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Elementary Geometry for Teachers

$33.00

In stock

Weight 1.55 lbs
Dimensions 8.5 × 11 × 0.5 in
Publisher

Sefton-Ash

ISBN

9780974814056

Pagecount

258

SKU: EGFT Category:

Elementary Geometry for Teachers is the sequel to Elementary Mathematics for Teachers (EMFT) by Parker and Baldridge. Elementary Geometry for Teachers is designed for the second semester of a mathematics course for prospective elementary teachers that is taught by mathematics faculty. This text takes prospective teachers through the development of measurement and geometry in grades K-8; it also includes material on probability and data analysis.

Elementary Geometry for Teachers covers both the mathematics and other aspects of the K-8 geometry curriculum. For this purpose, this text — like EMFT — is used in conjunction with six school textbooks from Singapore (two of these are also used with EMFT). The homework sets include exercises that ask students to read a section in a Primary Mathematics book, do the problems, and then study the material from a teachers’ perspective, thinking about which skills are developed, how the problems are organized, what the prerequisite knowledge is, what order topics are developed, etc.

Features:

  • The material focuses directly on the mathematics relevant to elementary teachers.
  • The focus is always on mathematics; this is not a “teaching methods” course.
  • The text is divided into short sections, each with a homework set, of a size appropriate for a single class session.
  • Prospective teachers are asked to write “Teacher’s Solutions” to problems and to write “Elementary Proofs”. These are special ways of presenting specific geometry content to elementary and middle school students that are standard in some of the world’s most highly-regarded curricula. The emphasis is on building and perfecting skill at writing clear, concise solutions.

The Primary Mathematics textbooks serve as teacher guides. They provide examples and activities that teachers can use in their classrooms and that help teachers understand what is important in K-8 geometry.

The Primary Mathematics books were chosen because of their clarity, organization, low cost and their exceptional fidelity to mathematics. Studying the Primary Mathematics books prepares teachers for teaching from any elementary school materials. Furthermore, as prospective teachers work though these books, they are constantly aware that the pace, the breadth and the difficulty of the problems in the Primary Mathematics books are at a higher level than what they experienced in their own elementary education. They come away with new expectations about the mathematics capabilities of elementary students.

Elementary Geometry for Teachers pays special attention to two themes:

Developing skills at solving problems involving measurements. International comparisons indicate that U.S. students are especially weak at solving problems involving measurements. These skills are important prerequisites for middle and high school science. Elementary Geometry for Teachers builds teachers’ facility at solving such problems by following the Primary Mathematics curriculum through the grades. The problem below is one of a sequence of Grade 5 “tank problems.”

 

A rectangular tank, 40 cm long and 20 cm wide, originally contains water to a depth of 9 cm. When a stone is added, the water rises to a depth of 15 cm, covering the stone. What is the volume of the stone in liters?

Unknown angle problems. One reason for studying geometry is to acquire skill at logical reasoning. The Primary Mathematics books develop geometric reasoning in depth. In grades 4-6, students are introduced to a specific collection of geometric facts (e.g. the sum of interior angles of a triangle is 180° and opposite angles in a parallelogram are equal. These are used to solve entertaining puzzles like the one below. As they work through Elementary Geometry for Teachers, teachers solve such problems and learn to write Teacher Solutions that display the reasoning.

 

Problem: Give a Teacher’s Solution to this Grade 5 unknown angle problem:

The figure below shows a parallelogram. Find the value of x.

Teacher Solution:

Supplementary Texts

The Elementary Geometry for Teacher textbook is designed to be used in conjunction with the following five Primary Mathematics books (all are U.S. Edition) and one New Elementary Mathematics book.

  • Primary Mathematics 3B Textbook (ISBN 9789810185039)
  • Primary Mathematics 4A Textbook (ISBN 9789810185060)
  • Primary Mathematics 5A Textbook (ISBN 9789810185107)
  • Primary Mathematics 5B Textbook (ISBN 9789810185144)
  • Primary Mathematics 6B Textbook (ISBN 9789810185152)
  • New Elementary Textbook 1 (ISBN 978981274114)


The Primary Mathematics books were developed by the Curriculum Planning and Development Division of Singapore’s Ministry of Education, and published by Marshall Cavendish. While these books were initially created for Singapore elementary students, they have been adapted for use in the United States and other countries. We will refer to them as “Primary Math 3B”, and so on.

The Primary Mathematics series is printed as one course book per semester, each with an accompanying workbooks. The semesters are labeled ‘A’ and ‘B’ , so ‘5A’ refers to the first semester of Grade 5. In each grade, the first semester focuses mainly on numbers and arithmetic, while the second semester focuses more on measurement and geometry.

For teachers using Primary Mathematics Standards Edition textbooks and workbooks, here is a link to the EGFT homework adaption for the Standards Edition. This homework adaption may be printed out and used at no cost by teachers using the EGFT textbook. They may not be sold or incorporated into any other document.



List of universities and colleges using Elementary Mathematics and Elementary Geometry for Teachers:

California State University Los Angeles
Los Angeles, California

California State University Northridge
Northridge, California

Los Angeles Pierce College
Los Angeles, California

University of Colorado Denver
Denver, Colorado

University of Northern Colorado
Greeley, Colorado

Greenville College
Greenville, Illinois

Indiana University
Bloomington, Indiana

Wartburg College
Wartburg, Iowa

Kansas State University
Manhattan, Kansas

Louisiana State University
Baton Rouge, Louisiana

Fitchburg State University
Fitchburg, Massachusetts

Middlesex Community College
Lowell, Massachusetts

Salem State University
Salem, Massachusetts

Worcester State College
Worcester, Massachusetts

Michigan State University
Lansing, Michigan

University of Michigan
Ann Arbor, Michigan

Wayne State College
Wayne, Nebraska

Westchester Community College
Valhalla, New York

Oklahoma State University
Stillwater, Oklahoma

Pennsylvania State University Altoona
Altoona, Pennsylvania

East Tennessee State University
Johnson City, Tennesee

Northeast State Technical Community College
Blountville, Tennesee

Tusculum College
Greeneville, Tennesee

University of Memphis
Memphis, Tennesee

Texas Tech University
Lubbock, Texas

Weber State University
Ogden, Utah

Longwood University
Farmville, Virginia

University of Wisconsin-Madison
Madison, Wisconsin

 

 

Our recommendation:
Elementary Geometry for Teachers is written primarily for elementary teachers. A number of universities use this book as course material in classes for students taking mathematics education. This book is also suitable for individuals who would like to learn more about teaching elementary mathematics.

Elementary Geometry for Teachers

1. Learning to Measure

1.1 Measurement Problems
1.2 Measuring Length
1.3 Measuring Weight and Capacity
1.4 Measuring Angles

2. Geometric Figures

2.1 Fundamental Geometric Ideas
2.2 Triangles
2.3 Symmetry and Triangles
2.4 Parallelograms, Rhombuses and Trapezoids
2.5 Geometric Constructions

3. Finding Unknown Angles

3.1 Unknown Angle Problems
3.2 Finding Angles Using Parallel Lines
3.3 Angles of a Polygon

4. Deductive Geometry

4.1 Unknown Angle Proofs
4.2 Congruent Triangles
4.3 Applying Congruences
4.4 Congruences in Quadrilaterals
4.5 Transformations and Tessellations

5. Area

5.1 Area Units
5.2 Rectangles and Area Properties
5.3 Area of Triangles, Parallelograms and Trapezoids

6. Pythagorean Theorem with Applications

6.1 Pythagorean Theorem
6.2 Square Roots and Pythagorean Triples
6.3 Special Triangles and Further Applications

7. Similarity

7.1 Introducing Similarity and Similar Right Triangles
7.2 Similar Triangles
7.3 Coordinate Systems and Slope
7.4 Similar Right Triangles and Trigonometry

8. Area Concepts and Circles

8.1 Converting Area Units and Scaling
8.2 Circles and Pi
8.3 Area of Circles and Sectors
8.4 Approximation and Accuracy

9. Volume and Surface Area

9.1 Introducing Volume
9.2 Metric Volume
9.3 Prisms and Cylinders
9.4 Pyramids and Cones
9.5 Spheres

10. Data Displays, Probability and Statistics

10.1 Data Displays
10.2 Center and Dispersion of Data Sets
10.3 Probability
10.4 Inferential Statistics
10.5. Appendix: Other Ways to Display Data

Bibliography

Index


Samples

Click here to see part of Chapter 2 on Geometric Figures (p. 27-35) and part of Chapter 3 on Finding Unknown Angles (p. 55-60).