Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999, 2003, 2007, and 2011. For countries with data back to 1995, TIMSS 2015 will provide the sixth in a series of trend measures collected over 20 years. Approximately 60 countries have TIMSS trend data, and new countries join TIMSS in each cycle. About 70 countries are expected to participate in TIMSS 2015. TIMSS uses the curriculum, broadly defined, as the major organizing concept in considering how educational opportunities are provided to students, and the factors that influence how students use these opportunities. The TIMSS Curriculum Model has three aspects: the intended curriculum, the implemented curriculum, and the attained curriculum (see Exhibit 1). These represent, respectively, the mathematics and science that students are expected to learn as defined in countries' curriculum policies and publications and how the educational system should be organized to facilitate this learning; what is actually taught in classrooms, the characteristics of those teaching it, and how it is taught; and, finally, what it is that students have learned and what they think about learning these subjects. To provide standard information across countries that supplements the chapters, countries complete a curriculum questionnaire about their mathematics and science curricula, school organizational approaches, and instructional practices. TIMSS also asks students, their teachers, and their school principals to complete questionnaires about their school and classroom instructional contexts for learning mathematics and science. Data from these questionnaires provide a dynamic picture of the implementation of educational policies and practices that can raise issues and provide avenues relevant to educational improvement efforts. With the current emphasis on college and career readiness and increasing global competitiveness in STEM fields, in 2015 TIMSS Advanced once again will be joined with TIMSS. This is the first time since 1995 that TIMSS together with TIMSS Advanced will provide countries with a complete profile of mathematics and science learning from elementary through the end of secondary school. Each country that participates in TIMSS Advanced 2015 gains critically valuable information on the following: (1) The numbers of students and the proportion of the overall student population who are participating in advanced mathematics and physics study at the end of secondary school; (2) The achievement of these students based on international benchmarks (advanced, high, and intermediate); and (3) A rich set of contextual data on curricula, teaching and learning strategies, teacher preparation, school resources, and student preparation and attitudes that can be used to guide education reform and policy planning in STEM fields. TIMSS 2015 at the fourth grade has a new, less difficult mathematics assessment called TIMSS Numeracy. TIMSS Numeracy is designed to assess mathematics at the end of the primary school cycle (4th, 5th, or 6th grades) for countries where most children are still developing fundamental mathematics skills. Together with IEA's prePIRLS reading assessment, TIMSS Numeracy is intended to be responsive to the needs of the global education community and efforts to work towards universal learning for all children. Following an introduction by Ina V. S Mullis, Chapter 1 (Liv Sissel Gronmo, Mary Lindquist, Alka Arora, and Ina V. S. Mullis) describes in some detail the major content and cognitive domains in mathematics. Chapter 2 (Lee R. Jones, Gerald Wheeler, and Victoria A. S. Centurino) presents the same information for the science framework. Chapter 3 (Martin Hooper, Ina V. S. Mullis, and Michael O. Martin) contains the TIMSS 2015 Contextual Framework describing the types of learning situations and factors associated with students' achievement in mathematics and science that will be investigated via the questionnaire data. Finally, Chapter 4 (Michael O. Martin, Ina V. S. Mullis, and Pierre Foy) provides an overview of the TIMSS 2015 Assessment Design, including general guidelines for item development. Appendices include: (1) Acknowledgements; (2) Example Mathematics Items for Grade 4 and Grade 8; and (3) Example Science Items for Grade 4 and Grade 8. [The TIMSS & PIRLS International Study Center works closely with the IEA Secretariat in Amsterdam and the IEA Data Processing and Research Center in Hamburg. Also, Statistics Canada is responsible for school and sampling activities and Educational Testing Service in Princeton, New Jersey provides guidance on psychometric methodology. In particular, a great deal of the credit for TIMSS is due the National Research Coordinators designated by the participating countries to be responsible for the complex tasks involved in implementing the studies in their countries.]