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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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