Discovering Geometry

MathGrades 9–12

About This Curriculum

A discovery-based geometry curriculum that engages students through hands-on investigations and cooperative learning to develop inductive and deductive reasoning skills.

What makes it unique: Uses an investigative approach where students discover geometric properties through hands-on activities and cooperative learning, making geometry engaging and meaningful.

Discovering Geometry: Inquiry-Based High School Geometry Through Investigation

Discovering Geometry is a discovery-based high school geometry curriculum that engages students through hands-on investigations, cooperative learning, and inductive reasoning to develop geometric understanding. The curriculum moves from concrete manipulative activities to abstract proof-writing, emphasizing mathematical thinking over memorization.

Best for

High school students in group settings or small classes who learn well through hands-on discovery, with teachers comfortable facilitating inquiry-based learning rather than direct instruction

Evaluation Criteria

5 strengths · 2 concerns · 2 neutral

Word ProblemsStrength

Features imaginative word problems with authentic real-life applications that connect geometry to practical contexts.

Review notes that word problems are imaginative and real-life applications are described as 'true-to-life'

Teacher TrainingStrength

Provides substantial teacher support through the teacher's edition with detailed explanations of philosophy, teaching strategies, and course planning guidance.

Teacher's edition includes author's philosophy explanation, course outlines for different schedules, teaching information in margins, and separate solutions manual

Sequencing ApproachStrength

Uses a mastery-based progression that builds understanding systematically, delaying formal two-column proofs until chapter 12 after students have mastered concepts and relationships.

Paragraph proofs introduced in chapter 2, flowchart proofs taught throughout most of the course, two-column proofs only after conceptual mastery is achieved

Visual RepresentationsStrength

Extensive use of hands-on manipulatives and visual tools including geometric constructions, art, and various concrete materials to support understanding.

Students use straightedge and compass, drinking straws, interlocking cubes, geoboards, patty paper, and other manipulatives; course begins with geometric art

Conceptual Procedural BalanceStrength

The curriculum strongly emphasizes conceptual understanding through discovery-based investigations, with procedural skills developed through construction activities using compass and straightedge.

Students discover postulates and theorems through inductive reasoning, work extensively with geometric constructions, and the text moves deliberately from concrete to abstract thinking

Worked ExamplesConcern

Limited evidence of traditional worked examples, as the curriculum relies primarily on student discovery and investigation rather than direct modeling.

The discovery-based approach has students investigate to find patterns rather than studying worked examples, though Dynamic Geometry Explorations are available online

Direct InstructionConcern

The curriculum minimizes direct instruction in favor of student-led discovery and cooperative learning, which may challenge teachers seeking explicit instruction frameworks.

Designed for classroom cooperative learning with students working together on investigations, requires more direct teaching time than some courses designed for homeschoolers

Retrieval PracticeNeutral

Includes regular review through exercise sets and comprehensive chapter reviews, though specific retrieval practice strategies are not highlighted.

Every exercise set includes review questions and chapter reviews consist of 50 or more problems

Assessment DiagnosticNeutral

Includes assessment resources with quizzes and tests available online, though specific diagnostic capabilities are not detailed.

Assessment resources including quizzes and tests are provided online, with answers available in the teacher's edition

Sources: cathyduffyreviews.com, homeschoolbase.com