Discovering Geometry

Discovering Geometry

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 fourth edition has added even more 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. The full-color student text is available in hardcover or as PDF files that include weblinks. The text has “Hints for Selected Exercises” and answer keys for chapter reviews.

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. Additional teacher information is in the fore-matter and at the beginning of each chapter. One valuable part of this information 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 shows the steps leading to the answers. Parents who are not strong in math might want to have this on hand in case they get stuck.

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. 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 author suggests that students have at least a scientific calculator and/or dynamic geometry software such a GeoGebra (free software at or Geometer’s Sketchpad (available at I expect that some form of dynamic geometry software might help compensate if you absolutely cannot find a second student. 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 would not want to use the software as a total substitute for a student learning to create constructions with compass and straightedge. Fathom Dynamic Data (free at is another computer-based tool you might want to utilize with this text. Some projects using it have been added to the fourth edition.

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.

Pricing Information

When comparison prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

List Prices:
student text - $85
student text online - $78.50
bundle of student text and Geometer's Sketchpad - $100.12
teacher's edition - $98.53
solutions manual - $42.35
assessment resources - $77.86

Discovering Geometry: An Investigative Approach

Discovering Geometry: An Investigative Approach
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Instant Key

  • Learning Environment: group or one-on-one
  • Religious Perspective: secular
  • Grade Level: grades 8-12
  • Educational Approaches: Charlotte Mason, classical, eclectic
  • Educational Methods: activities, critical thinking, discovery or inquiry, interactive, life applications

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