A sketch of possible varieties of quantitative literacy (or numeracy, as it is sometimes called) based on ideas that emerged from an on-going study of QL in different contexts. Other definitions can be found in the volume "Why Numbers Counts." Comments, corrections, and additions are welcome by e-mail toLynn A. Steen. (QL Home Page)
Algebra for All. Embodied in many state standards and high-stakes tests; also, a slogan in the federal government's "mathematics initiative". As typically implemented, it expects every graduate to pass a test similar to parts of the SAT I (math) that requires modest ability in reading and interpreting formulas, understanding graphs, and solving very simple equations. (See the report of the Algebra Colloquium for evidence that not even mathematicians can agree on what algebra is.)
Civic Literacy. The quantitative skills necessary to make wise decisions about public matters, whether as an elected official or just as a single voter. Understanding the need for data; ability to sort through conflicting claims; skepticism about the reliability or significance of data; recognizing the limits of computer models.
Computer Mathematics. A common desire of employers--for skills in solving (and presenting the solutions of) quantitative problems using standard computer packages such as spreadsheets, simulation programs, and other mathematical computer models. Usually ignored by mathematics teachers, but taught (often poorly) in business courses. [A bank manager once said, comparing computer-based methods with those taught by mathematics teachers: "I would fire anyone I caught doing calculations by hand."]
Cultural Literacy. The goal of many mathematicians: for the average citizen to recognize the contributions of mathematicians just as they acknowledge (and to some degree appreciate) the accomplishments of writers, musicians, and artists. Reflected in the many "Math for Poets" courses on college campuses, and in the popularizations of mathematics by writers such as Ivars Peterson and Keith Devlin. Rarely thought about in the K-12 system.
Functional Mathematics. A full NCTM-like curriculum that gives priority to the kinds of mathematical topics and skills needed by ordinary people in life and work. Includes topics not ordinarily studied (financial mathematics, planning and scheduling) and postpones until grade 12 topics needed only for specialized college work. (An outline of functional mathematics is one outgrowh of the NCRVE's Beyond Eighth Grade project.)
Instrumental Mathematics. Described by John Dossey in an Appendix to Why Numbers Count as the ability to interpret and apply aspects of mathematics and to understand, predict, and control relevant factors in a variety of contexts. More a schema than a definition, this approach focuses on comprehensive mastery of both procedural and conceptual understanding over six aspects and four levels.
Language of Science. The traditional focus of high school mathematics--to support prospective scinentists and engineers. In recent years broadened to include statistics and combinatorics that are increasingly important in the life sciences. Focuses more on advanced skills than on breadth.
Mathematical Modeling. A cycle of interaction between real-world issues and abstract reasoning akin to the process of hypothesis-building and testing in science. The substance of Henry Pollak's essay in Why Numbers Counts, this interpreation includes all aspects of the cycle, from mathematicizing the problem to analyzing the mathematics, from collecting data to verifying (or refuting) predictions of the model.
NCTM Standards. A vigorous, comprehensive curriculum in mathematics that takes three years for the average student and would leave them well prepared for further study in any career. In effect, a proposed high level alternative to the K-8 core that is now the de facto low standard for schools and employers. Stresses mathematics at the expense of less commonly recognized aspects of QL.
Parental Literacy. Appropriate understandings to enable parents to help children learn quantitative methods as they grow up, including recognition of how quantitative skills emerge (and can be encouraged) in young children. Involves attitudes as well as skills, dispositions as well as abilities. Central to Family Math.
Preparation for AP. Traditional mathematical skills, well practiced, embedded in core theory and embroidered with template-style problems that echo major classics of mathematics exams of the past. The criteria for topics is their utility in (traditional) calculus. The dominant ideal of the suburban Volvo crowd.
Problem Solving. A long-lasting NCTM mantra, often interpreted in a very broad sense that moves way beyond the boundaries of traditional mathematics (e.g., where to site a new shopping center in a community). In this perspective, the problem and its possible solutions are paramount; particular mathematical skills involved in the solution are secondary.
Quantitative Practice. Stresses the importance of practices which can be learned but which cannot be accurately described. The substance of Peter Denning's essay in Why Numbers Counts, this perspective shifts the burden away from "literacy," book learning, and classroom instruction to apprenticeship environments in which mathematics is used and learned by use but perhaps never explicitly exhibited in words and symbols.
Quantitative Reasoning. The substance of George Cobb's essay in Why Numbers Counts, and the name of many college degree requirements. Emphasizes broad synthesis of logical, visual, verbal, and computational thinking. Manipulative algebra is incidental to this goal.
SCANS Skills. Covers broad categories required of employees, entrepreneurs, and community leaders: acquiring information, allocating resources, working with others, improving systems, and working with technology. QL is embedded in (but not easily separable from) the SCANS skills. A rather popular innovation in some charter schools (including many of those focused on the fine arts), this approach places considerable emphasis on communication skills not found in other QL programs.