Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

This professional learning programme for Key Stage 3 mathematics teaching is grounded in the latest research on the characteristics of effective professional development. The materials help teachers: - deepen their content knowledge for important mathematical concepts in their grade - increase their understanding of how students learn these mathematical ideas - use their knowledge to develop effective lessons and improve instruction - enhance their collaboration skills. The mathematical content of Teaching by Design in Mathematics matches content topics in number and operations identified for each grade by the NCTM Curriculum Focal Points. The culminating activity of the programme is the co-creation of a prototype lesson which is taught to students by team members; the team then investigates the impact of the lesson on student learning. The cycle of investigating, planning, teaching, observing, debriefing, and revising a lesson together contributes to a climate of continuous professional learning.

Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge, Steiner, and other great mathematical minds. Features squaring the circle, pi, and similar problems. No advanced math is required. Includes 100 problems with proofs.

One of the 18th century's greatest mathematicians delivered these lectures at a training school for teachers. An exemplar among elementary expositions, they combine original ideas and elegant expression. 1898 edition.

Sure-fire techniques of visualizing, dramatizing, and analyzing numbers promise to attract and retain students' attention and understanding. Topics include basic multiplication and division, algebra, word problems, graphs, negative numbers, fractions, many other practical applications of elementary mathematics. 1964 ed. Answers to Problems.

Packed with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention.