Transcript Document

Qu i c k T i m e ™ a n d a
T I F F (L Z W ) d e c o m p re s s o r
a re n e e d e d t o s e e t h i s p i c tu re .
This resource was developed by CSMC faculty and doctoral
students with support from the National Science Foundation
under Grant No. ESI-0333879. The opinions and
information provided do not necessarily reflect the views of
the National Science Foundation. 12-6-04
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Committees and Reports that Have Influenced
the Changing Mathematics Curriculum
This set of PowerPoint slides is one of a series of resources
produced by the Center for the Study of Mathematics
Curriculum. These materials are provided to facilitate greater
understanding of mathematics curriculum change and
permission is granted for their educational use.
Report of the National Committee of Fifteen
on the Geometry Syllabus Report • 1912
Qu i c k T i m e ™ a n d a
T I F F (L Z W ) d e c o m p re s s o r
a re n e e d e d t o s e e t h i s p ic tu re .
http://www.mathcurriculumcenter.org
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Final Report of the National Committee
of Fifteen on the Geometry Syllabus
National Education Association
American Federation of Teachers of the Mathematical
and Natural Sciences
Mathematics Teacher, December 1912
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Committee of Fifteen on
the Geometry Syllabus
Appointed 1909
Final Report 1912
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Forces at Work
• Increasing enrollments placed pressure on high
schools to provide education to a broader student
population
• Geometry courses varied widely between two
extremes
– Formal proof approach
– Utilitarian approach
• There were rising failure rates in algebra and
geometry
• Psychology of “Mental Discipline” was losing favor
and both mathematicians and teachers were calling
for reform
• A common syllabus and direction for geometry was
needed
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Committee of Fifteen
7 members from higher education
8 members from secondary schools
Charles Bouton, Harvard University
Florian Cajori, Colorado College
Herbert Hawkes, Columbia University
Earle Hedrick, University of Missouri
Henry Rietz, University of Illinois
David Eugene Smith, Teachers
College, Columbia University
Herbert Slaught, University of
Chicago, Chair
William Betz, East High School,
Rochester, NY
Edward Brown, North High School,
Denver, CO
William Fuller, Mechanic Arts High School,
Boston, MA
Walter Hart, Shortridge High School,
Indianapolis, IN
Fredrick Newton, Andover Academy,
Andover, MA
Eugene Smith, Park School,
Baltimore, MD
Robert Short, Technical High School,
Cleveland, OH
Mabel Sykes, Bowen High School,
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Chicago, IL
Final report had 5 general sections
•
•
•
•
•
Historical overview of school geometry
Logical considerations
Special courses
Exercises and problems
Syllabus of geometry
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Historical Overview of School
Geometry
• Reviewed the nature of school geometry in
several European countries.
• Provided a brief review of popular geometry
textbooks being used in the United States.
• Identified books and resources that illustrated
attempts to reform the teaching of geometry.
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Logical Considerations
• Recommended axioms, postulates, and definitions
that should be included in the syllabus for a
geometry course.
• Addressed the strengths and dangers associated
with
informal proofs, and argued that nearly 100 of the
propositions (theorems) “must receive formal proof in
any well-regulated course in geometry.”
• Recommended algebra as a ninth-grade course,
geometry in the tenth grade, and algebra and
geometry in the eleventh.
• Recommended that algebraic approaches and
notations be utilized in geometry.
• Recommended incorporation of some solid geometry9
and trigonometry in geometry.
Special Courses
• Rather than special courses, a single syllabus for high
school geometry was recommended. The syllabus could
be altered by omission of some theorems and by
increased emphasis on theorems supporting practical
applications.
• Guidelines were provided for the study of geometry across
the grades, including informal geometry in the elementary
grades.
• Definitions should be “stated formally only after the
concept is clearly forms in the student’s mind.”
• Theorems need not all be proved; for some, heuristic
arguments to convince students of their truth would be
sufficient.
• Making scale drawings and models that apply important
theorems on measurement was recommended.
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Exercises and Problems
• Expressed concern about the lengthy sets of exercises and
their lack of application as found in prevailing textbooks.
• Recommended distributing exercises by difficulty so that
each theorem was accompanied by immediate concrete
exercises and applications and more difficult exercises were
delayed to a later part of the course.
• Urged a balance of formal reasoning exercises and
application problems to make geometry more appealing
to the average student.
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Geometry Syllabus
• Proposed a list of theorems, often stated algebraically,
that would be a basic set for a geometry course.
• For plane geometry, 106 theorems were listed; and for
solid geometry, 75 theorems were listed.
• Used different fonts to convey to teachers and examiners
the relative importance of listed theorems.
• Identified some theorems that could be developed with
informal arguments.
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Significance of the Report
of the Committee of 15
• Called for a balance of informal and formal work in geometry
and more concrete examples.
• Emphasized the need for good pedagogy to support the
learning of geometry.
• Recommended a full-year of plane geometry in 10th grade to
be followed by more geometry and algebra in 11th grade.
• Geometry textbooks published after 1910 acknowledged the
Committee of Fifteen and noted their alignment with the
Committee’s report.
• Theorems listed by the Committee of Fifteen were included
in forthcoming high school geometry textbooks.
• College Entrance Examination Board limited testing of
propositions to the Committee’s list of basic theorems.
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