Overview
GPSASP is a step-by-step method designed to help students systematically approach and complete geometry proofs. This method ensures logical sequencing, clarity, and engagement while reinforcing core mathematical principles.
GPSASP Breakdown
- G – Given
- Identify the information provided in the problem.
- Highlight key facts, relationships, and definitions.
- Write down all given statements.
- P – Prove
- Determine what needs to be proven.
- Clearly define the objective of the proof.
- Restate the proof goal in simpler terms if necessary.
- S – Sketch & Show
- Draw or annotate the diagram, marking given information.
- Use color-coding or symbols to highlight congruences and relationships.
- Label important points, angles, and segments.
- A – Apply Theorems, Definitions, & Identities
- Identify the key theorems, postulates, or definitions relevant to the proof.
- Recall geometric properties that can be applied to establish relationships.
- Connect these principles to the given information.
- S – Statements & Reasons
- Construct a logical sequence of statements leading to the proof conclusion.
- Ensure each step has a corresponding reason (e.g., a definition, theorem, or postulate).
- Maintain a structured two-column format where applicable.
- P – Proof Completion
- Finalize the proof by clearly restating the conclusion.
- Confirm that the statements logically lead to the desired proof.
- Review for any missing steps or possible simplifications.
Why GPSASP Works
- Encourages Logical Sequencing: Prevents jumping between steps and ensures a structured approach.
- Enhances Conceptual Understanding: Reinforces how different geometric properties and theorems interact.
- Integrates Multiple Learning Modalities: Combines visual, auditory, and kinesthetic learning styles.
- Boosts Confidence: Provides a repeatable framework that helps students feel more in control of the proof process.
- Applicable Across Various Proof Types: Works for triangle congruence, similarity, circle theorems, coordinate proofs, and more.
Implementation Strategies
- Use a Whiteboard: Engage students visually and encourage active participation.
- Encourage Verbalization: Have students explain each step out loud to reinforce understanding.
- Use Mnemonics & Associations: Relate GPSASP to a navigation system (e.g., “Use Your GPS as Proof”) to make it memorable.
- Provide Step-by-Step Practice: Gradually build complexity, starting with simpler proofs before moving to more advanced ones.
Conclusion
GPSASP is a structured and engaging approach to teaching geometry proofs, designed to enhance comprehension, sequencing, and confidence. By applying this method consistently, students can develop a deeper understanding of geometric reasoning and problem-solving.