Discovering Geometry: An Investigative Approach - Student Edition

With Discovering Geometry, students learn by doing, working both individually and in cooperative groups. Students use the tools of geometry to conduct investigations, compare ideas, and make conjectures about geometric relationships. Through the investigative process, students discover important principles of geometry, developing conceptual understanding and preparing to succeed with formal proof. 

Distinguishing Features Support NCTM Recommendations 

• Inductive, as well as deductive, approach: The approach is one of hands-on investigation and exploration. It's more active and involving than information-driven texts and students retain more by learning through doing geometry. 
• Develop understanding of the proof process: Unlike traditional texts that place a heavy emphasis on two-column proof, Discovering Geometry builds the concept of proof as students first learn how to do paragraph, flowchart, and algebraic proofs. No other book develops student appreciation and understanding of the proof process in as rigorous and deliberate a manner. 
• The van Hiele model for geometry education:Discovering Geometry is partially based on the van Hiele model, which states that students must progress through five stages of learning as they develop mastery of abstract concepts, beginning with concrete models and visualization. 
• Student-centered investigations: Students discover properties of geometry through guided investigations. They perform investigations with the traditional tools of geometry, as well as with patty paper for quick and easy-to-follow results. 
• Cooperative learning: The benefits of cooperative learning are well known—better communication skills, self-empowerment, increased problem-solving skills, reduction of math anxiety, and better preparation for both college and the workplace. 
• Students build self-reliance: Consistent with a constructivist approach, whose benefits are well recognized, each student must take an active responsibility for his or her own learning. The conjectures, definitions, and postulates are incomplete, and students are led to correctly complete them through their investigations. 
• Extensive algebra: Algebra is incorporated where appropriate to keep it fresh in students’ minds and to highlight the connections between fields of math. 
• Multicultural connections: The geometry of other cultures, in art and architecture for example, is embedded throughout. 
• Technology: Algebra applications use the graphing calculator, and various investigations have the option of being conducted with The Geometer's Sketchpad^®.