Features for the future classroom demonstrate the relevance of the concepts students are learning, the ways in which the mathematical concepts will be employed in the classroom, provide perspective on the importance of learning the material, and engage students to learn by doing. NEW! The 8 Standards for Mathematical Practice (SMP) from the Common Core State Standards for Mathematics have been integrated throughout the text. These 8 standards encourage growing mathematical maturity, deepening conceptual understanding, and engaging with the subject matter. Instances where one of the SMP standards is particularly applicable are called out in the margins, helping future teachers to make the connection between the standards they may encounter as teachers, and the content and eventual implementation. NEW! Completely updated Into the Classroom features provide insights from active teachers, providing a window into their classroom via activities, projects, discussions, and ideas to engage children in the mathematics being covered in that particular chapter of the text. NEW! Integrating Mathematics and Pedagogy (IMAP) video references have been added to the Annotated Instructor''s Edition and allow future teachers to see elementary and middle school students working out numerical concepts. NEW! Responding to Students Problems (RTS) throughout the problem sets have been updated. These questions show how children try to use mathematical techniques and illustrate that future teachers will need a thorough understanding of mathematical content in order to answer students'' questions.
From the NCTM Principles and Standards are extensive excerpts from The Principles and Standards to help students understand how what they are currently learning is reflected in what they will eventually be teaching. Highlights from History provides a cultural, historical, and personal perspective on the development of mathematical concepts and thought while illustrating the contributions that individuals have made to mathematics. Did You Know? Discussions provide examples of recent advancements in mathematics; often demonstrating the important role the subject has in today''s world and in our lives. This feature also highlights mathematical literature when it is relevant to the classroom teacher. The Chapter in Relation to Future Teachers is a brief concluding essay that puts the chapter into context, summarizing how the content fits into the bigger picture of teaching. Cooperative investigations are activities that small groups can use to explore and discuss concepts. There is one Cooperative Investigation per chapter and additional Cooperative Investigations can be found in MyMathLab. The Activity Manual features annotations in the margins of the Annotated Instructor''s Edition.
These annotations indicate which activities are appropriate for each concept. Strong pedagogical tools help students to understand the concepts and reason mathematically. Chapter Previews prepare students for the upcoming chapter and point out Key Ideas. Examples are often presented in a problem-solving framework, which ask students to independently obtain a solution that can be compared with the solution presented in the text. Solutions are frequently structured in the Polya four-step format. Think Clouds serve as quick reminders and clarify key points in discussions. Hands On Activities begin each chapter, offering content-related games and puzzles that motivate the chapter. These can be easily adapted for use in the elementary classroom.
Cooperative investigations are activities that small groups can use to explore and discuss concepts. There is one Cooperative Investigation per chapter and additional Cooperative Investigations can be found in MyMathLab. Problem sets end each section and include a wide variety of question types. Understanding Concepts problems provide drill exercises and reinforce basic concepts. Teaching Concepts problems ask prospective teachers to carefully consider how they might clarify subtle and often misunderstood points for their own future students. Responding to Students exercises give future teachers insight into what mathematical questions and procedures children will come up with on their own, with ways to respond to them. Thinking Critically problems have students delve more deeply into the section topic. Many of these problems can be used as classroom activities or with small groups.
Thinking Cooperatively questions provide problem-solving experiences specifically for small groups. Making Connections problems apply the section concepts to solving real-life problems and to other parts of mathematics. Communicating exercises ask students to write about mathematics and to investigate mathematics as a language. Using a Calculator problems give students the opportunity to practice using their calculators to solve problems. Using a Computer problems require students to use various types of software. From State Student Assessments problems provide examples of problems from the high-stakes standardized exams now used in many states. These problems help make future teachers aware of the types of knowledge that their future students will be asked to master. End-of-Chapter materials are designed to help students study efficiently.
The Chapter Summary has been reorganized into a chart format pulling together the Key Concepts, Vocabulary and Notation for easier study & review. Chapter Review Problems cover all of the main topics from the chapter. Chapter Test prepares students for the real thing.