See the complete review in 102 Top Picks for Homeschool Curriculum.
I used this text twice, each time with groups of three students with widely diverse mathematical aptitudes. Amazingly, after completion of the course, all my students actually thought geometry was fun! That’s because Discovering Geometry truly uses a different approach to teaching the subject. This is a complete, college-preparatory course that is more inviting than any other I have seen. It is now in its fourth edition, although the fourth is very similar to the third edition. Some chapters have been reorganized. An illustrated glossary and “Dynamic Geometry Explorations” have been added along with a few more projects, investigations, and opportunities for students to apply algebra skills in every chapter.
The first thing that students encounter in the book is art—geometric art. The art leads students into their first investigations about lines and shapes. Investigations by students help them discover postulates and theorems by inductive reasoning. Many investigations involve students in activities, especially making and working with constructions using a straightedge and compass.
Word problems are imaginative, and real-life applications are true-to-life. Mathematical thinking is the goal of this text rather than mere memorization of postulates and theorems.
The text moves from the concrete to the abstract—a strategy essential for many students to be able to succeed in geometry. In the teacher’s edition, the author explains his philosophy of gradually working through levels of thinking to the point where students are able to deal with proofs.
Paragraph proofs are introduced in chapter two as a means of getting students to organize data and explain their thinking process. Paragraph proofs and flowchart proofs are taught from chapters four through twelve, and directed two-column proofs are saved for the last chapter after students have mastered concepts and understand relationships between theorems. Even though two-column proofs are not taught at the beginning of the course, students are applying both inductive and deductive reasoning and working with logic and language leading up to the use of two-column proofs. In fact work with proofs is probably stronger and more effective than in many other texts....The text continually challenges students to explain why.
While I love this text, there’s a reason why more homeschoolers are not using it. It was definitely designed for classroom use. It requires cooperative learning with two or more students working together. It is possible that a parent could function as a second student for some of the activities, but it is more than a bit tricky for a parent to function simultaneously as teacher and student. Lest you view the cooperative learning requirement as a negative, I must tell you that it is one of the features that make it so enjoyable. This is primarily where students have the many “Aha!” experiences of this course. It will be well worth your while to pull together even a small group class to make this course work.
You need both the student text and the teacher’s edition. The full-color student text is available in hardcover or as PDF files that include weblinks....
In addition to the aforementioned straightedge and compass, students will need a protractor and a ruler. Numerous other items are used to make this a hands-on course, although most of the time their use is optional. Among these items are drinking straws, interlocking cubes, geometric shapes, geoboards, meter stick, modeling clay, patty paper (the lightweight paper used to separate burger patties), toothpicks, and uncooked spaghetti.
The teacher’s edition is a larger hardcover edition that includes reproductions of student pages, with some answers overprinted in magenta. Other answers don’t fit on student pages, so those are in the margins at the bottom of the page of the teacher's edition along with teaching information and other helps....Answers to all problems are found either in the chapter or at the back of the teacher’s edition. A separate solutions manual shows the steps leading to the answers....
Every exercise set in the student book includes some review questions. Reviews at the end of each chapter consist of about 50 or more problems. Assessment resources (quizzes and tests) are available separately.
The fourth edition has increased the number of opportunities to incorporate technology into learning, although use of technology is not absolutely required....
The author suggests that students have at least a scientific calculator and/or dynamic geometry software such a GeoGebra (free software at www.geogebra.org) or Geometer’s Sketchpad (available at www.keycurriculum.com)....Fathom Dynamic Data (free at http://concord.org/fathom-dynamic-data-software) is another computer-based tool you might want to utilize with this text....
You can see an entire chapter online to preview the text, and a free online 30-day trial is also available.
Videos to accompany Discovering Geometry lessons are available for rental on Vimeo On Demand. The author himself teaches the investigations for chapters 3 through 11. You can rent the videos chapter by chapter with prices varying from $2.99 to $4.99 depending upon the length of each chapter. (You need to register at Vimeo first, then click here to rent the videos.)
Note that while Discovering Geometry is published in a new edition from time to time, changes are not very significant, so older editions will be fine as long as you can also get the teacher's edition and solutions manual.