Elementary Geometry for Teachers

by Parker & Baldridge

This sequel to the authors' text Elementary Mathematics for Teachers (EMT) 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 EMT --- is used in conjunction with six school textbooks from Singapore (two of these are also used with EMT). The homework sets include exercises that ask students to read a section in a Primary Math 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 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 Math books were chosen because of their clarity, organization, low cost and their exceptional fidelity to mathematics. Studying the Primary Math 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 Math 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 US 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 Math 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 Math 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 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 Cavedish. 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 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, California

California State University Northridge, California

East Tennessee State University, Tennessee

Fitchburg State University, Massachusetts

Greenville College, Illinois

Indiana University, Indiana

Kansas State University, Kansas

Longwood University, Virginia

Los Angeles Pierce College, California

Louisiana State University, Louisiana

Michigan State University, Michigan