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Freitag's MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS: A PROCESS APPROACH was developed using the five Content Standards from the NCTM Principles and Standards for School Mathematics, and the Common Core State Standards for Mathematics. Traditionally, textbooks for pre-service elementary teachers have focused on problem solving. However, problem solving is not the only process through which mathematics is learned. It is also learned through mathematical reasoning, communication, representation, and connections. Recent trends in mathematics education now advocate implementing all five processes as a vital part of learning and doing mathematics. Consequently, pre-serve teachers need to have concrete experiences with these processes that they will be required to teach. The goal of this textbook is to treat each of the processes equitably by using an approach in which the five processes serve as the central pedagogical theme. Most of the examples, exercises, and activities are designed to either model the processes or to have students become directly engaged in working with them. By doing so, pre-service teachers will not only come to understand the different processes, but also appreciate them as an integral to learning and doing mathematics. If this broader view can be instilled in pre-service teachers, they are more likely to give their students a more well-rounded and holistic view of mathematics once they enter the classroom. The content of the book is directly related to the mathematics that is taught in grades K – 8. The purpose is not to reteach elementary mathematics. Rather, the intent is to look at the content from a theoretical or generalized point of view, so that elementary and middle-grades teachers can better understand the concepts and processes behind the mathematics they will teach. In short, the book focuses on the "why" behind the mathematics in addition to the "how."
- The FIVE MATHEMATICAL PROCESSES identified in the NCTM Principles and Standards are used as a framework for this textbook through which the content is stated, explained, demonstrated, and engaged. This "process approach" can be seen in the EXAMPLES and each process is identified by the appropriate icon.
- ACTIVITIES provide students with an opportunity to engage the material of each subsection by solving a problem often using a hands-on manipulative. Activities in the book are designed to take up minimal classroom time usually taking only five to ten minutes. Answers to all items are given after the chapter review exercises.
- The LEARNING ASSESSMENTS at the end of each section are the main opportunity for students to engage the mathematics that they are learning. They are specifically designed to help students engage in the mathematical processes and deepen their understanding of the content.
- Each chapter concludes with a CHAPTER REVIEW that contains a SUMMARY OF KEY CONCEPTS, which provides an overview of the key concepts found in the chapter, and REVIEW EXERCISES that provide students another opportunity to work the different types of exercises encountered throughout the chapter.
- REVIEWING THE BIG IDEAS are cross-chapters reviews that provide students with another opportunity to work with the content from previous chapters. Each review clearly identifies the major themes from three chapters, which not only synthesizes the big ideas of the content, but also shows students which content is essential to master and take away from the course.
- The text also integrates relevant technology into the discussions, examples, and assessment items as appropriate. The technology icon is used to indicate when it is expected that technology will be used in a given situation, as well as when specific information on how to use the technology is given. Specific technological tools include but are not limited to calculators of various types, spreadsheets, and Geometer's Sketchpad.
- An OPENING PROBLEM appears on the first page of each chapter and provides an application of the upcoming content. The problems can be answered by using specific content contained within the chapter. Answers are given directly before the Chapter Review.
- InfoTrac® Student Collections are specialized databases expertly drawn from the Gale Academic One library. Each InfoTrac® Student Collection enhances the student learning experience in the specific course area related to the product. These specialized databases allow access to hundreds of scholarly and popular publications - all reliable sources - including journals, encyclopedias, and academic reports. Learn more and access at: http://gocengage.com/infotrac.
- GETTING STARTED introduces each chapter and relates the mathematical content of the chapter to how the concepts are used in an elementary classroom.
- CLASSROOM LEARNING OBJECTIVES are tables that feature specific learning outcomes from the K - 8 classroom and are adapted from the Common Core State Standards for Mathematics. Each table lists the learning objectives that are relevant to the content of the chapter and then indicates the grade level at which the objective is most likely to be taught.
- DEFINITIONS and THEOREMS are clearly identified.
- STUDENT PAGES from elementary textbooks provide further connections to the elementary classroom by demonstrating how concepts are often presented to elementary students.
- HISTORICAL NOTES provide a context for the content by identifying historical figures or occurrences relevant to the content of the section.
- CHECK YOUR UNDERSTANDING in-text quizzes provide an opportunity for students to monitor their understanding of the content through quick skill-check exercises. Answers to all items are given after the chapter review exercises.
- TALK ABOUT IT questions are included in Check Your Understanding and give students the opportunity to discuss the content they have just learned. You can use these questions to start a lecture or give them to small groups of students to respond to.
Getting Started: The NCTM Process Standards. Communication Through Mathematical Representations. Inductive Reasoning and Patterns. Deductive Reasoning and Proof. Mathematical Problem Solving. Problem Solving with Different Strategies. Chapter 1 Review. Answers to Check Your Understandings and Activities.
Getting Started: Sets in the Classroom. Set Basics. Set Operations. Chapter 2 Review. Answers to Chapter 2 Check Your Understandings and Activities.
3. NUMBERS AND NUMERATION.
Getting Started: Numbers and Numeration in the Classroom. A Brief History of Numeration. The Hindu-Arabic or Decimal System. Other Base Numeration Systems. Chapter 3 Review. Answers to Chapter 3 Check Your Understandings and Activities. Reviewing the Big Ideas Chapters 1-3.
4. WHOLE-NUMBER COMPUTATION.
Getting Started: Whole-Number Computation in the Classroom. Understanding Whole-Number Addition and Subtraction. Adding and Subtracting Large Numbers. Understanding Whole-Number Multiplication and Division. Multiplying and Dividing Large Numbers. Computation in Base b. Chapter 4 Review. Answers to Chapter 4 Check Your Understandings and Activities.
5. BASIC NUMBER THEORY.
Getting Started: Number Theory in the Classroom. Divisibility, Primes, and Composites. Greatest Common Factors and Least Common Multiples. Modular and Clock Arithmetic. Chapter 5 Review. Answers to Chapter 5 Check Your Understandings and Activities.
6. THE INTEGERS.
Getting Started: Integers in the Classroom. Integer Basics, Addition, and Subtraction. Integer Multiplication and Division. Chapter 6 Review. Answers to Chapter 6 Check Your Understandings and Activities. Reviewing the Big Ideas Chapters 4-6.
7. FRACTIONS AND THE RATIONAL NUMBERS.
Getting Started: Fractions and the Rational Numbers in the Classroom. Fractions and the Set of Rational Numbers. Adding and Subtracting Rational Numbers. Multiplying and Dividing Rational Numbers. Chapter 7 Review. Answers to Check Your Understandings and Activities.
8. DECIMALS, REAL NUMBERS, AND PROPORTIONAL REASONING.
Getting Started: Decimals and Proportional Reasoning in the Classroom. Decimals and the Real Numbers. Decimal and Real Number Operations. Proportional Reasoning. Percents. Chapter 8 Review. Answers to Chapter 8 Check Your Understandings and Activities.
9. ALGEBRAIC THINKING.
Getting Started: Algebraic Thinking in the Classroom. Numerical Sequences. Functions and Their Representations. Linear Functions and Constant Change. Solving Equations and Inequalities. Algebraic Thinking and Mathematical Modeling. Chapter 9 Review. Answers to Chapter 9 Check You Understandings and Activities. Reviewing the Big Ideas Chapters 7-9.
10. GEOMETRICAL SHAPES.
Getting Started: Geometrical Shapes in the Classroom. Lines, Planes, and Angles. Triangles. Quadrilaterals, Polynomials, and Circles. Geometric Surfaces and Solids. Chapter 10 Review. Answers to Chapter 10 Check Your Understandings and Activities.
11. CONGRUENCE, SIMILARITY, AND CONSTRUCTIONS.
Getting Started: Congruence, Constructions, and Similarity in the Classroom. Congruent Shapes. Similar Shapes. Basic Geometrical Constructions. Constructing Shapes. Chapter 11 Review. Answers to Chapter 11 Check Your Understandings and Activities.
12. COORDINATE AND TRANSFORMATION GEOMETRY IN THE CLASSROOM.
Getting Started: Coordinate and Transformation Geometry in the Classroom. Coordinate Geometry. Transformations. Congruence, Similarity, and Symmetry with Transformations. Geometric Patterns. Chapter 12 Review. Answers to Chapter 12 Check Your Understandings and Activities. Reviewing the Big Ideas Chapters 10-12.
Getting Started: Measurement in the Classroom. Length and the Measurement Process. Perimeter and Area. Surface Area. Volume. Other Measures. Chapter 13 Review. Answers to Chapter 13 Check Your Understandings and Activities.
14. STATISTICAL THINKING.
Getting Started: Statistical Thinking in the Classroom. Formulating Questions and Collecting Data. Representing and Analyzing Data with Statistical Graphs. Representing and Analyzing Data with Descriptive Statistics. Abuse of Statistics. Chapter 14 Review. Answers to Chapter 14 Check Your Understandings and Activities.
Getting Started: Probability in the Classroom. Experimental Probability and Making Predictions from Data. Theoretical Probability. Conditional and Geometric Probability, Odds, and Expected Value. Counting Techniques and Probability. Chapter 15 Review. Answers to Chapter 15 Check Your Understandings and Activities. Reviewing the Big Ideas Chapters 13-15.
"I think that this book would address the needs of my students better. It definitely stresses understanding over just sets of algorithms. I think it does a very nice job of setting up the relevance of each topic through the NCTM information along with the shots of elementary school books."
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.
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Instructors Resource Manua
Student Solutions Manual
To facilitate those instructors that use a more hands-on approach to teaching, an extensive Exploration Activities manual accompanies the text. The manual contains a variety of explorations for each section, which are referenced in the text by an icon in the margin. Some explorations deal directly with the content of the chapter, often making use of relevant manipulatives or other hands-on activities. Other explorations extend the content of the section either mathematically or by building a connection to the K – 8 classrooms. Most of the explorations can be done individually or with groups and should take about 30 – 45 minutes to complete.
Student Solutions Manual
Exploration Activities contains a variety of explorations for each section, which are referenced in the text by an icon in the margin. Some explorations deal directly with the content of the chapter, often making use of relevant manipulatives or other hands-on activities. Other explorations extend the content of the section either mathematically or by building a connection to the K – 8 classrooms. Most of the explorations can be done individually or with groups and should take about 30 – 45 minutes to complete.