Elementary Mathematics for Teachers

Elementary Mathematics for Teachers is a textbook for a semester or two-quarter university course for pre-service teachers. It is also appropriate for courses for practicing teachers.

This book focuses exclusively on K-8 mathematics. It develops elementary mathematics at the level of "teacher knowledge". To that end, the text uses five Primary Mathematics Textbooks as a source of problems and to repeatedly illustrate several themes, including:

(a) How the nature of a mathematics topic suggests an order for developing it in the classroom.
(b) How topics are developed through "teaching sequences" which begin with easy problems and incrementally progress until the topic is mastered.
(c) How the mathematics builds on itself through the grades.

This approach is explained more fully in the following except, taken from the beginning of the textbook and addressed to the student.

Elementary Mathematics for Teachers is organized around numbers and arithmetic. The topics are covered roughly in the order they are developed in elementary school. The first three chapters cover most of the arithmetic of Grades K-3. Chapters 4 and 5 jump ahead to topics (prealgebra and prime numbers) usually covered in Grades 6 and 7; that jump allows us to review ideas about algebra and proofs which are needed for a “teacher’s understanding” of the subsequent material. Chapters 6 and 7 return to the original timeline, developing fractions (as is done beginning in Grades 3 or 4) and the follow-up topics of ratios, proportions, percentages, and rates. The last two chapters complete the development of elementary arithmetic by discussing negative and real numbers.

The textbook is divided into short sections, each on a single topic, and each followed by a homework set focused on that topic. The homework sets were designed with the intention that all or most of the exercises will be assigned. Many of the homework exercises involve solving problems in actual elementary school textbooks (the ‘Primary Mathematics’ books described below). Others involve “studying the textbook” — carefully reading a section of the book and answering questions about the mathematics being presented, with attention to the prerequisites, the ordering, and the variety of problems on that topic. Both types of exercises will help you develop a teacher’s understandingof elementary mathematics.

Supplementary Texts

This textbook is designed to be used in conjunction with the following five Primary Mathematics books (all are U.S. Edition).

• Primary Mathematics 3A Textbook
• Primary Mathematics 4A Textbook
• Primary Mathematics 5A Textbook
• Primary Mathematics 5A Workbook
• Primary Mathematics 6A Textbook

These books were developed by the Curriculum Planning and Development Division of Singapore’s Ministry of Education, and published by Federal Publications. 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 3A”, “Workbook 5A”, 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.