There is currently a LOT of confusion surrounding this course as it being revised and renamed at the same time. Discovering Mathematics is being renamed Dimensions Math and as levels 1 & 2 have been revised, they've also been relabeled Grades 7 and 8. The revised books meet the new "Common Core" standards.
Yet another option from Singapore for secondary math instruction, Discovering Mathematics will appeal especially to those looking for a largely student-directed program. The colorful worktexts present concepts clearly and completely, without being verbose or overly repetitive. Singapore is noted for its superior math instruction, and this series is a worthy addition to the already impressive selection.
The course covers grades 7-10. For each grade there are two student textbooks and two teacher guides. The student texts are not consumable; students complete exercises on a separate sheet of paper. Each text is divided into several chapters which are further divided into digestible units. Chapters open with a brief interesting history or real-life application relating to the topic, followed by text and a number of examples.
Exercises are grouped according to purpose. After the chapter unit students complete basic practice problems which serve as the practical introduction to the topic. Further practice problems are more complicated and nuanced, and the rest of the exercises are designed to show the practical application of the topic and help kids improve their logic and analytical skills. Students are also encouraged to keep a math journal where they record real-life contexts in which various topics might be useful.
This is a fairly fast-moving course. By the final book students are doing statistics and probability and advanced trigonometry. From there, they can move on to calculus and physics for the final years of high school, though they will also be prepared to move on to most first-level college math courses.
There isn't a lot of review. Topics are taught for mastery, and thoroughly covered and practiced before moving on to the next one. Since instruction is so clear and there are so many worked examples in the text, most students who can pay attention and apply themselves shouldn't have too much trouble getting through lessons. Since the emphasis is on practical application of mathematical concepts, exercises are constructed to help students internalize information by following each step in the process carefully.
Discovering Mathematics is more or less a student-directed course. The teacher guides include a yearly lesson plan, brief teaching notes and fully worked solutions to all exercises. While the teaching notes are helpful, they aren't nearly enough to teach the course on, and are really only supplemental bits of information and suggestions for class activities and presentation. Of all the secondary Singapore math courses, this is the least teacher-reliant. As with any course, teacher involvement can't hurt, but you'll need to put together your own lesson plans and should probably have a pretty thorough knowledge of each topic you introduce.
It's hard to say anything negative about Singapore math products. Clear text, high standards of student progress and tough yet workable exercises have become the rule for their courses. Discovering Mathematics is no exception, and is even one of the best programs Singapore has to offer. If your students like math or want to pursue a math or science related career or course of study in college, this would be an excellent place to start. Even students who don't like math as much will benefit greatly from the logical presentation of advanced math concepts. Overall, this is one of the best junior high/high school math courses we offer.