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

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

3 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

4 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.

5 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

6 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.

7 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)

8 Basic Academic Competencies Broad intellectual skills that are essential for success in all fields of college study Developed abilities that are outcomes of learning and intellectual discourse Basic Academic Competencies are reading, writing, speaking and listening, mathematics, reasoning, and studying.

9 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

10 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

11 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

12 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.

13 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.

14 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.

15 Specific Preparation in Mathematics 1 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 1 Blue 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.

16 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 Specific Preparation in Mathematics

17 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

18 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 Specific Preparation in Mathematics

19 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

20 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

21 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

22 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.