Over the last 50 years, the International Association for the Evaluation of Educational Achievement (IEA) has conducted more than 23 large-scale comparative studies of student achievement. The work associated with teacher preparation as well as experience gained in many of IEA's studies, such as TIMSS, led to a request from members of the organization for an in-depth investigation of teacher preparation and training, particularly in terms of the subject area of mathematics. This document provides the framework and specifications for the first IEA study of teacher preparation and training of primary and lower secondary mathematics teachers. The framework outlines a comprehensive approach to investigating and understanding teacher preparation around the world and includes an attempt to understand how national policies and institutional practices influence the outcomes of beginning teachers. This focus on what beginning teachers know and can do makes this study the first of its kind. The overall study has three overlapping components: (1) Component I: Studies of teacher education policy, schooling, and social contexts at the national level; (2) Component II: Studies of primary and lower secondary mathematics teacher education routes, institutions, programs, standards, and expectations for teacher learning; and (3) Component III: Studies of the mathematics and related teaching knowledge of future primary and lower secondary school mathematics teachers. The key research questions for the study focus on the relationships between these components, such as relationships between teacher education policies, institutional practices, and future teacher outcomes. Appended are: (1) Study Design and Data Sources; (2) Item Samples; (3) Expert Panel Meetings; and (4) List of National Research Centers Participating in TEDS-M. (Contains 1 figure, 17 tables, 4 boxes, and 14 footnotes.) [This paper was written with contributions from William Schmidt, Kiril Bankov, Michael Rodriguez, Martin Carnoy, Richard Houang, Lee Cogan, Lynn Paine, and Eduardo Rodrigues.]