Visible Thinking in Mathematics 4A 3rd Edition
Visible Thinking in Mathematics is a series of eleven supplementary books that promotes critical and creative thinking in mathematics. It is designed to help make thinking visible by providing the child with opportunities to think, explore and reflect.
While practice leads to better performance, practice without contextual and conceptual understanding prevents the child from thinking critically and creatively. In this series, instead of learning procedures and formulas by rote, the child masters concepts through:
Thinking routines: functional questions to direct the child's thinking on key concepts and cultivate the child's thinking skills.
Parallel questions: consecutive mathematical problems with the same context but different key words to highlight differences between problems; ensuring that the child understands and retains concepts and skills better.
This approach not only instills in the child mathematical skills but also inspires discipline in thinking and greater motivation for learning.
Additional support is provided to the child through Notes. Notes present opportunities for parents and teachers to clarify misconceptions, simplify difficult concepts and address areas of difficulty for the child.
Answers are in the back of each book.
Note: The 2nd edition has not been revised for U.S. usage. Currency images in the money chapters at the lower levels are Singapore coins and bills. Also, only metric measurement units are used.
What is visible thinking? In this case, to think visibly means that you can easily see or visualize something in your head. This skill, of course, is vital to the study of mathematics - you must be able to make the leap from pictorial representations to abstract ideas. Sometimes, this leap is difficult which makes learning math extremely frustrating. These resource books focus on the pictorial stage and helping the student move from the pictorial to the abstract stage of mathematical thinking. It is meant to be used as a supplement and not a replacement for Singapore Math Primary Math. While it is less than a complete program, the content is fairly comprehensive and would be good for students having trouble with math or for re-teaching concepts.
Please note these books are transitioning to the 3rd edition, which is based on the newest Primary Maths (MOE) syllabus. New editions include US money, but retain metric measurements. The 2nd editions may depict Singapore coins and bills in the early grades and use metric units throughout. Books range from 115-224 pgs.
This series consists of 11 consumable books, two semesters each for Grades 1-5 and one book for Grade 6. The books are a blend of both teacher and student books. Each lesson within a chapter consists of 2 types of pages Thinking Platform and Attaining Mastery. Both teacher and student should go through Thinking Platform pages together. This is where the math concept is introduced, examples worked, and constructive mathematical thinking is modeled. It is highly suggested that the teacher preview the lesson by reading the Notes provided at the bottom of the Thinking Platform page. These concise yet descriptive notes point out teaching tips, common errors, and areas of difficulty. Attaining Mastery pages follow the Thinking Platform. Here, the student can practice new skills on a series of problems that feature Parallel Questions. Parallel Questions are actually a series of similar yet different math questions which are strategically presented so that the differences between the questions either solidify concept understanding or provide opportunities to clarify fuzzy thinking. Answers are provided in the back of the book.~ Anh
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 was working.
“Singapore Approach Math” is a general term referring to a type of mathematical instruction (i.e. curriculum) developed from a syllabus designed by Singapore’s Ministry of Education in the 1980s. There were a number of revisions and the 3rd edition was the last edition used in Singapore. The good test scores were associated with this material and all of our Singapore Approach Math programs are based primarily on the 3rd edition although it is no longer available for sale. Components from different editions are not interchangeable but a student can move between the editions in-between levels.
Primary Math US (1-6) is an adaptation of the 3rd edition for use in the U.S. Although a small amount of content (division of fractions) from the 2nd edition was added back into the US edition, it is almost identical to the 3rd edition. The US edition adds sections for U.S. customary measurements and uses U.S. spelling and conventions. We expect this edition to be available indefinitely. ©2003
Primary Math S/E (Standards Edition) (K-6) was adapted to meet the pre-Common Core CA math standards. An additional amount of content (probability, data analysis, negative numbers, coordinate graphing) from the 2nd edition was added back in and topics were rearranged but it is similar to the US edition. Cumulative Reviews at the end of each Unit and practice sets within each unit were added. Textbooks are in color. ©2008 This edition includes Earlybird Kindergarten Math.
Primary Math CC (Common Core) (K-5) is aligned to the Common Core State Standards and is another adaptation of the 3rd edition. Only minor changes were made to the scope and sequence. Unit Reviews are no longer cumulative and Practices were removed although some of the content was incorporated into the lessons. ©2014 Includes Earlybird Kindergarten Math CC. This edition will be available for the foreseeable future.
Primary Math 2022 Edition (K-5) is a completely new revision retaining all the excellent teaching methods of the earlier Primary Math programs. Incorporating both cumulative assessments and challenging problem solving, mastery learning is emphasized. The scope and sequence is similar to previous editions and topics are aligned to state and national standards. ©2021-2022
New Elementary Math (7-8) is a no-frills program based on an older Singaporian program and covering integrated algebra and geometry. It’s considered a sequel to the Primary Math programs.
Math in Focus (K-8) was developed by Great Source (a division of Houghton Mifflin Harcourt) in conjunction with Marshall Cavendish (the original publisher in Singapore). Although the basic instructional sequences are similar and the content is very close to the SE, material added to the most recent editions brings it into alignment with CC. Math in Focus has a more American look and “feel.” ©2010, 2014
View the Singapore Approach Math Comparison Chart.