribute equally to the calculation of the relationship between student characteristics and achievement. To investigate how the application of this method empirically changes value-added estimates, we use data from District of Columbia Public Schools. We find that there are very small empirical differences between the two methods.

Keywords:

• Full Roster Method
• co-teaching
• value added

Notes

In all variants of the FRM and FRM+, each teacher variable is a column vector with a “1” for every student whom the teacher taught, and a “0” for all other students. The dosage for each student is implemented as a weight, and the model is estimated via weighted least squares. See the appendix for details.

For computational reasons, it is a good practice to add one to the dosage of the student with the maximum dosage to set the total dosage for all students. For example, if the greatest student dosage is three (hundred percent), set the total dosage at four. For a student who is claimed by only one teacher for the whole year, the associated shadow teacher would then have a dosage of three for a total dosage of four for this student. This step ensures that all teacher-student records are replicated. Otherwise, students who are at the maximum total dosage value would not be replicated, which can lead to computational problems if some shadow teachers are linked to few students. This adjustment has no practical consequences for standard errors or point estimates.