Committees and Reports that have Influenced the Changing Mathematics Curriculum

1. 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.

2. 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

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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

9. 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) Sub-committees addressed these subjects

10. 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

11. 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

12. 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

13. 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.

14. 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”.

15. 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.

16. 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.

17. 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.

18. Proposed Time allocation* for Mathematics *Each subject subcommittee met independent of others and made their recommendations

19. 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.

20. 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.

21. 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 recommendations.