Primary Math US 1B Workbook
The Primary Mathematics U.S. Edition series of elementary math textbooks and workbooks is meant to be part of a system of learning in which adult supervision and independent practice go hand in hand. The main feature of this series is the use of the Concrete > Pictorial > Abstract approach.
Students are provided with the necessary learning experiences beginning with the concrete and pictorial stages, followed by the abstract stage to enable them to learn mathematics meaningfully. This approach encourages active thinking process, communication of mathematical ideas and problem solving. This helps develop the foundation students will need for more advanced mathematics.
The above extract is from Preface of Primary Mathematics U.S. Edition (reproduced with the permission of the publishers).
The workbooks are consumable and should be used in conjunction with the textbooks. They contain the exercises the student does independently.
Answers or answer keys for Primary Mathematics U.S. Edition textbooks and workbooks are found in the teacher's guides and home instructor's guides. Answer keys booklets are also available for purchase - one for Primary 1-3 and one for Primary 4-6.
Countries around the world first became interested in Singapore's math curriculum when results of the Third International Math and Science Study (TIMSS) were published in 1995. Conducted by the International Study Center at Boston College, achievement tests in both math and science were administered to students in over 40 countries. Students from Singapore ranked highly in mathematics achievement: 1st in the fourth, seventh, and eighth grade levels and 2nd at the third grade level. Results for the U.S. were disappointing: 10th in the third grade, 11th in the fourth grade, 23rd in the seventh grade, and 27th at the eighth grade level. In a follow-up study in 1999, Singapore again ranked 1st in eighth grade math achievement while U.S. eighth graders ranked 19th. Although a first place ranking does not necessarily imply the best program, something about Singapore's math program seems to be working.
"Singapore Approach Math" is a general term referring to the math curriculum, or syllabus, designed by Singapore's Ministry of Education. The curriculum has been regularly revised over the last two decades, with most recent revisions in 2001. We carry two different lines. From SingaporeMath.com we carry Earlybird Kindergarten Math (PK-K), Primary Math (1-6), and New Elementary Math (7-10). From Great Source Educational we carry Math in Focus (K-6).
Both of these programs are produced by the same company, Marshall Cavendish Education (Singapore). The U.S. Primary Math editions have a 2003 copyright, while the newer, Standards Edition have a 2008 copyright. These are both modifications of the original edition of Singapore math. These programs are distributed in the U.S. by SingaporeMath.com. They are essentially the same, though the Standards Edition has a small amount of added material and some of the sequences have been rearranged to better meet U.S. standards. Math in Focus has a 2009 copyright. It is distributed in the U.S by Great Source, a division of Houghton Mifflin Harcourt, and packaged for the homeschool community by Saxon Homeschool. So, the programs have common origins.
Primary Math and New Elementary Math are based on the 1997 mathematics syllabus. New Elementary Math has since been "phased out" of schools in Singapore (probably in favor of texts following the 2001 syllabus). However, Primary Math and New Elementary Math are the series that originally gained Singapore international recognition for excellence in mathematics.
There are now manipulatives especially designed to be used with the Singapore approach. Look for these at the end of this section.
I'll admit, my initial reaction to this program was skeptical. The textbooks are thin and have a straightforward, no-nonsense appearance. Texts switch from full-color to two-toned pages after second grade, and all workbooks are printed in black and white. After spending a great deal of time evaluating the program's contents, however, my opinion has improved considerably. Primary Math uses a concrete-to-pictorial-to-abstract approach to teaching. Concrete illustrations are incorporated heavily in the early grades, gradually giving way to more abstract representations so that math is learned meaningfully. The program builds strong problem solving, critical thinking, and computational skills through well-chosen practice problems.
Each grade consists of two semester sets to be completed in one year. For example, the complete first grade curriculum requires the 1A and 1B textbooks (non-consumable) and the 1A and 1B workbooks (consumable). Workbook assignments are directly correlated with each textbook. Small arrows, usually located in the lower left hand corner of a page, specify when to pause in the text and what exercise number to complete.
Brief teacher's instructions are provided in each textbook's preface, which I highly suggest reading. Although the pace of the course really depends on the individual student, 2-3 pages in the text is usually enough for one day's lesson. To effectively use the textbook, the teacher should study the examples ahead of time in order to determine the best way to verbally explain a concept to the student. Teacher-student or student-student discussions are an important part of this program. Unfortunately, the text doesn't tell you how to facilitate discussions. Teacher's guides are now available for several grades. Also, to help you find the appropriate entry level for your child, printable placement tests and a scoring guide are available at www.singaporemath.com. Users of Singapore Math can also seek support with specific problems or general concerns at www.singaporemath.com through the "forum" link. A select number of exercise solutions, made available by other users of the program, as well as answer key and text corrections, are at http://www.singmath.com.
Extra practice sets are included in all textbooks, except first grade. These problem sets are optional and should be done only after the workbook exercises for that section have been completed. Cumulative review sections are also incorporated into the text, although not on a daily basis like Saxon. Review sections are also included in each workbook. Although these problem sets are optional, I would strongly suggest completing the extra practice. Some of the review sets are quite lengthy, and you might want to consider devoting a day's lesson to review whenever a longer set arises. I suspect a key factor to this program's success in Singapore is that students are both motivated and expected to practice their math skills through homework and optional problem sets. Calculator use is strictly up to the teacher, although Primary Math tends to emphasize mental calculations.
While some believe that Primary Math contains "just the right amount of practice", others believe not enough is provided. For students who feel they need more practice to really "own" a concept or skill, a variety of supplements, specifically designed to complement Primary Math, are available.
Although we used to carry the original Singapore editions, we now only carry the U.S. editions. In a side-by side comparision of the two, these books are virtually identical. For the most part, the same content is covered and presented in the same order. Exceptions include additional lessons and practice problems on standard measurements such as yards, pounds, and gallons. Also, an additonal unit on fractions was added to the beginning of the 6B U.S edition textbook. Other changes are as follows: American money has replaced Singaporean money, British spellings have been converted to American spellings, and the majority, but not all, foreign sounding names and objects have been changed. The most notable difference between the two versions is that there is only one U.S. edition workbook for each semester (parts one and two have been combined into one book). Also, answers to the U.S. edition textbooks and workbooks are only available in separate answer key booklets.
Compared to Saxon or Exploring Mathematics, Primary Math encompasses a narrower scope. While Saxon and Exploring Mathematics both cover coordinate graphing, negative numbers, square roots, and probability, these topics are omitted from Primary Math. They are not covered until New Elementary Math. The smaller scope, however, allows the program to emphasize the basics. Primary Math focuses on topics that Singapore's Ministry of Education believe to be fundamentally important: the four arithmetic operations (using whole numbers, fractions, and decimals), perimeter, area, volume, angles, quadrilaterals, symmetry, time, length, weight, money, graphs, and algebraic expressions.
In terms of pace and difficulty, Primary Math is similar to Exploring Mathematics. Of course, there are some differences. Primary Math introduces multiplication and division in first grade, but Exploring Mathematics quickly catches up in second grade. Exploring Mathematics introduces a broader range of geometry concepts in earlier grades, but Primary Math includes more complicated geometry exercises. Primary Math introduces algebraic expressions in sixth grade while Exploring Mathematics does not. Saxon moves a bit slower introducing Algebra in Math 87. Miquon, which only covers grades 1-3, correlates very well with Primary Math.