Transcript prep4college_slides - Center for the Study of Mathematics

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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
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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
Competencie
s
“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 9
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
• Ability 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.
Expansion 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 NCTM’s 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.
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