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 ic tu re .
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 • 1899
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 .
http://www.mathcurriculumcenter.org
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 . . .
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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
• 45-50 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