Elementary Geometry for Teachers

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 Teacherscovers 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 fromSingapore(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 Teacherspays 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 Teachersbuilds 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”.

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: