This accessible book helps readers to see the bigger picture of advanced mathematics. The book contains carefully selected, challenging problems in an easy-to-follow, step-by-step process. Neither prior preparation nor any mathematical sophistication is required. The authors guide the reader to “train their brain” to think and express themselves in a rigorous, mathematical way, and to extract facts, analyze the problem, and identify main challenges. A firm foundation in a diverse range of topics is presented. Moreover, the authors show how to draw appropriate, true conclusions. Computer support is used to better intuition into discussed problems. The book is designed for self-study. It can be used to bridge the gap between introductory calculus/linear algebra courses and more advanced courses offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. The reader will develop a deeper understanding in preparation to succeed in more advanced course work. Features •The authors employ a six-step process: 1.SOURCE 2.PROBLEM 3.THEORY 4.SOLUTION 5.REMARK 6.EXERCISES •An Appendix introduces programming in Julia This book is also suitable for high school students that are interested in competing in math competitions or simply for people of all ages and backgrounds who want to expand their knowledge and to challenge themselves with interesting questions.

This developmentally sound, research-based, practical text speaks directly to preservice elementary mathematics students about the multitude of ways they can help their future students learn to see the power, beauty, necessity, and usefulness of mathematics in the world.Part 1 deals with guiding principles that permeate the text, while Parts 2-11 deal with the specific NCTM Standards for grades K-6. Teaching K-6 Mathematics: *is aligned with the current NCTM Curriculum and Evaluation Standards for School Mathematics; *integrates content and methodology; *emphasizes use of technology as a teaching/learning tool; *stresses problem solving; *provides basic information on current research in mathematics education; *focuses on identification of error patterns and analysis; *uses a down-to-earth, friendly writing style that engages the student rather than prescribing what to do; and *includes many activities and exercises, including games, tricks, and amusements that can be used in the classroom to increase student interest in mathematics. Features: *Technology is integral throughout the text. Students are expected to perform Internet searches, investigate new sites appropriate for elementary students, sample new software that could be used in the classroom, and develop ways to blend calculators into the curriculum. *Manipulatives are considered essential for students to learn elementary mathematics concepts. Cuisenaire rods, base 10- blocks, chips, number lines, and geoboards are all part of the manipulative landscape that is created in this text. *Careful attention is given to blending rote work, developmental activities, fun, application, technology, manipulatives, assessment, and planning, so that prospective teachers become accustomed to using varied approaches and decision making as a curriculum is determined. *Tricks, Activities, and Games (TAG) provide a wealth of ideas to attract students to learning mathematics.

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

THE book for elementary education mathematics content courses! Designed to help prospective teachers of elementary school mathematics learn content beyond the rote level, this text stimulates readers to think beyond just getting the problem right and fosters their development into thoughtful, reflective, self-motivated, life-long learners. It stresses the what and why of elementary school mathematics content. Hints are provided about how to teach the content but this is mostly left to courses and texts that are dedicated to that purpose. The text is organized around the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The Standards dictate the basic sections of the text. Within each section, appropriate specific topics are developed, intertwined with technology, problem solving, assessment, equity issues, planning, teaching skills, use of manipulatives, sequencing, and much more. In addition, major focal points of the Standards are emphasized throughout: effective teachers of mathematics should be able to motivate all students to learn, should understand the developmental levels of how children learn, should concentrate on what children need to become active participants in the learning environment, and should be engaged in ongoing investigations of new mathematical concepts and teaching strategies. Mathematics Content for Elementary Teachers is based on several fundamental premises: *The focus of mathematics education should be on the process, not the answer. *Elementary teachers should know the mathematics content they are teaching, know more than the content they are teaching, and teach from the overflow of knowledge. *It is important for teachers to be flexible in allowing students to use different procedures--teaching from the "overflow of knowledge" implies knowing how to do a given operation more than one way and being willing to examine many different ways. *Teachers need to learn to carefully cover the topics to be taught, to reflect upon them, and to be able to organize them. To help prospective elementary teachers concentrate on the mathematics content they will be expected to teach and begin to build the foundation for the methods they will use, this text includes only elementary mathematics content and does not address middle school concepts. Pedagogical features: *The text is organized according to NCTM Standards. *An informal writing style speaks directly to readers and is geared to pre-service teachers. *Focus is given to multiple methods of problem solving at four developmental levels. *Questions, exercises, and activities are interspersed throughout each section rather than gathered at the end of each chapter. *Complete solutions for exercises are provided.

The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.