*Contributors to "Why Numbers Count" offer many different views of
quantitative literacy, as well as several variations on the term
itself--including numeracy, quantitative practices, quantitative
reasoning, mathematical literacy, problem solving, quantitative
competencies. *

*Quantitative literacy* involves understanding the **role of
numbers** in the world. It provides the ability to see below the
surface and to demand enough information to get at the real issues.

-- Ted Porter, historian

Beyond arithmetic and geometry, *quantitative literacy* also requires
logic,
data analysis, and probability.... It enables individuals to analyze
evidence, to read graphs, to understand logical arguments, to detect
logical fallacies, to understand evidence, and to evaluate risks.
Quantitative literacy means knowing **how to reason and how to think.**

-- Gina Kolata, journalist

*Quantitative literacy* can be defined as the **level of mathematical
knowledge and skills** required of all citizens. It includes the
ability to apply aspects of mathematics (including measurement, data
representation, number sense, variables geometric shapes, spatial
visualization, and chance) to understand, predict, and control routine
events in people's lives.

-- John Dossey, mathematics educator

*Quantitative literacy* requires one to **understand the nature of
mathematics** and its role in scientific inquiry and technological
progress; to grasp sufficient mathematics to **understand important
scientific and engineering concepts**; and to possess quantitative
skills sufficient for **responding critically to scientific issues** in
the media and public life.

-- F. James Rutherford, physics educator

The heart of *quantitative literacy* is real world **problem
solving**--the use of mathematics in everyday life, on the job, and as
an intelligent citizen. Problem solving must be both mathematically
defensible and useful in the real world.

-- Henry Pollak, applied mathematician

**Numeracy** is not the same as mathematics. It is an aggregation
of skills, knowledge, beliefs, dispositions, habits of mind, communication
capabilities, and problem solving skills that people need in order to
engage effectively and autonomously in quantitative situations arising in
life and work.

-- Iddo Gal, cognitive scientist

Practices are the habitual patterns of actions engaged in routinely by
people, usually without thought; they include standard patterns,
routines, procedures, processes, and habits. **Quantitative practices**
deal with numbers, uncertainty, errors in data, design of experiments,
creation of models, validations, inferences, making tradeoffs, etc.

-- Peter Denning, computer scientist

*Quantitative reasoning* as **an interpretive activity** that takes
place within a deductively structured framework. It involves a tapestry
of meaning provided by a warp of abstract patterns and a weft of context
and story line. In quantitative reasoning, context provides meaning.

-- George Cobb, statistician

Important *quantitative competencies* are those that can be used
to **solve problems people would frequently encounter on the job** or in
their roles as citizens or parents. Quantitative competencies require
identifying and solving problems not in algebra and geometry, but in the five
SCANS competency domains such as planning, information, and systems
analysis.

-- Arnold Packer, economist

*Quantitative literacy* involves understanding the **mathematical
concepts and skills that are necessary for everyday life**. It includes
computation, interpretation, inquiry, and application of mathematical
concepts that are critical for life in the contemporary world.

-- Glenda Price, college provost

*
Contrasting views were expressed by mathematicians who were
asked to reflect on the definitions offered by these authors.
Mathematicians distinguished rather sharply between "quantitative"
and "mathematical" literacy:*

*Quantitative literacy* involves reasoning with numbers (Jim
Lewis); reading, interpreting and making simple applications (Carole
Lacampagne); understanding operations on rational numbers (Jack Price);
constructing and recognizing a sound argument (Keith Devlin); and
understanding variability and how to quantify it (Gail Burrill).

In contrast, *mathematical literacy* offers a big-picture view of
how to work with numbers, relationships, and patterns (Jim Lewis); higher
order thinking, including all the goals of the NCTM Standards (Jack
Price); mostly qualitative issues, not quantitative ones (Keith Devlin);
the language of algebra as well as geometric and spatial experience (Zal
Usiskin).

-- Mathematicians and mathematics educators

* Adapted with permission from "Why Numbers Count: Quantitative
Literacy for Tomorrow's America," Copyright (c) College Entrance
Examination Board, 1997. All rights reserved.*

*Last Update: * July 17, 1997