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Learning Interchange
Units of Practice

History: People and Places Influencing
the Fundamental Theorem of Calculus

Lesson Details


Subjects: Math, Social Studies
Learning Level: High School
Author(s): Marshall Ransom
Submitted by:

Abstract

Upon completion of this unit, students will be able to explain and illustrate the connection between the early attempts to measure non-rectangular and curvilinear objects to the formal methods of elementary calculus. Students should be able to describe social and political influences upon the people using these early methods and how the times in which they lived impacted the development of the fundamental theorem.

Lesson fundamental understandings:
Essential Questions:


Standards

National Standards

Connections: Recognize, use and learn about mathematics in contexts outside of mathematics. This is a study of the historical attempts to solve problems before the fundamental theorem was known. Knowing about the people and their efforts as well as the influences of the era in which they lived can provide an important connection of mathematics to history.

State Standards


Lesson

Prerequisite Skills

Students should have experienced the use of rectangles or other elementary shapes to estimate area of regions bounded by curves. Knowledge of the historical context for the more famous applications of these methods is not necessary. Students will investigate several persons famous in the history of mathematics. These investigations may lead to others not specifically mentioned in the student activity. it may be helpful to construct a timeline showing where and when some of these people lived and worked.

Teacher Information/Situations/Setting/Time

This lesson requires computers and access to the internet, but no special materials.

Assessment

Understanding the history of this concept, the fundamental theorem of calculus, should include a knowledge of early calculation methods and the use of rectangles or other basic shapes to approximate area of irregular figures. The historical context in which these early methods were used involves knowing about the people and the circumstances under which they lived and worked. Students can demonstrate an understanding of this by answering questions posed in the activity. Also, the impact of social and political conditions was both helpful and restrictive to these early mathematicians. Students should be able to articulate the effect of such conditions and generalize in other historical contexts.

Student Activity/Tasks

Understanding the history of this concept, the fundamental theorem of calculus, should include a knowledge of early calculation methods and the use of rectangles or other basic shapes to approximate area of irregular figures. The historical context in which these early methods were used involves knowing about the people and the circumstances under which they lived and worked. Students can demonstrate an understanding of this by answering questions posed in the activity. Also, the impact of social and political conditions was both helpful and restrictive to these early mathematicians. Students should be able to articulate the effect of such conditions and generalize in other historical contexts.

Enrichment/Alternate Activity:

Cross-Curricular:

Technology Requirements/Tools/Materials

Internet access is a requirement. Access should be available to computer stations which make use of a browser and word processor simple for the student.

Acknowledgements:


Additional Resources

Main URL:

Related Lessons

Related Resources




Copyright © 1997-2003
Career Connection to Teaching with Technology
USDOE Technology Innovation Challenge Grant
Marshall Ransom, Project Manager
All rights reserved.

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