This resource was developed by CSMC faculty and doctoral students with support from the National Science Foundation under Grant No. ESI-0333879. The opinions and information provided do not necessarily reflect the views of the National Science

1
This resource was developed by CSMC faculty and
doctoral students with support from the National
Science Foundation under Grant No. ESI-0333879.
The opinions and information provided do not
necessarily reflect the views of the National
Science Foundation. 12-7-05
2
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. These materials are
provided to facilitate greater understanding of
mathematics curriculum change and permission is
granted for their educational use.
Academic Preparation for College What Students
Need to Know and Be Able to Do
Report of the College Entrance Examination Board
1983

http//www.mathcurriculumcenter.org
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Academic Preparation for College What Students
Need to Know and Be Able to Do
College Board Educational EQuality Project
Represents the combined judgments of hundreds of
school and college educators of the knowledge and
skills students need in order to be successful in
college
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Background
In the late 70s and early 80s Many college
entrants did not have the knowledge and skills
necessary for higher education. Background
preparation of many college entrants limited
their choice of college and/or choice of
programs. Many inadequately prepared
students dropped out of college. Academic
records of college graduates prevented them
from pursuing graduate or professional study.
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Mathematical Sciences Advisory Committee
Donald L. Kreider, Professor of Mathematics,
Department of Mathematics, Dartmouth College,
Chair Floyd L. Downs, Mathematics Teacher,
Hillsdale High School, San Mateo,
California Stephen J. Garland, Professor of
Mathematics and Chairman of Program in Computer
and Information Services, Dartmouth
College John W. Kenelly, Visiting Professor of
Mathematics, United States Military
Academy Jeremy Kilpatrick, Professor of
Mathematics Education, University of
Georgia Jane Cronin Scanlon, Professor of
Mathematics, Rutgers University Ara B.
Sullenberger, Associate Professor of Mathematics,
Tarrant County Junior College-South Campus, Fort
Worth, Texas
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Academic Preparation for College Focuses on
what students should learn
specific knowledge and skills in 6 Basic
Academic Subjects general skills in 6 Basic
Academic Competencies computer competency
Recognizes that personal characteristics such as
motivation, interest, adaptation, intelligence,
experience, and drive are also important for
success in college.
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Basic Academic Subjects
Basic Academic Competencies
Learning the Basic Academic Subjects depends on
the Basic Academic Competencies. At the same
time, learning the Basic Academic Subjects
further develops those competencies. (p. 2)
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Basic Academic Competencies
Basic Academic Competencies are reading, writing,
speaking and listening, mathematics, reasoning,
and studying.
Broad intellectual skills that are essential
for success in all fields of college
study Developed abilities that are outcomes of
learning and intellectual discourse
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Selected Basic Academic Competencies Mathematics
Ability to add, subtract, multiply and divide
natural numbers, fractions, decimals, and
integers with reasonable accuracy Ability to
make and use measurements with traditional and
metric units Ability to use effectively the
mathematics of integers, fractions, and
decimals ratios, proportions, and percentages
roots and powers algebra and
geometry Ability to make estimates and
approximate solutions, and to judge the
reasonableness of a result Ability to
formulate and solve a problem in mathematical
terms Ability to select and use appropriate
approaches and tools in solving problems
mental computation, trial and error, paper-and
pencil techniques, calculator, and
computer Ability to use elementary concepts of
probability and statistics
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Selected Basic Academic Competencies Reasoning
Ability to identify and formulate problems, and
the ability to propose and evaluate effective
ways to solve them Ability to recognize and use
inductive and deductive reasoning, and to
recognize fallacies in reasoning Ability to
draw reasonable conclusions from information
found in various sources (written, spoken, or
displayed in tables and graphs) and defend
conclusions rationally Ability to comprehend,
develop, and use concepts and generalizations Ab
ility to distinguish between fact and opinion
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Computer Competency
Recognized as an emerging skill for students
entering college Viewed as a basic skill
complementary to other competencies Defined as
including Basic knowledge of how computers
work and common terminology Ability to use
computers and software for self-instruction,
collection/retrieval of information, word
processing, modeling and simulation, and
problem solving Awareness of how computers are
used in the academic disciplines Some
understanding of the social and economic effects
of computers and the ethics involved in their
use
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Basic Academic Subjects
Study in the Basic Academic Subjects
English, the arts, mathematics, science,
social studies, and foreign language provide the
detailed knowledge and skills necessary for
effective work in college.

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Why is preparation in Mathematics important for
college entrants?
Mathematics is the language of science and
technology, as well as of business and finance,
and all people need to be able to communicate in
this language to participate in and contribute to
society. Knowledge and appreciation of
mathematics is essential to students
intellectual development. Mathematics opens the
door to a wide range of career choices. Expansio
n of computer science and technical fields have
created new opportunities for those who study
mathematics.
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What preparation in Mathematics is important for
college entrants?
Basic mathematical proficiencies needed by
college entrants ability to apply
mathematical techniques when solving real-life
problems and to know when to apply the
techniques familiarity with the language,
notation, and deductive nature of mathematics and
the ability to express quantitative ideas with
precision ability to use computers and
calculators familiarity with the basic
concepts of statistics and statistical
reasoning knowledge in considerable depth and
detail of algebra, geometry, and functions.
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Specific Preparation in Mathematics1

• Computing
• Familiarity with programming and the use of
  mathematical software programs
• Ability to use mental computation and estimation
  to evaluate calculator and computer results
• Familiarity with the methods used to solve
  mathematical problems when calculators or
  computers are the tools
• Ability to write computer programs to solve a
  variety of mathematical problems
• Familiarity with developing computer programs and
  considerations of design, structure, and style
  that are an important part of this methodology

1Blue statements detail the preparation needed by
all college entrants. Green statements specify
preparation needed by college entrants expecting
to major in science or engineering or to take
advanced courses in mathematics or computer
science and need more extensive mathematical
proficiency.
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Specific Preparation in Mathematics

• Statistics
• Ability to gather and interpret data and to
  represent data graphically
• Ability to apply techniques for summarizing data
  using statistical concepts including average,
  median, and mode
• Familiarity with techniques of statistical
  reasoning, as well as the common misuses of
  statistics
• Understanding of simulation techniques used to
  model experimental situations
• Knowledge of elementary concepts of probability
  needed in the study and understanding of
  statistics

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Specific Preparation in Mathematics

• Algebra
• Skill in solving equations and inequalities
• Skill in operations with real numbers
• Skill in simplifying algebraic expressions,
  rational and radical expressions
• Familiarity with permutations, combinations,
  simple counting problems, and the binomial
  theorem
• Skill in solving trigonometric, exponential, and
  logarithmic equations
• Skill in operations with complex numbers
• Familiarity with arithmetic and geometric series
  and with proofs by mathematical induction
• Familiarity with simple matrix operations and
  their relation to systems of linear equations

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Specific Preparation in Mathematics

• Geometry
• Knowledge of two- and three-dimensional figures
  and their properties
• Ability to think of two- and three-dimensional
  figures in terms of symmetry, congruence, and
  similarity
• Ability to use the Pythagorean theorem and
  special right triangle relationships
• Ability to draw geometric figures and use
  geometric modes of thinking in the solving of
  problems
• Appreciate the role of proofs and axiomatic
  structure in mathematics and the ability to write
  proofs
• Knowledge of analytic geometry in the plane
• Knowledge of the conic sections
• Familiarity with vectors and with the use of
  polar coordinates

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Specific Preparation in Mathematics

• Functions
• Knowledge of relations, functions, and inverses
• Ability to graph linear and quadratic functions
  and use them in the interpretation and solution
  of problems
• Knowledge of various types of functions including
  polynomial, exponential, logarithmic, and
  circular functions
• Ability to graph such functions and to use them
  in the solution of problems

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• Specific Preparation in Science
• Mathematic Skills
• A quantitative understanding of at least one
  field of science
• Ability to interpret data presented in tabular
  and graphic form
• Ability to draw conclusions or make inferences
  from data
• Ability to select and apply mathematical
  relationships to scientific problems
• Ability to use mathematical relationships to
  describe results obtained through experiments and
  observations
• Ability to interpret relationships presented in
  mathematical forms in nonmathematical language

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Significance of Report
Created a tool for parents, teachers,
guidance counselors, principals and school boards
to identify educational excellence to assist
with planning and prioritizing curricular and
instructional programs Defined the basic
academic subjects why these subjects are
important and what students need to know how to
do in each area Defined basic academic
competencies as developed abilities, the
outcomes of learning that are essential to
effective work in college Brought the work of
all academic areas together in one
document Incorporated recommendations from
NCTMs Agenda for Action Demonstrated forward
thinking by addressing requirements concerning
technology
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References
College Entrance Examination Board. (1983).
Academic preparation for college What students
need to know and be able to do. New York
Author. College Entrance Examination Board.
(1985). Academic preparation in mathematics
Teaching for transition from high school to
college. New York Author.