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Mathematics for Elementary School Teachers is designed to give you a profound understanding of the mathematical content that you are expected to know and be able to teach. The chapters integrate the National Council of Teachers of Mathematics (NCTM) Standards and Expectations and the new Common Core State Standards, as well as research literature. The five NCTM Process Standards of problem solving, reasoning and proof, communication, connections, and representation highlight ways that teachers present content, the ways that students learn content, and various ways that students can demonstrate procedural and conceptual understanding. The worked examples and homework questions provide prospective elementary school teachers with opportunities to develop mathematical knowledge, understanding, and skills that they can apply in their own classrooms effectively. The learning path begins with the "Where Are We Going?" Chapter Openers, worked Examples with Yellow Markers that indicate the Process Standards throughout the text, to the Concept Maps, to the Section Question Sets with their "refreshers" of Process Standards, to the Chapter Organizers with Learning Outcomes and a list of the corresponding Review Questions, and finally, conclude at the Chapter Tests with their overarching Learning Outcomes.
- The relevant NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM) PRINCIPLES AND STANDARDS OF MATHEMATICS (2000) appear in the exposition. These Principles and Standards that are adopted by the NCTM represent the most significant and influential collaboration among educators to improve mathematics education at a national level. It is the gold standard used by many states to meet the No Child Left Behind Act of 2001 that requires challenging standards for grades 3-8 mathematics and annual assessment.
- The National Center for Education Statistics administers a nationwide standardized test—National Assessment of Educational Progress (NAEP)—to a pooled random sample of fourth, eighth, and twelfth graders. NAEP has released selective questions, called RELEASED ITEMS in the textbook, from various fourth- and eighth-grade tests to help improve student learning. A sampling of these questions appear in the text, as do questions from state tests, to illustrate what elementary students will see in standardized assessment tests.
- BOXED DEFINITIONS AND THEOREMS/PROPERTIES: allow instructors and students to easily distinguish between definitions, which present the working vocabulary of mathematics, and properties and theorems, which are mathematical techniques and concepts.
- COMMON CORE STATE STANDARDS (CCSS) are also referenced in the text. The CCSS are "aligned with college and work expectations; build upon strengths and lessons of current state standards; and include rigorous content and application of knowledge through high-order skills." The idea behind CCSS is that "Common standards will help ensure that students are receiving a high quality education consistently, from school to school and state to state. Common standards will provide a greater opportunity to share experiences and best practices within and across states that will improve our ability to best serve the needs of students." States that voluntarily accept the Common Core standards would eliminate their own state standards.
- In addition to the NCTM Content Standards, there are five NCTM PROCESS STANDARDS: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. The Process Standards are integrated by an icon throughout the text that highlights where the standard appears and specifies which standard is being used. In addition, the homework problems are categorized by the applicable Process Standard to give prospective teachers a chance to explore a particular process in more depth and improve their perception of problems that assess the process. This unique differentiation is important because the processes connect students to the teaching and learning of mathematical content.
- "Where Are We Going?" CHAPTER OPENERS identify upcoming topics and help to place the material to be presented in a manageable context.
- Unique CONCEPT MAPS visually recap ideas and help you synthesize the material by showing how key mathematical ideas are related.
- PreK–8 problems from actual elementary math textbooks appear in CLASSROOM CONNECTIONS—with explanations—giving prospective teachers another opportunity to see that the topics they are studying are relevant to the elementary curriculum. Actual pages from these textbooks are also shown as appropriate to provide context.
- A VARIETY OF HOMEWORK PROBLEMS appears at the end of each section and chapter to increase interest and flexibility in teaching. They reflect the content and processes that prospective elementary school teachers need to know and teach. They support the national trend of integrating instruction, assessment, content standards, and process standards.
- Over several hundred WORKED EXAMPLES are included to illustrate concepts, techniques, and processes of mathematics for students to master.
- A CHAPTER ORGANIZER grid summarizes key learning outcomes and ideas presented in the chapter followed by a set of review questions which offers a variety of additional problems to reinforce students' learning. The chapter test is organized by learning outcomes so students connect the link between objectives and concepts, and how knowledge is acquired which reflects the national trend of integrating instruction, assessment, and NCTM content and process standards.
Patterns and Inductive Reasoning. Problem-Solving Strategies. Algebra and Problem Solving. Logic and Deductive Reasoning. Chapter Review. Chapter Test.
2. SETS, NUMERATION, AND ADDITION AND SUBTRACTION WITH WHOLE NUMBERS.
Sets and Operations. Numbers and Numeration. Models and Properties of Addition and Subtraction. Algorithms for Whole-Number Addition and Subtraction. Chapter Review. Chapter Test.
3. MULTIPLICATION AND DIVISION WITH WHOLE NUMBERS.
Models and Properties of Multiplication. Models of Division. Algorithms for Whole-Number Multiplication and Division. Chapter Review. Chapter Test.
4. ELEMENTARY NUMBER THEORY AND INTEGERS.
Divisibility of Counting Numbers. Prime and Composite Numbers, LCM, and GCF. Integers. Chapter Review. Chapter Test.
5. RATIONAL NUMBERS AND FRACTIONS.
Concept of Fractions and Representations. Addition and Subtraction with Rational Numbers. Multiplication and Division with Rational Numbers. Ratios and Proportional Reasoning. Chapter Review. Chapter Test.
6. DECIMALS, REAL NUMBERS, AND PERCENTS.
Decimals and Operations. Repeating Decimals, Irrational Numbers, and Real Numbers. Percent and Percent Change. Chapter Review. Chapter Test.
7. ALGEBRA AND FUNCTIONS.
Representing and Creating Functions. Solving Equations. Algebra Tiles. Chapter Review. Chapter Test.
8. DESCRIPTIVE STATISTICS.
Graphical Representation of Data. Measures of Center and Variation. Percentiles, Box Plot, and Outliers. Chapter Review. Chapter Test.
Basics of Probability. Probability Rules. Expected Value, Odds, Simulation, and Normal Distribution. Chapter Review. Chapter Test.
10. INTRODUCTION TO GEOMETRY.
Representation of Building Blocks of Geometry. Pairs of Angles and Types of Polygons. Three-Dimensional Shapes. Chapter Review. Chapter Test.
Concept of Measurement and Measurement Systems. Perimeter and Area. The Pythagorean Theorem and Triangle Inequalities. Volume and Surface Area. Chapter Review. Chapter Test.
12. TRIANGLES AND QUADRILATERALS.
Congruence Axioms for Triangles. Euclidean Constructions. Similarity. Chapter Review. Chapter Test.
13. COORDINATE GEOMETRY AND PLANE TRANSFORMATIONS.
Representations of Lines. Properties of Polygons Using Coordinate Geometry. Transformations of the Plane. Chapter Review. Chapter Test.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Instructor's Resource Manual
The Instructor's Resource Manual provides worked-out solutions to all of the problems in the text.
PowerLecture with ExamView®
PowerLecture™ instructor resources are a collection of book-specific lecture and class tools on either CD or DVD. The fastest and easiest way to build customized, media-rich lectures, PowerLecture includes chapter-specific PowerPoint® presentations, ExamView® computerized testing, images, animations and video, instructor manuals, test banks, useful web links, and more. PowerLecture media-teaching tools are an effective way to enhance the educational experience.
The activities manual is geared toward helping students grasp the main ideas of each section that is covered in the text with open-ended activities that allow students to practice and apply the knowledge that they have learned.
Student Solutions Manual
ontains fully worked-out solutions to selected exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Student Solutions Manual