Geometry: Seeing, Doing, Understanding, third edition

MathGrades 10–12

About This Curriculum

A proof-based Euclidean geometry textbook that uses innovative discussions, cartoons, anecdotes, and real-world applications to teach geometric concepts through understanding rather than memorization.

What makes it unique: Combines rigorous proof-based geometry with engaging humor, real-world applications, and visual elements to make the subject enjoyable and understandable for students.

Geometry: Seeing, Doing, Understanding: Proof-Based Euclidean Text

This is a traditional proof-based Euclidean geometry textbook for grades 10-12 that emphasizes deductive reasoning and logical thinking. The curriculum uses humor, real-world applications, and visual elements to make geometric concepts engaging while maintaining mathematical rigor.

Best for

Abstract thinkers in grades 10-12 who enjoy logical reasoning and proof-based mathematics, particularly suited for homeschool families seeking an engaging geometry curriculum with strong real-world connections.

Evaluation Criteria

4 strengths · 5 neutral

Word ProblemsStrength

The curriculum excels at real-world applications with extensive use of practical problems tied to various fields.

Reviews praise 'the most realistic and compelling' real-life applications tied to 'art, architecture, nature, sports, astronomy' and 'engaging word problems'

Direct InstructionStrength

The curriculum supports teacher-led instruction with comprehensive teacher materials and structured lesson format.

Reviews mention teacher preparation takes 'about 30 minutes per lesson' and includes teacher guide with all answers, plus optional instructional DVDs

Sequencing ApproachStrength

The curriculum uses a mastery-based approach with unusual but logical topic arrangement that builds continuously from foundational concepts.

Reviews mention 'clear continuity to topics, building one upon another' and that trigonometry is introduced as a natural progression in triangle study rather than separately

Visual RepresentationsStrength

The curriculum extensively uses visual elements including over 2,200 photographs, drawings, and cartoons to support learning.

Reviews highlight 'full-color third edition with over 2,200 photographs, drawings, and cartoons' and 'entertaining illustrations' that make concepts engaging

Worked ExamplesNeutral

The curriculum includes examples and problem-solving demonstrations but limited evidence of systematic worked examples.

Optional DVDs feature 'Dr. Callahan teaching lessons and working through examples' and the text provides 'good explanations' with 'plenty of examples'

Teacher TrainingNeutral

The curriculum provides teacher support materials but limited evidence of comprehensive professional development resources.

Includes teacher guide with all answers and optional solutions manual, with recommendation that 'parents review the entire book before beginning instruction'

Retrieval PracticeNeutral

The curriculum includes some review features but limited evidence of systematic retrieval practice or spaced review.

Each chapter includes 'algebra review' sections to help students retain prior learning, but no mention of cumulative review or retrieval practice strategies

Assessment DiagnosticNeutral

The curriculum provides varied problem sets at different difficulty levels but limited evidence of diagnostic assessment tools.

Each lesson has 'three problem sets' with exercises that 'progress from simple terminology checks to challenging problems requiring thinking'

Conceptual Procedural BalanceNeutral

The curriculum strongly emphasizes conceptual understanding through deductive reasoning and proof construction, with less focus on procedural fluency.

Reviews note the emphasis on 'understanding rather than memorization' and 'development of logical thinking skills' with students working on proofs throughout the text

Sources: cathyduffyreviews.com, mathmammoth.com