Update: Singapore Math has discontinued carrying the books for grades 9 and 10; thus, we can no longer obtain them.
In Singapore, "elementary mathematics" refers to the basics of upper level math, like algebra and geometry. New Elementary Mathematics is a secondary math course for grades 710 that begins with review of basic arithmetic and moves through algebra and geometry to introductory advanced math (trigonometry). It's a fastpaced course with lots of tough problems, and a great segue to higher mathematics and collegelevel courses.
This is not intended as a studentdirected course. Lessons are meant to be taught, and while there is enough information in the teacher guides for presentation, the instructor should have some outside knowledge of his or her own. There is no scripting, and teachers will need to do some work beforehand.
How Do These Work?
For grades 78 there is a student text, teacher's manual, and nonconsumable workbook; a solutions manual for intext problems is also available courtesy of Sonlight. The student texts aren't flashy. Each chapter begins with a brief presentation of concepts followed by several examples with solutions. While there is technically enough material in the student text for kids to selfteach, most will not be able to or will become frustrated. This is a fastpaced course with lots of hard exercises that crams into four years what many curricula spread over five or six.
The teacher's manuals are slim books that provide notation on, and extra information for, exercises and concepts. Textbook pages are not reproduced, nor are lessons scripted. These are support texts, not standalone guidebooks, though they do offer a useful weekbyweek lesson scheme. The workbooks are optional. While they provide extra practice that corresponds to material covered in the textbooks, there are plenty of problems in the student text including regular chapter review. The solutions manuals provide complete solutions and answers to all student text exercises and problem sets.
In grades 910 the format shifts. There are two student texts for each grade, a teacher's guide for each student text, and a single nonconsumable supplementary workbook. The teacher guides are longer than for the earlier levels, but are still not comprehensive. Answers to intext problem sets are in the back of the student texts; there are no solutions. The workbook is still optional.
The course authors have taken a systematic approach to mathematics instruction. The program overall sustains a continuous arc—year one covers introductory algebra and geometry, year two is intermediate, and year three covers advanced; the fourth year is review and introduces advanced math (mostly trigonometry). There is order within each text as well, as in each algebra is covered first and then geometry. This isn't the incremental approach (used by Saxon and others); once topics are introduced they are covered fully. They may come up again in review, but students won't be surprised by new aspects of old concepts popping up seemingly at random.
Of all the math courses used in Singapore for secondary students that we carry, this is the most intense. Problems are more difficult and the pace is faster, though coverage is also more comprehensive and thorough. The emphasis is on getting students to reason and think mathematically, and to communicate using the language of mathematics. Nonrequired questions in the student text allow those who want to push themselves further to do so. There isn't anything flashy or "fun" here (other than some goofy animestyle cartoons here and there throughout the text), but overall this is a solid, nononsense approach to secondary math instruction.
OurHonest Opinion:
Singapore educators don't take math lightly. For years students from Singapore have scored at the top of international math and science tests, and it isn't hard to see why. The New Elementary Mathematics series gives students the skills they need to operate within the realm of mathematics, rather than simply teaching them how to solve certain types of problems. Concrete examples clearly define abstract concepts so that kids learn not only the principles, but their practical applications.
Students coming to any secondary Singapore math course from a more traditional program may have a hard time. The pace is quicker, and if you're planning to switch from a program like Saxon, there will be gaps in their understanding that will need to be filled before they can fully understand some of the concepts they're learning. But for those who can stick with it, they will be well prepared for any further math instruction they may receive, and ready to put their skills to use in a wide range of practical situations.
Additional Information:

Review by C. Hollis Crossman
C. Hollis Crossman used to be a child. Now he is a husband and father, teaches adult Sunday school in his Presbyterian congregation, and likes weird stuff. He might be a mythical creature, but he's definitely not a centaur.Read more of his reviews here.

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