- Primary Mathematics 3A Textbook (ISBN 9789810185022)
- Primary Mathematics 4A Textbook (ISBN 9789810185060)
- Primary Mathematics 5A Textbook (ISBN 9789810185107)
- Primary Mathematics 5A Workbook (ISBN 9789810185121)
- Primary Mathematics 6A Textbook (ISBN 9789810185145)
- The absence of clutter and distraction. These books contain mathematics and nothing but mathematics. The presentation is very clean and clear, and is done using simple, concise explanations.
- The coherent development. Each topic is introduced by a very simple example. It is then incrementally developed until, quite soon, difficult problems are being done. Topics are revisited for ‘review’ and the level of the mathematics is constantly ratcheted upward.
- The short, precise definitions. The children pictured in the margins give the precise definitions and key ideas in very few words. These ‘student helpers’ often clearly convey an idea that might otherwise take an entire paragraph!
- The “concrete ⇒ pictorial ⇒ abstract” approach. This approach results in a very clear introduction to a topic.
- The books serve as teacher guides. The books make the mathematical content of each lesson clear to the teacher and help teachers plan lessons. They also provide examples and activities to be done in class and allow teachers flexibility in designing lessons.
- Measurement and the metric system.
- Area and perimeter.
- Introduction to lines and angles.
- Volume, surface area, and density.
- Pythagorean theorem.
- Basic probability and statistics.
- Congruence and similarity.
- Linear and quadratic equations.

Description

* 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 excerpt, taken from the beginning of the textbook and addressed to the student.

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 understanding of elementary mathematics.

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 workbook. 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.

To order Elementary Mathematics for Teachers and the above five Primary Mathematics U.S. Edition books, click here

We will read and study these books with two goals in mind: understanding the mathematics and understanding the curriculum development. The Primary Mathematics books give an extraordinarily clear presentation of what elementary mathematics is and how it is organized and developed. They lay out the subject in depth, and they include a rich supply of exercises and word problems. The mathematics is always clean and correct, and topics are repeatedly covered from different approaches. Viewed from a broader perspective, these books provide much useful guidance about curriculum issues. They exhibit the principles of a well-designed curriculum better, it seems, than any textbook series currently available in English.

It is not surprising, then, that the Primary Mathematics books are also successful with children! The Third International Mathematics and Science Study (TIMSS) rated Singapore’s elementary students the best in the world in mathematics (it also found that the curriculum is highly coherent). These beautifully designed books are a major factor in student success.

As you read and do problems from these books, notice the following:

If you compare the Primary Mathematics books to other elementary textbooks, you will appreciate these points. Many textbooks feature distracting side-bar messages, unnecessary drawings, showy photographs and highlighted boxes, and frequent font changes. The mathematics is obscured and perhaps lost altogether.

Study and enjoy these books — and keep them! When you become a teacher, these books will be a valuable resource, helping with explanations, providing extra problems, and giving guidance in how to present mathematics.

This textbook also includes “learning exercises” exercises embedded in the text, many with boxes of various sizes prompting you to answer. Some of these exercises will be discussed in class, but usually you will encounter them while reading on your own. Do these exercises as you read! Most only take a minute or two. Pencil your answers next to the boxes (the boxes themselves are usually not large enough to hold answers). These exercises are designed to clarify the text and help make mathematical discussions more concrete. Some mathematical ideas are difficult to communicate in words, but quickly become clear by

That same principle — that mathematics is best learned by solving problems — applies to the course as a whole. Read each section of the textbook, but leave plenty of time for doing the homework sets. They are the most important part of the course.

Make your answers clear, concise, legible, and simple. They should look like an answer key to be handed out to an elementary school class. |

This idea — clear, concise solutions — is one of the main themes of this course. You will earn many tricks and teaching devices which will help you craft such solutions, including models (introduced in §1.1), number bonds (§1.4), bar diagrams (§2.2), and “Teacher’s Solutions” (§2.3). These devices convey mathematical ideas without words, making short explanations possible. In mathematics, longer explanations are often more confusing. Consequently, you should avoid writing out paragraph-long explanations —short solutions are less work for you and are clearer to students (and to your instructor!) If you practice brevity in your homework solutions you will find yourself becoming increasingly comfortable giving teacher-quality mathematical explanations.

Above is an extract from the preface of Elementary Mathematics for Teachers.

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

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