This module is intended to help teachers explore methods by which students work with numbers to formulate generalizations about operations. By expanding students understanding of the properties that underlie the number systems introduced in the elementary grades, they will be prepared to think algebraically for success in middle school and beyond.

What are the "big ideas" in elementary school mathematics? How do students understand them? How can teachers best offer help and support as their students grapple with these ideas? These and other questions about the practice of teaching K-8 mathematics are the focus of Developing Mathematical Ideas (DMI), a powerful, engaging professional development curriculum for current and future teachers. At the heart of a DMI seminar is the casebook, sets of classroom episodes (cases) illustrating student thinking as described by their teachers. In addition to case discussions, the curriculum offers teachers opportunities: to explore mathematics in lessons led by facilitators; to share and discuss the work of their own students; to view and discuss DVD clips of mathematics classrooms; to write their own classroom cases; and to read overviews of related research.

Engineering education in K-12 classrooms is a small but growing phenomenon that may have implications for engineering and also for the other STEM subjects-science, technology, and mathematics. Specifically, engineering education may improve student learning and achievement in science and mathematics, increase awareness of engineering and the work of engineers, boost youth interest in pursuing engineering as a career, and increase the technological literacy of all students. The teaching of STEM subjects in U.S. schools must be improved in order to retain U.S. competitiveness in the global economy and to develop a workforce with the knowledge and skills to address technical and technological issues. Engineering in K-12 Education reviews the scope and impact of engineering education today and makes several recommendations to address curriculum, policy, and funding issues. The book also analyzes a number of K-12 engineering curricula in depth and discusses what is known from the cognitive sciences about how children learn engineering-related concepts and skills. Engineering in K-12 Education will serve as a reference for science, technology, engineering, and math educators, policy makers, employers, and others concerned about the development of the country's technical workforce. The book will also prove useful to educational researchers, cognitive scientists, advocates for greater public understanding of engineering, and those working to boost technological and scientific literacy.

Cash transfers have become a key social protection tool in developing countries and have expanded dramatically in the last two decades. However, the impacts of cash transfers programmes, especially in Sub-Saharan Africa, have not been substantially documented. This book presents a detailed overview of the impact evaluations of these programmes, carried out by the Transfer Project and FAO’s From Protection to Production project. The 14 chapters include a review of eight country case studies: Kenya, Ghana, Ethiopia, Zambia, Zimbabwe, Lesotho, Malawi, South Africa, as well as a description of the innovative research methodologies, political economy issues and good practices to design cash transfer programmes. The key objective of the book is to enhance the understanding of these development programmes, how they lead to a broad range of social and productive impacts and also of the role of programme evaluation in the process of developing policies and implementing programmes.

This book provides insights into the principles of operation of the cerebral cortex. These principles are key to understanding how we, as humans, function. The book includes Appendices on the operation of many of the neuronal networks described in the book, together with simulation software written in Matlab.

This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

The process of developing models, known as modeling, allows scientists to visualize difficult concepts, explain complex phenomena and clarify intricate theories. In recent years, science educators have greatly increased their use of modeling in teaching, especially real-time dynamic modeling, which is central to a scientific investigation. Modeling in science teaching is being used in an array of fields, everything from primary sciences to tertiary chemistry to college physics, and it is sure to play an increasing role in the future of education. Models and Modeling: Cognitive Tools for Scientific Enquiry is a comprehensive introduction to the use of models and modeling in science education. It identifies and describes many different modeling tools and presents recent applications of modeling as a cognitive tool for scientific enquiry.