This resource was developed by CSMC faculty with support from the National Science Foundation. The opinions and information provided are not necessarily supported by the NSF. (September 2004)

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. 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 of Committee on College Entrance Requirements

Why this committee? In 1800s-- Secondary schools offered a wide range of courses Course syllabi differed greatly from school to school and region to region Colleges and universities were requesting more agreement among content/scope for courses used for admission

In response 1896 the NEA appointed a committee to address the problem 7 representatives from higher education 6 representatives of secondary schools This committee relied heavily on recommendations for mathematics from the Chicago Section of the AMS

Composition of Chicago Section Committee 10 members--2 Principals, 8 Mathematicians J. W. A. Young, University of Chicago-Chair Other universities represented: Harvard, Northwestern, John Hopkins, Kansas State, Michigan Military Academy, Mississippi A & M, University of Nebraska

Time line July 1896: Committee appointed July 1899: Final report published

Report included content recommendations... Course in arithmetic be completed by 6th grade 45 minute courses meeting 4 periods a week Algebra in 7th & 8th grades be literal arithmetic Concrete geometry taught prior to 7th grade Demonstrative geometry should be preceded by concrete geometry Time for algebra and geometry in 9th & 10th grades be equally divided

Report included content recommendations... Outlined content for algebra to include equations of first degree, solution of equations with one or two unknowns, radicals and fractional exponents, quadratic equations in one and two unknowns, binominal theorem for positive integral exponents and logarithms Outlined content for advanced algebra to include binomial theorem for fractional/negative exponents, determinants and infinite series Credit for elementary algebra (1.5) & advanced algebra (1), plane geometry (1), solid geometry (0.5) and trigonometry (0.5) Students take mathematics each year, including their senior year

Report addressed pedagogy such as... Teachers should use multiple methods Different presentations -- “more may be obtained by proving one proposition in three different ways than by proving three propositions in the same way.” Teaching should “cultivate independent thinking” Students should ‘learn to prove’ rather than ‘learn proofs’ Correlation of work -- “arithmetic, geometry, algebra should be treated as branches of one whole... And each freely applied in illustrating and broadening the others.” Providing reviews or synopses--”at the close of each chapter... A synopsis in schematic form of its definitions, methods and results should be made.”

Report also addressed teacher preparation... New mathematics teachers should have careful supervision from experienced teachers their first year or two. New and experienced teachers should visit each other’s classes and engage in discussions about teaching. In schools with more than one mathematics teacher, teachers should meet regularly to study some mathematics and also discuss pedagogy of (i.e., how to teach) specific mathematical topics. Mathematics teachers should learn new mathematical content every year.

Significance of the Report Many high schools lengthened their school day minute periods 4-5 days a week led to standard unit of high school credit--Carnegie unit Placing specific mathematical content in specific courses influenced the nature and scope of courses. Recommended order of algebra, geometry,... courses influenced high school offerings Led to the establishment of the College Entrance Examination Board in 1900