PowerPoint Presentation - Committee of Ten

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This resource was developed by CSMC faculty with
support from the National Science Foundation
under Grant No. ESI-0333879. The opinions and
information provided are not necessarily
supported by the NSF.
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Committees and Reports that have Influenced the
Changing Mathematics Curriculum
This PP is one of a series of resources produced
by the Center for the Study of Mathematics
Curriculum. The CSMC is one of the Centers for
Learning and Teaching supported by the National
Science Foundation. These materials are provided
to facilitate greater understanding of
mathematics curriculum change and permission is
granted for its educational educational use.
The NEA report from the Committee of Ten--1894
http//www.mathcurriculumcenter.org
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Report of the Committee of Ten on Secondary
School Studies with Reports of the Conferences
Arranged by CommitteesNational Educational
Association, New York American Book Co., 1894
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In 1880s--two prevailing philosophies for
secondary school existed

• To serve as college preparatory institution--thus
  reflecting a classics curriculum and thereby
  precluding many potential students.
• To serve a broader range of students--thus having
  a wider curriculum, including practical courses.

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• These two opposing philosophies created a
  dissatisfaction with the state of secondary
  education.
• Survey of secondary schools revealed that more
  than 40 different subjects were taught and the
  amount of time allocated to each subject varied
  greatly.

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In response the NEA addressed these problems by

• Appointing the Committee of Ten
• Its purpose was to provide a national force for
  standardizing the secondary school curricula and
  serving more students.

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Time line Charge

• July 1892 Committee of Ten appointed
• Charge--select school and college teachers of
  certain subjects to consider the proper limits of
  each subject, the best methods of instruction,
  the most desirable allotment of time for the
  subject, and the best methods of testing the
  pupils attainments.

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Committee of Ten

• Higher Education
• Charles W. Elliot, President of Harvard
  University, Chairman
• William T. Harris, Commissioner of Education,
  Washington, DC
• James B. Angell, President of the University of
  Michigan
• James H. Baker, President of the University of
  Colorado
• Richard H. Jesse, President of the University of
  Missouri
• Henry C. King, Professor in Oberlin College,
  Oberlin, OH
• James M. Taylor, President of Vassar College,
  Poughkeepsie, NY
• Members from secondary
• James C. Mackenzie, Head Master of the
  Lawrenceville School, Lawrenceville, NJ
• Oscar D. Robinson, High School Principal, Albany,
  NY
• John Tetlow, Head Master of the Girls High
  School and the Girls Latin School, Boston, MA

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Sub-committees addressed these subjects

• Latin
• Greek
• English
• Other Modern Languages
• Mathematics

• Physics, Chemistry, and Astronomy
• Natural history (Biology, Botany, Zoology
  Physiology)
• History, Civil Government, and Political Economy
• Geography (Physical geography, Geology
  Meteorology)

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The Mathematics Conference(Sub-committee on
Mathematics)

• Prof. William E. Byerly, Harvard University
• Prof. Florian Cajori, Colorado College, Colorado
  Springs, CO
• Prof. Henry B. Fine, College of New Jersey,
  Princeton, NJ
• Prof. Simon Newcomb, Johns Hopkins University
• Prof. George D. Olds, Amherst College, Amherst,
  MA
• Prof. T. H. Safford, Williams College,
  Williamstown, MA
• Arthur H. Cutler, Private School for Boys
  Principal, New York
• W. A. Greeson, High School Principal, Grand
  Rapids, MI
• Andrew Ingraham, Swain Free School, New Bedford,
  MA
• James L. Paterson, Lawrenceville School,
  Lawrenceville, NJ

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Mathematics Subcommittee

• Appointed by members of the Committee of 10
• 6 mathematicians and 4 from secondary schools
• Met for 3 days at Harvard University in December
  1892
• Submitted report to Committee of 10 in March 1893

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Report had these general sections

• General statement of conclusions
• Special report on teaching arithmetic
• Special report on teaching concrete geometry
• Special report on teaching algebra
• Special report on teaching formal geometry

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General statement of conclusions--including

• Textbooks should be subordinate to the teacher.
• Topics should be examined with the idea of
  eliminating or giving less attention to some and
  more attention to others.
• Teaching should exercise the pupils mental
  activity and rules should be derived
  inductively instead of being stated
  dogmatically.
• Better preparation of mathematics teachers is
  needed to implement the proposed changes.

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Report on teaching arithmetic

• A radical change in the teaching of arithmetic
  was needed.
• The arithmetic curriculum should be mapped out
  and completed by the end of eighth grade.
• The study of arithmetic should be intimately
  associated the study of algebra, of concrete
  geometry, and of elementary physics.

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Report on teaching concrete geometry

• At about age 10, one hour per week should be
  devoted to systematic instruction of concrete or
  experimental geometry.
• Focus on concrete and not on logical deduction.
  Thus properties of figures and solids should not
  be proved but be illustrated by cutting up and
  re-arranging drawings or models.
• Students should learn to estimate by the eye
  and then measure accurately.

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Report on teaching algebra

• Study of systematic algebra should begin at the
  age of 14, but be done in connection with the
  study of arithmetic.
• Algebra should be studied about 5 hours per week
  during the first year and an average of 2.5 hours
  per week for the next two years.
• Oral exercises in algebra are recommended.

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Report on teaching formal geometry

• Demonstrative geometry should begin at the end of
  the first year of algebra, and be done with
  algebra for the next two years.
• An abundance of oral exercises is recommended,
  and all demonstrations which are not exact and
  formally perfect should be rejected.
• Independent work in geometry is rewarding and
  should be encouraged as a means of stimulating
  creative talent in mathematics.

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Proposed Time allocation for Mathematics
Each subject subcommittee met independent of
others and made their recommendations
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Proposed Time Allocation for 11th Grade
Latin 5 periods Greek 4 periods English 5
periods Modern languages 8 periods Mathematics 5
periods
Physics, . . 5 periods Natural history 5
periods History 3 periods Geography 2.5
periods
The total number of periods exceeded the time
available. A reminder that each discipline
wanted a significant amount of instructional time.
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General Significance of the Mathematics Report

• Reshaped high school by offering alternatives to
  the classic curriculum and put forth the notion
  that high schools should help prepare all
  students to do well in life.
• Recommended an 8-4 organization for elementary
  and secondary schools. Also influenced
  distribution of algebra geometry in high
  school.
• Stimulated thoughtful discussion of mathematics
  curriculum as it recommended deletion of some
  topices and more attention to others.
• Opened the way for subsequent modifications of
  the theory of mental discipline.
• Provided an orientation of instruction
  (e.g.concrete geometry) that paved the way for
  learning that reflected an activist orientation.
• Although directed toward high schools, the report
  had direct relevance to the elementary school.

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Signi?cance of the Committee

• Reactions to the report were generally positive.
  Most commentary on education during the remainder
  of the decade and early part of the 20th century
  alluded to the report.
• Many mathematics textbooks published during the
  next 10 years cited the Committee of Ten in their
  preface and reflected some of their specific
  recommendations.