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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
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Report of the Committee of Ten on
Secondary School Studies with Reports of
the Conferences Arranged by Committees
National Educational Association,
New York: American Book Co., 1894
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In 1880s--two prevailing
philosophies for secondary school
• To serve as college preparatory institution-thus reflecting a classics curriculum and
thereby precluding many potential
• To serve a broader range of students--thus
having a wider curriculum, including
practical courses.
•These two opposing philosophies created a
dissatisfaction with the state of secondary
•Survey of secondary schools revealed that
more than 40 different subjects were taught
and the amount of time allocated to each
subject varied greatly.
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
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.
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
Sub-committees addressed these
Other Modern
• Mathematics
• Physics, Chemistry, and
• Natural history (Biology, Botany,
Zoology & Physiology)
• History, Civil Government, and
Political Economy
• Geography (Physical geography,
Geology & Meteorology)
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
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
• Submitted report to Committee of 10 in March
Report had these general
• General statement of conclusions
• Special report on teaching arithmetic
• Special report on teaching concrete
• Special report on teaching algebra
• Special report on teaching formal
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 pupil’s 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.
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
Report on teaching concrete
• At about age 10, one hour per week should be devoted to
systematic instruction of concrete or experimental
• 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
• Students should learn to “estimate by the eye” and then
measure accurately.
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.
Report on teaching formal
• 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.
Proposed Time allocation* for Mathematics
*Each subject subcommittee met independent
of others and made their recommendations
Proposed Time Allocation for 11th Grade
5 periods
Physics, . .
4 periods
Natural history
5 periods
3 periods
2.5 periods
Modern languages 8 periods
5 periods
5 periods
5 periods
The total number of periods exceeded the time
available. A reminder that each discipline wanted a
significant amount of instructional time.
General Significance of the Mathematics
• 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
• 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.
Significance 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