GENERAL EDUCATION MATHEMATICS REQUIREMENT IN MARYLAND

 

The Preamble and Attributes below were approved unanimously by the Statewide Mathematics General Education Subcommittee, June 14, 2002

 

PREAMBLE:

 

During the 21st century our nation will depend on an ever stronger mathematical competence among its citizenry if our nation is to compete successfully in the increasingly technologically sophisticated global world. Students in courses in physical science, biological science, social science, engineering and architecture are required to have a facility with no less sophisticated mathematics than calculus and probability. Moreover, lawyers, social workers, business managers and executives, and medical professionals, among others, increasingly need to be able to interpret data, think logically and deductively, have a sense of numbers that make sense in various contexts, and apply algebra where appropriate. These are some of the qualities of what is often called quantitative literacy, and they apply to everyday living, such as in estimating a tip at a restaurant or evaluating credit card rates. Thus a major goal of mathematics training is to prepare students for success in other disciplines, as well as in mathematics and in everyday life.

 

It follows that mathematics serves as a foundation for a student's future as an educated person and a person in the workforce. Although some high school students have such a mathematical maturity when they graduate from high school, many don't, and it remains for them to obtain it in college. In fact, the real achievement of general education mathematical literacy should not be expected to be achieved merely by one college mathematics course. It comes only from the general education curriculum at the college level. Moreover, with the broadening use of, and reliance on, quantitative methods in all kinds of subjects, it is increasingly critical that faculty across all of the disciplines be encouraged to use mathematics and statistics and data analysis in their courses when appropriate. One cannot expect students to achieve mathematical maturity unless they are constantly called on to use the mathematics that they have learned.

 

There are many diverse college mathematics courses that can provide mathematical maturity and literacy. Among them are college algebra, statistics, mathematical modeling (also called finite mathematics), and "liberal arts" mathematics. However, these courses can only be considered as appropriate for college credit if they are of college caliber. Both 2-year college and 4-year mathematics faculty in Marylands public higher education institutions agree that credit bearing college mathematics courses need to have as prerequisite the equivalent of college Intermediate Algebra or the traditional high school Algebra II. This is also in keeping with General Education Mathematics definitions in other states such as Missouri. Thus the minimum state high school graduation requirement in mathematics of 3 units (including one in algebra and one in geometry) does not suffice as adequate preparation for any General Education Mathematics course in a Maryland public higher education institution.

 

ATTRIBUTES:

 

Upon successful completion of such a course, which needs to have as a prerequisite a level of mathematical maturity including Intermediate Algebra (in college) or the traditional Algebra II (in high school), the student should be able to:

 

(1) interpret mathematical models given verbally, or by formulas, graphs, tables, or schematics, and draw inferences from them,

 

(2) represent mathematical concepts verbally, and where appropriate, symbolically, visually, and numerically,

 

(3) use arithmetic, algebraic, geometric, technological, or statistical methods (as needed or appropriate) to solve problems,

 

(4) use mathematical reasoning, e.g., to solve problems, to formulate and test conjectures, to judge the validity of arguments, to formulate valid arguments, and to communicate the reasoning and the results,

 

(5) estimate and check answers to mathematical problems in order to determine reasonableness,

 

(6)      recognize and use connections within mathematics and between mathematics and other disciplines.

 

HOW TO USE THIS DOCUMENT:

 

A college-level mathematics course should reflect Marylands Attributes for College Level Mathematics Courses (listed above). By necessity these attributes require as a prerequisite an Intermediate Algebra level of mathematical maturity. The tables that accompany each of the four courses to follow in this document (College Algebra, Finite Mathematics, Liberal Arts Mathematics, and Statistics) are typical of problems typically found in the respective college courses. Where applicable, a college-level problem will be paired with an Intermediate algebra problem to show how the college-level course expands upon the Intermediate algebra skills. If one were to rate the college-level problems from easy to difficult, the sample problems would generally be on the moderate to difficult end of the scale. This is because we are trying to illustrate the mathematical maturity reached by a college-level course. Of course it would be possible to crate a similar course containing only simple problems, but such a course would no be a college-level course.

 

The six attributes given are very general. This is because they must apply to many diverse college-level mathematics courses, not just a single such course. As shown in the tables accompanying the four course discussions, most of the examples encompass several of the attributes. Taken as a whole, these problems define the level of mathematical maturity expected in a college-level mathematics course. The problems listed are not meant to define all syllabi for the corresponding course; rather they are merely examples that reflect the six attributes listed for the course. Typical outcomes for the courses are also given, as guidelines.

 

Finally, the document has been ratified overwhelmingly by the Statewide Mathematics Group, and represents its best effort to address the request of the Intersegmental Chief Academic Officers to address the issue of appropriateness of Intermediate Algebra (or its equivalent) as prerequisite to a college-level mathematics course. If you have questions, you may address them to the chair of the Statewide Mathematics Group: Professor Denny Gulick, Department of Mathematics, University of Maryland, College Park, MD 20742 dng@math.umd.edu.