Discovering Geometry helps students develop inductive and deductive reasoning skills by creating conjectures, and reporting and justifying conclusions as they explore the principles of geometry. Congruence, similarity, and symmetry are studied from the perspective of geometric transformation to create connections within the mathematics. Written to the Common Core State Standards using a student-centered, discovery-based pedagogy, Discovering Geometry helps students become mathematically fluent, prepared for future study, and career-ready. View the Discovering Mathematics Brochure.
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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! 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. 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. 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. 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. It will be well worth your while to pull together even a small group class to make this course work. 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. Additional teacher information is in the fore-matter and at the beginning of each chapter.
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. The student textbook notes when and where to access them. 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.
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 day trial is also available. The author himself teaches the investigations for chapters 3 through 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.
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Discovering Geometry: An Investigative Approach.
How It Works Identify the lessons in the textbook chapter with which you need help. Find the corresponding video lessons within this online chapter. Watch fun videos that cover the similarity topics you need to learn or review. Complete the quizzes to test your understanding. If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors. Chapter Topics You'll learn all of the geometry topics covered in the textbook chapter, including:.
Discovering Geometry, Fifth Edition