Mathematical proofs
http://www.sciencenetlinks.com/Lessons.cfm?DocID=109
A lesson plan for Grades 8–12 Introductory Mathematics, Geometry, and Integrated Mathematics 3
About this resource
- Appropriate grades
- 8–12
- Subjects
- mathematics (geometry)
- Provider
- American Association for the Advancement of Science
Legal
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The purpose of this lesson is to explore that nature of logic, evidence, and proofs in the context of mathematics. In this lesson, students will explore the nature of mathematical proofs and mathematical inquiry.
This lesson would be appropriate after students are familiar with the Pythagorean Theorem. The nature of logic and evidence are topics that should come up frequently in science, history, social studies, and mathematics. Research on students' development of the ability to construct proofs is somewhat conflicting. Piagetian research suggests that students can reason deductively from any assumptions once they reach the formal operational stage (around age 12 and beyond). Other research suggests that the ability to construct proofs depends on the amount and organization of particular knowledge they have. Still other research suggests that students may need to understand the nature of proof and how it differs from everyday argumentation before they are able to construct proofs.
North Carolina Curriculum Alignment
Mathematics (2004)
Grade 8
- Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
- Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.
Grades 9–12 — Geometry
- Goal 2: Geometry and Measurement - The learner will use geometric and algebraic properties of figures to solve problems and write proofs.
- Objective 2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
- Triangles.
- Quadrilaterals.
- Other polygons.
- Circles
- Objective 2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
Grades 9–12 — Integrated Mathematics 3
- Goal 2: Geometry and Measurement - The learner will use properties of geometric figures to solve problems.
- Objective 2.03: Apply the properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
- Triangles.
- Quadrilaterals.
- Other polygons.
- Circles.
- Objective 2.03: Apply the properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
Grades 9–12 — Introductory Mathematics
- Goal 2: Geometry and Measurement - The learner will use properties and relationships in geometry and measurement concepts to solve problems.
- Objective 2.04: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.
