Developing anchor points to enhance the meaning of the mathematical and mathematical pedagogy score scales from the TEDS-M study

Abstract

The Teacher Education and Development Study (TEDS-M), a cross-national study of teacher education programs that prepare future primary and secondary mathematics teachers, included a series of measures of mathematics achievement designed to determine what prospective teachers knew and could do concerning the mathematics that they would likely teach. One of the goals of the study was to report the information about prospective teachers' knowledge and skills in a way that is easy to understand by the numerous audiences for the results of the study. The values that are reported are often obtained using an item response theory (IRT) model that gives estimates of a location on the latent scale for a hypothetical construct. For any of these numerical values, it is difficult to interpret what a person knows or can do. At best, the numbers can be used to order persons or groups according to the magnitude of what they know or can do, but not whether they have particular capabilities such as being able to solve systems of linear equations. Meaning was added to the reporting scales by attaching detailed substantive descriptors to selected points on the scale called anchor points. The logic and methodology used to add descriptions to anchor points is similar in many ways to methodologies used elsewhere, such as item mapping or scale anchoring. However, there are some important differences between the procedure used for TEDS-M and those used with other testing programs such as NAEP, TIMSS, and PISA. The purpose of this chapter is to describe how the descriptive information was added to the scales using the TEDS-M anchor points, and to discuss how the interpretations derived from these descriptions differ from those used with other assessment programs.