**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.