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 fifth edition, although changes are not huge from one edition to another—some chapter reorganization and other minor changes.
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. In addition to the straightedge and compass, students will need a protractor and a ruler, but these are used less frequently. 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.
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 through most of the course. Two-column proofs are taught in chapter twelve (of thirteen chapters) 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. There are many exercises that are specifically focused on reasoning and proof skills. 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, and you should really get the teacher edition that includes online resources. The full-color student text is available in hardcover or via an ebook (with a one-year license). 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. The text has “Hints for Selected Exercises” and answer keys for chapter reviews.
The teacher’s edition is a larger hardcover edition that includes reproductions of student pages, with some answers overprinted in magenta. Answers that don’t fit on the student pages are in the margins at the bottom of the page of the teacher's edition along with teaching information and other helps. Additional teacher information is in the fore-matter and at the beginning of each chapter. One valuable resource in the fore-matter is course outlines that will help you schedule lessons, tailoring the course for “standard,” “enriched,” or “block” schedules. Answers to all problems are found either in the chapter or at the back of the teacher’s edition. A separate solutions manual, found among the online resources, shows the steps leading to the answers. Assessment resources (quizzes and tests) are also online.
The fifth edition has increased the number of opportunities to incorporate technology into learning, although the use of technology is not absolutely required. Students can access “Dynamic Geometry Explorations” that help demonstrate concepts; these are free online and are often well worth exploring. The student textbook notes when and where to access them.
The ebook version of the student textbook and the teacher's edition both have graphing technology by ClassPad.net built in. There are other graphing software programs students can use if they don't have the ebook. The graphing software helps students learn the technology used in actual business and industry math applications. In addition, some form of geometry software can help compensate if you have a student working alone. Students can create numerous constructions quickly on the computer and compare results, whereas it would be too time consuming to do many of them manually. However, you do not want to use the software as a total substitute for a student learning to create constructions with compass and straightedge.
Videos to accompany Discovering Geometry lessons (either the fourth or fifth edition) are available for rental on Vimeo On Demand. You can rent the videos chapter by chapter with prices varying from $3.99 to $4.99 depending upon the length of each chapter. (You need to register at Vimeo first, then click here to rent the videos.)
Summary
Discovering Geometry was designed for classroom use, so it's a little cumbersome and expensive for homeschoolers. It also requires more direct teaching time than do some other geometry courses designed for homeschoolers. Nevertheless, it remains my favorite course because its methodology is both effective and enjoyable for a wide range of students---something that can't be said about most geometry courses.
